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

Percentage Accurate: 73.4% → 81.8%

Time: 31.6s

Alternatives: 26

Speedup: 0.5×

• 58.9% 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: 73.4% 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: 81.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(t * i))) + Float64(x * Float64(Float64(t * a) - Float64(y * z)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	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))) - ((b * ((z * c) - (t * i))) + (x * ((t * a) - (y * z))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $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 94.7%

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

   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 c around inf 51.5%

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

      1. *-commutative 51.5%

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

   5. Simplified 51.5%

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

4. Final simplification 85.4%

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

Alternative 2: 51.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_4 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.1 \cdot 10^{+122}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{+79}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{+69}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq -0.12:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.12 \cdot 10^{-131}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.95 \cdot 10^{-304}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-136}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{-76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-19}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* i (- (* t b) (* y j))))
        (t_4 (* c (- (* a j) (* z b)))))
   (if (<= c -1.1e+122)
     t_4
     (if (<= c -2.4e+79)
       t_3
       (if (<= c -4.5e+69)
         t_4
         (if (<= c -0.12)
           t_1
           (if (<= c -1.12e-131)
             (* y (- (* x z) (* i j)))
             (if (<= c -1.5e-158)
               t_1
               (if (<= c -1.95e-304)
                 t_2
                 (if (<= c 9.5e-136)
                   t_3
                   (if (<= c 4.3e-76)
                     t_2
                     (if (<= c 1.65e-19)
                       t_3
                       (if (<= c 4.5e+64)
                         (* b (- (* t i) (* z c)))
                         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 = a * ((c * j) - (x * t));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = i * ((t * b) - (y * j));
	double t_4 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.1e+122) {
		tmp = t_4;
	} else if (c <= -2.4e+79) {
		tmp = t_3;
	} else if (c <= -4.5e+69) {
		tmp = t_4;
	} else if (c <= -0.12) {
		tmp = t_1;
	} else if (c <= -1.12e-131) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= -1.5e-158) {
		tmp = t_1;
	} else if (c <= -1.95e-304) {
		tmp = t_2;
	} else if (c <= 9.5e-136) {
		tmp = t_3;
	} else if (c <= 4.3e-76) {
		tmp = t_2;
	} else if (c <= 1.65e-19) {
		tmp = t_3;
	} else if (c <= 4.5e+64) {
		tmp = b * ((t * i) - (z * c));
	} 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 = a * ((c * j) - (x * t))
    t_2 = x * ((y * z) - (t * a))
    t_3 = i * ((t * b) - (y * j))
    t_4 = c * ((a * j) - (z * b))
    if (c <= (-1.1d+122)) then
        tmp = t_4
    else if (c <= (-2.4d+79)) then
        tmp = t_3
    else if (c <= (-4.5d+69)) then
        tmp = t_4
    else if (c <= (-0.12d0)) then
        tmp = t_1
    else if (c <= (-1.12d-131)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= (-1.5d-158)) then
        tmp = t_1
    else if (c <= (-1.95d-304)) then
        tmp = t_2
    else if (c <= 9.5d-136) then
        tmp = t_3
    else if (c <= 4.3d-76) then
        tmp = t_2
    else if (c <= 1.65d-19) then
        tmp = t_3
    else if (c <= 4.5d+64) then
        tmp = b * ((t * i) - (z * c))
    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 = a * ((c * j) - (x * t));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = i * ((t * b) - (y * j));
	double t_4 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.1e+122) {
		tmp = t_4;
	} else if (c <= -2.4e+79) {
		tmp = t_3;
	} else if (c <= -4.5e+69) {
		tmp = t_4;
	} else if (c <= -0.12) {
		tmp = t_1;
	} else if (c <= -1.12e-131) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= -1.5e-158) {
		tmp = t_1;
	} else if (c <= -1.95e-304) {
		tmp = t_2;
	} else if (c <= 9.5e-136) {
		tmp = t_3;
	} else if (c <= 4.3e-76) {
		tmp = t_2;
	} else if (c <= 1.65e-19) {
		tmp = t_3;
	} else if (c <= 4.5e+64) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = x * ((y * z) - (t * a))
	t_3 = i * ((t * b) - (y * j))
	t_4 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -1.1e+122:
		tmp = t_4
	elif c <= -2.4e+79:
		tmp = t_3
	elif c <= -4.5e+69:
		tmp = t_4
	elif c <= -0.12:
		tmp = t_1
	elif c <= -1.12e-131:
		tmp = y * ((x * z) - (i * j))
	elif c <= -1.5e-158:
		tmp = t_1
	elif c <= -1.95e-304:
		tmp = t_2
	elif c <= 9.5e-136:
		tmp = t_3
	elif c <= 4.3e-76:
		tmp = t_2
	elif c <= 1.65e-19:
		tmp = t_3
	elif c <= 4.5e+64:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_4 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.1e+122)
		tmp = t_4;
	elseif (c <= -2.4e+79)
		tmp = t_3;
	elseif (c <= -4.5e+69)
		tmp = t_4;
	elseif (c <= -0.12)
		tmp = t_1;
	elseif (c <= -1.12e-131)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= -1.5e-158)
		tmp = t_1;
	elseif (c <= -1.95e-304)
		tmp = t_2;
	elseif (c <= 9.5e-136)
		tmp = t_3;
	elseif (c <= 4.3e-76)
		tmp = t_2;
	elseif (c <= 1.65e-19)
		tmp = t_3;
	elseif (c <= 4.5e+64)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = x * ((y * z) - (t * a));
	t_3 = i * ((t * b) - (y * j));
	t_4 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.1e+122)
		tmp = t_4;
	elseif (c <= -2.4e+79)
		tmp = t_3;
	elseif (c <= -4.5e+69)
		tmp = t_4;
	elseif (c <= -0.12)
		tmp = t_1;
	elseif (c <= -1.12e-131)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= -1.5e-158)
		tmp = t_1;
	elseif (c <= -1.95e-304)
		tmp = t_2;
	elseif (c <= 9.5e-136)
		tmp = t_3;
	elseif (c <= 4.3e-76)
		tmp = t_2;
	elseif (c <= 1.65e-19)
		tmp = t_3;
	elseif (c <= 4.5e+64)
		tmp = b * ((t * i) - (z * c));
	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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.1e+122], t$95$4, If[LessEqual[c, -2.4e+79], t$95$3, If[LessEqual[c, -4.5e+69], t$95$4, If[LessEqual[c, -0.12], t$95$1, If[LessEqual[c, -1.12e-131], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.5e-158], t$95$1, If[LessEqual[c, -1.95e-304], t$95$2, If[LessEqual[c, 9.5e-136], t$95$3, If[LessEqual[c, 4.3e-76], t$95$2, If[LessEqual[c, 1.65e-19], t$95$3, If[LessEqual[c, 4.5e+64], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.1e122 or -2.39999999999999986e79 < c < -4.4999999999999999e69 or 4.49999999999999973e64 < c

   1. Initial program 60.6%

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

   3. Taylor expanded in c around inf 78.0%

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

      1. *-commutative 78.0%

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

   5. Simplified 78.0%

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

   if -1.1e122 < c < -2.39999999999999986e79 or -1.94999999999999987e-304 < c < 9.5000000000000007e-136 or 4.2999999999999999e-76 < c < 1.6499999999999999e-19

   1. Initial program 88.9%

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

   3. Taylor expanded in i around inf 66.9%

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

   4. Taylor expanded in i around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. mul-1-neg 72.2%

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

      3. unsub-neg 72.2%

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

      4. *-commutative 72.2%

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

      5. *-commutative 72.2%

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

   6. Simplified 72.2%

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

   if -4.4999999999999999e69 < c < -0.12 or -1.12000000000000001e-131 < c < -1.5e-158

   1. Initial program 77.7%

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

   3. Taylor expanded in a around inf 77.8%

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

      1. +-commutative 77.8%

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

      2. mul-1-neg 77.8%

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

      3. unsub-neg 77.8%

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

      4. *-commutative 77.8%

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

   5. Simplified 77.8%

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

   if -0.12 < c < -1.12000000000000001e-131

   1. Initial program 58.0%

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

   3. Taylor expanded in y around inf 51.5%

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

      1. +-commutative 51.5%

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

      2. mul-1-neg 51.5%

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

      3. unsub-neg 51.5%

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

      4. *-commutative 51.5%

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

      5. *-commutative 51.5%

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

   5. Simplified 51.5%

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

   if -1.5e-158 < c < -1.94999999999999987e-304 or 9.5000000000000007e-136 < c < 4.2999999999999999e-76

   1. Initial program 91.9%

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

   3. Taylor expanded in x around inf 71.6%

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

   if 1.6499999999999999e-19 < c < 4.49999999999999973e64

   1. Initial program 84.1%

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

   3. Taylor expanded in b around inf 66.6%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.1 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{+79}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{+69}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -0.12:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;c \leq -1.12 \cdot 10^{-131}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-158}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;c \leq -1.95 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-136}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-19}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -1.12 \cdot 10^{+182}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot \frac{z}{a} - t\right)\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-256}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.02 \cdot 10^{-304}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-186}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 4 \cdot 10^{-102}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+21}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (* t i)) (* j (- (* y i) (* a c)))))
        (t_2 (+ (* x (* y z)) (* b (- (* t i) (* z c))))))
   (if (<= j -1.12e+182)
     (* j (- (* a c) (* y i)))
     (if (<= j -1.7e+174)
       (* x (* a (- (* y (/ z a)) t)))
       (if (<= j -1.2e+27)
         t_1
         (if (<= j -6.6e-256)
           t_2
           (if (<= j -1.02e-304)
             (* t (- (* b i) (* x a)))
             (if (<= j 6e-186)
               t_2
               (if (<= j 4e-102)
                 (* a (- (* c j) (* x t)))
                 (if (<= j 2.8e+21) (* z (- (* x y) (* b c))) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * (t * i)) - (j * ((y * i) - (a * c)));
	double t_2 = (x * (y * z)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -1.12e+182) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -1.7e+174) {
		tmp = x * (a * ((y * (z / a)) - t));
	} else if (j <= -1.2e+27) {
		tmp = t_1;
	} else if (j <= -6.6e-256) {
		tmp = t_2;
	} else if (j <= -1.02e-304) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 6e-186) {
		tmp = t_2;
	} else if (j <= 4e-102) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= 2.8e+21) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * (t * i)) - (j * ((y * i) - (a * c)))
    t_2 = (x * (y * z)) + (b * ((t * i) - (z * c)))
    if (j <= (-1.12d+182)) then
        tmp = j * ((a * c) - (y * i))
    else if (j <= (-1.7d+174)) then
        tmp = x * (a * ((y * (z / a)) - t))
    else if (j <= (-1.2d+27)) then
        tmp = t_1
    else if (j <= (-6.6d-256)) then
        tmp = t_2
    else if (j <= (-1.02d-304)) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 6d-186) then
        tmp = t_2
    else if (j <= 4d-102) then
        tmp = a * ((c * j) - (x * t))
    else if (j <= 2.8d+21) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * (t * i)) - (j * ((y * i) - (a * c)));
	double t_2 = (x * (y * z)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -1.12e+182) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -1.7e+174) {
		tmp = x * (a * ((y * (z / a)) - t));
	} else if (j <= -1.2e+27) {
		tmp = t_1;
	} else if (j <= -6.6e-256) {
		tmp = t_2;
	} else if (j <= -1.02e-304) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 6e-186) {
		tmp = t_2;
	} else if (j <= 4e-102) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= 2.8e+21) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * (t * i)) - (j * ((y * i) - (a * c)))
	t_2 = (x * (y * z)) + (b * ((t * i) - (z * c)))
	tmp = 0
	if j <= -1.12e+182:
		tmp = j * ((a * c) - (y * i))
	elif j <= -1.7e+174:
		tmp = x * (a * ((y * (z / a)) - t))
	elif j <= -1.2e+27:
		tmp = t_1
	elif j <= -6.6e-256:
		tmp = t_2
	elif j <= -1.02e-304:
		tmp = t * ((b * i) - (x * a))
	elif j <= 6e-186:
		tmp = t_2
	elif j <= 4e-102:
		tmp = a * ((c * j) - (x * t))
	elif j <= 2.8e+21:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * Float64(t * i)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))))
	t_2 = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (j <= -1.12e+182)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (j <= -1.7e+174)
		tmp = Float64(x * Float64(a * Float64(Float64(y * Float64(z / a)) - t)));
	elseif (j <= -1.2e+27)
		tmp = t_1;
	elseif (j <= -6.6e-256)
		tmp = t_2;
	elseif (j <= -1.02e-304)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 6e-186)
		tmp = t_2;
	elseif (j <= 4e-102)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (j <= 2.8e+21)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * (t * i)) - (j * ((y * i) - (a * c)));
	t_2 = (x * (y * z)) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (j <= -1.12e+182)
		tmp = j * ((a * c) - (y * i));
	elseif (j <= -1.7e+174)
		tmp = x * (a * ((y * (z / a)) - t));
	elseif (j <= -1.2e+27)
		tmp = t_1;
	elseif (j <= -6.6e-256)
		tmp = t_2;
	elseif (j <= -1.02e-304)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 6e-186)
		tmp = t_2;
	elseif (j <= 4e-102)
		tmp = a * ((c * j) - (x * t));
	elseif (j <= 2.8e+21)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.12e+182], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.7e+174], N[(x * N[(a * N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.2e+27], t$95$1, If[LessEqual[j, -6.6e-256], t$95$2, If[LessEqual[j, -1.02e-304], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6e-186], t$95$2, If[LessEqual[j, 4e-102], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.8e+21], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -1.11999999999999994e182

   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 j around inf 84.1%

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

   if -1.11999999999999994e182 < j < -1.7000000000000001e174

   1. Initial program 60.0%

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

   3. Taylor expanded in x around inf 81.0%

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

   4. Taylor expanded in a around inf 100.0%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if -1.7000000000000001e174 < j < -1.19999999999999999e27 or 2.8e21 < j

   1. Initial program 74.4%

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

   3. Taylor expanded in i around inf 69.5%

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

   if -1.19999999999999999e27 < j < -6.6e-256 or -1.01999999999999992e-304 < j < 6.0000000000000003e-186

   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 j around 0 79.8%

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

   4. Taylor expanded in y around inf 74.0%

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

      1. *-commutative 29.7%

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

   6. Simplified 74.0%

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

   if -6.6e-256 < j < -1.01999999999999992e-304

   1. Initial program 70.5%

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

   3. Taylor expanded in t around -inf 81.0%

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

   if 6.0000000000000003e-186 < j < 3.99999999999999973e-102

   1. Initial program 70.4%

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

   3. Taylor expanded in a around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

      4. *-commutative 61.0%

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

   5. Simplified 61.0%

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

   if 3.99999999999999973e-102 < j < 2.8e21

   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 83.8%

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

      1. *-commutative 83.8%

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

      2. *-commutative 83.8%

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

   5. Simplified 83.8%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.12 \cdot 10^{+182}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot \frac{z}{a} - t\right)\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.02 \cdot 10^{-304}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{-102}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+21}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;c \leq -1.05 \cdot 10^{+122}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{+69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -4.6 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;c \leq -5.9 \cdot 10^{-304}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 6.7 \cdot 10^{-136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-74}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j))))
        (t_2 (* c (- (* a j) (* z b))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= c -1.05e+122)
     t_2
     (if (<= c -5.2e+81)
       t_1
       (if (<= c -3.6e+69)
         t_2
         (if (<= c -4.6e-161)
           (* a (- (* c j) (* x t)))
           (if (<= c -5.9e-304)
             t_3
             (if (<= c 6.7e-136)
               t_1
               (if (<= c 1.5e-74)
                 t_3
                 (if (<= c 1.8e-18)
                   t_1
                   (if (<= c 5e+64) (* b (- (* t i) (* z c))) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = c * ((a * j) - (z * b));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (c <= -1.05e+122) {
		tmp = t_2;
	} else if (c <= -5.2e+81) {
		tmp = t_1;
	} else if (c <= -3.6e+69) {
		tmp = t_2;
	} else if (c <= -4.6e-161) {
		tmp = a * ((c * j) - (x * t));
	} else if (c <= -5.9e-304) {
		tmp = t_3;
	} else if (c <= 6.7e-136) {
		tmp = t_1;
	} else if (c <= 1.5e-74) {
		tmp = t_3;
	} else if (c <= 1.8e-18) {
		tmp = t_1;
	} else if (c <= 5e+64) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = c * ((a * j) - (z * b))
    t_3 = x * ((y * z) - (t * a))
    if (c <= (-1.05d+122)) then
        tmp = t_2
    else if (c <= (-5.2d+81)) then
        tmp = t_1
    else if (c <= (-3.6d+69)) then
        tmp = t_2
    else if (c <= (-4.6d-161)) then
        tmp = a * ((c * j) - (x * t))
    else if (c <= (-5.9d-304)) then
        tmp = t_3
    else if (c <= 6.7d-136) then
        tmp = t_1
    else if (c <= 1.5d-74) then
        tmp = t_3
    else if (c <= 1.8d-18) then
        tmp = t_1
    else if (c <= 5d+64) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = c * ((a * j) - (z * b));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (c <= -1.05e+122) {
		tmp = t_2;
	} else if (c <= -5.2e+81) {
		tmp = t_1;
	} else if (c <= -3.6e+69) {
		tmp = t_2;
	} else if (c <= -4.6e-161) {
		tmp = a * ((c * j) - (x * t));
	} else if (c <= -5.9e-304) {
		tmp = t_3;
	} else if (c <= 6.7e-136) {
		tmp = t_1;
	} else if (c <= 1.5e-74) {
		tmp = t_3;
	} else if (c <= 1.8e-18) {
		tmp = t_1;
	} else if (c <= 5e+64) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = c * ((a * j) - (z * b))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if c <= -1.05e+122:
		tmp = t_2
	elif c <= -5.2e+81:
		tmp = t_1
	elif c <= -3.6e+69:
		tmp = t_2
	elif c <= -4.6e-161:
		tmp = a * ((c * j) - (x * t))
	elif c <= -5.9e-304:
		tmp = t_3
	elif c <= 6.7e-136:
		tmp = t_1
	elif c <= 1.5e-74:
		tmp = t_3
	elif c <= 1.8e-18:
		tmp = t_1
	elif c <= 5e+64:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (c <= -1.05e+122)
		tmp = t_2;
	elseif (c <= -5.2e+81)
		tmp = t_1;
	elseif (c <= -3.6e+69)
		tmp = t_2;
	elseif (c <= -4.6e-161)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (c <= -5.9e-304)
		tmp = t_3;
	elseif (c <= 6.7e-136)
		tmp = t_1;
	elseif (c <= 1.5e-74)
		tmp = t_3;
	elseif (c <= 1.8e-18)
		tmp = t_1;
	elseif (c <= 5e+64)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = c * ((a * j) - (z * b));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (c <= -1.05e+122)
		tmp = t_2;
	elseif (c <= -5.2e+81)
		tmp = t_1;
	elseif (c <= -3.6e+69)
		tmp = t_2;
	elseif (c <= -4.6e-161)
		tmp = a * ((c * j) - (x * t));
	elseif (c <= -5.9e-304)
		tmp = t_3;
	elseif (c <= 6.7e-136)
		tmp = t_1;
	elseif (c <= 1.5e-74)
		tmp = t_3;
	elseif (c <= 1.8e-18)
		tmp = t_1;
	elseif (c <= 5e+64)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.05e+122], t$95$2, If[LessEqual[c, -5.2e+81], t$95$1, If[LessEqual[c, -3.6e+69], t$95$2, If[LessEqual[c, -4.6e-161], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.9e-304], t$95$3, If[LessEqual[c, 6.7e-136], t$95$1, If[LessEqual[c, 1.5e-74], t$95$3, If[LessEqual[c, 1.8e-18], t$95$1, If[LessEqual[c, 5e+64], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.05000000000000008e122 or -5.19999999999999984e81 < c < -3.6000000000000003e69 or 5e64 < c

   1. Initial program 60.6%

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

   3. Taylor expanded in c around inf 78.0%

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

      1. *-commutative 78.0%

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

   5. Simplified 78.0%

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

   if -1.05000000000000008e122 < c < -5.19999999999999984e81 or -5.9000000000000001e-304 < c < 6.6999999999999998e-136 or 1.50000000000000003e-74 < c < 1.80000000000000005e-18

   1. Initial program 88.9%

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

   3. Taylor expanded in i around inf 66.9%

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

   4. Taylor expanded in i around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. mul-1-neg 72.2%

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

      3. unsub-neg 72.2%

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

      4. *-commutative 72.2%

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

      5. *-commutative 72.2%

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

   6. Simplified 72.2%

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

   if -3.6000000000000003e69 < c < -4.6e-161

   1. Initial program 68.0%

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

   3. Taylor expanded in a around inf 57.3%

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

      1. +-commutative 57.3%

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

      2. mul-1-neg 57.3%

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

      3. unsub-neg 57.3%

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

      4. *-commutative 57.3%

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

   5. Simplified 57.3%

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

   if -4.6e-161 < c < -5.9000000000000001e-304 or 6.6999999999999998e-136 < c < 1.50000000000000003e-74

   1. Initial program 91.9%

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

   3. Taylor expanded in x around inf 71.6%

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

   if 1.80000000000000005e-18 < c < 5e64

   1. Initial program 84.1%

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

   3. Taylor expanded in b around inf 66.6%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{+81}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{+69}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -4.6 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;c \leq -5.9 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 6.7 \cdot 10^{-136}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-18}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -5 \cdot 10^{+121}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{+82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{+69}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-276}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 8.6 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* i (- (* t b) (* y j))))
        (t_3 (* c (- (* a j) (* z b)))))
   (if (<= c -5e+121)
     t_3
     (if (<= c -2.9e+82)
       t_2
       (if (<= c -9.2e+69)
         t_3
         (if (<= c -1.05e-166)
           t_1
           (if (<= c -2.7e-276)
             (* z (* x y))
             (if (<= c -5.2e-304)
               t_1
               (if (<= c 1.7e-29)
                 t_2
                 (if (<= c 8.6e+64) (* b (- (* t i) (* z c))) t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -5e+121) {
		tmp = t_3;
	} else if (c <= -2.9e+82) {
		tmp = t_2;
	} else if (c <= -9.2e+69) {
		tmp = t_3;
	} else if (c <= -1.05e-166) {
		tmp = t_1;
	} else if (c <= -2.7e-276) {
		tmp = z * (x * y);
	} else if (c <= -5.2e-304) {
		tmp = t_1;
	} else if (c <= 1.7e-29) {
		tmp = t_2;
	} else if (c <= 8.6e+64) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = i * ((t * b) - (y * j))
    t_3 = c * ((a * j) - (z * b))
    if (c <= (-5d+121)) then
        tmp = t_3
    else if (c <= (-2.9d+82)) then
        tmp = t_2
    else if (c <= (-9.2d+69)) then
        tmp = t_3
    else if (c <= (-1.05d-166)) then
        tmp = t_1
    else if (c <= (-2.7d-276)) then
        tmp = z * (x * y)
    else if (c <= (-5.2d-304)) then
        tmp = t_1
    else if (c <= 1.7d-29) then
        tmp = t_2
    else if (c <= 8.6d+64) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -5e+121) {
		tmp = t_3;
	} else if (c <= -2.9e+82) {
		tmp = t_2;
	} else if (c <= -9.2e+69) {
		tmp = t_3;
	} else if (c <= -1.05e-166) {
		tmp = t_1;
	} else if (c <= -2.7e-276) {
		tmp = z * (x * y);
	} else if (c <= -5.2e-304) {
		tmp = t_1;
	} else if (c <= 1.7e-29) {
		tmp = t_2;
	} else if (c <= 8.6e+64) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = i * ((t * b) - (y * j))
	t_3 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -5e+121:
		tmp = t_3
	elif c <= -2.9e+82:
		tmp = t_2
	elif c <= -9.2e+69:
		tmp = t_3
	elif c <= -1.05e-166:
		tmp = t_1
	elif c <= -2.7e-276:
		tmp = z * (x * y)
	elif c <= -5.2e-304:
		tmp = t_1
	elif c <= 1.7e-29:
		tmp = t_2
	elif c <= 8.6e+64:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -5e+121)
		tmp = t_3;
	elseif (c <= -2.9e+82)
		tmp = t_2;
	elseif (c <= -9.2e+69)
		tmp = t_3;
	elseif (c <= -1.05e-166)
		tmp = t_1;
	elseif (c <= -2.7e-276)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= -5.2e-304)
		tmp = t_1;
	elseif (c <= 1.7e-29)
		tmp = t_2;
	elseif (c <= 8.6e+64)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = i * ((t * b) - (y * j));
	t_3 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -5e+121)
		tmp = t_3;
	elseif (c <= -2.9e+82)
		tmp = t_2;
	elseif (c <= -9.2e+69)
		tmp = t_3;
	elseif (c <= -1.05e-166)
		tmp = t_1;
	elseif (c <= -2.7e-276)
		tmp = z * (x * y);
	elseif (c <= -5.2e-304)
		tmp = t_1;
	elseif (c <= 1.7e-29)
		tmp = t_2;
	elseif (c <= 8.6e+64)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5e+121], t$95$3, If[LessEqual[c, -2.9e+82], t$95$2, If[LessEqual[c, -9.2e+69], t$95$3, If[LessEqual[c, -1.05e-166], t$95$1, If[LessEqual[c, -2.7e-276], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.2e-304], t$95$1, If[LessEqual[c, 1.7e-29], t$95$2, If[LessEqual[c, 8.6e+64], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -5.00000000000000007e121 or -2.9000000000000001e82 < c < -9.20000000000000067e69 or 8.5999999999999995e64 < c

   1. Initial program 60.6%

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

   3. Taylor expanded in c around inf 78.0%

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

      1. *-commutative 78.0%

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

   5. Simplified 78.0%

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

   if -5.00000000000000007e121 < c < -2.9000000000000001e82 or -5.19999999999999993e-304 < c < 1.69999999999999986e-29

   1. Initial program 89.8%

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

   3. Taylor expanded in i around inf 58.3%

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

   4. Taylor expanded in i around inf 62.4%

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

      1. +-commutative 62.4%

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

      2. mul-1-neg 62.4%

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

      3. unsub-neg 62.4%

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

      4. *-commutative 62.4%

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

      5. *-commutative 62.4%

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

   6. Simplified 62.4%

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

   if -9.20000000000000067e69 < c < -1.05e-166 or -2.69999999999999985e-276 < c < -5.19999999999999993e-304

   1. Initial program 70.2%

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

   3. Taylor expanded in a around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

      4. *-commutative 60.3%

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

   5. Simplified 60.3%

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

   if -1.05e-166 < c < -2.69999999999999985e-276

   1. Initial program 89.1%

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

   3. Taylor expanded in z around inf 58.8%

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

      1. *-commutative 58.8%

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

      2. *-commutative 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in y around inf 53.9%

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

      1. *-commutative 53.9%

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

   8. Simplified 53.9%

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

   if 1.69999999999999986e-29 < c < 8.5999999999999995e64

   1. Initial program 84.1%

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

   3. Taylor expanded in b around inf 66.6%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5 \cdot 10^{+121}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{+69}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-166}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-276}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-304}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-29}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 8.6 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 30.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot b\right) \cdot \left(-c\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+218}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-240}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-268}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z b) (- c))) (t_2 (* a (* c j))))
   (if (<= x -5.8e+218)
     (* y (* x z))
     (if (<= x -7.4e-57)
       (* x (* t (- a)))
       (if (<= x -3.7e-240)
         t_2
         (if (<= x -2.6e-268)
           (* b (* t i))
           (if (<= x 6.8e-307)
             t_1
             (if (<= x 3.9e-250)
               (* t (* b i))
               (if (<= x 5.5e-197)
                 t_2
                 (if (<= x 4.5e+120) t_1 (* z (* x y))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * b) * -c;
	double t_2 = a * (c * j);
	double tmp;
	if (x <= -5.8e+218) {
		tmp = y * (x * z);
	} else if (x <= -7.4e-57) {
		tmp = x * (t * -a);
	} else if (x <= -3.7e-240) {
		tmp = t_2;
	} else if (x <= -2.6e-268) {
		tmp = b * (t * i);
	} else if (x <= 6.8e-307) {
		tmp = t_1;
	} else if (x <= 3.9e-250) {
		tmp = t * (b * i);
	} else if (x <= 5.5e-197) {
		tmp = t_2;
	} else if (x <= 4.5e+120) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	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 = (z * b) * -c
    t_2 = a * (c * j)
    if (x <= (-5.8d+218)) then
        tmp = y * (x * z)
    else if (x <= (-7.4d-57)) then
        tmp = x * (t * -a)
    else if (x <= (-3.7d-240)) then
        tmp = t_2
    else if (x <= (-2.6d-268)) then
        tmp = b * (t * i)
    else if (x <= 6.8d-307) then
        tmp = t_1
    else if (x <= 3.9d-250) then
        tmp = t * (b * i)
    else if (x <= 5.5d-197) then
        tmp = t_2
    else if (x <= 4.5d+120) then
        tmp = t_1
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * b) * -c;
	double t_2 = a * (c * j);
	double tmp;
	if (x <= -5.8e+218) {
		tmp = y * (x * z);
	} else if (x <= -7.4e-57) {
		tmp = x * (t * -a);
	} else if (x <= -3.7e-240) {
		tmp = t_2;
	} else if (x <= -2.6e-268) {
		tmp = b * (t * i);
	} else if (x <= 6.8e-307) {
		tmp = t_1;
	} else if (x <= 3.9e-250) {
		tmp = t * (b * i);
	} else if (x <= 5.5e-197) {
		tmp = t_2;
	} else if (x <= 4.5e+120) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * b) * -c
	t_2 = a * (c * j)
	tmp = 0
	if x <= -5.8e+218:
		tmp = y * (x * z)
	elif x <= -7.4e-57:
		tmp = x * (t * -a)
	elif x <= -3.7e-240:
		tmp = t_2
	elif x <= -2.6e-268:
		tmp = b * (t * i)
	elif x <= 6.8e-307:
		tmp = t_1
	elif x <= 3.9e-250:
		tmp = t * (b * i)
	elif x <= 5.5e-197:
		tmp = t_2
	elif x <= 4.5e+120:
		tmp = t_1
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * b) * Float64(-c))
	t_2 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (x <= -5.8e+218)
		tmp = Float64(y * Float64(x * z));
	elseif (x <= -7.4e-57)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (x <= -3.7e-240)
		tmp = t_2;
	elseif (x <= -2.6e-268)
		tmp = Float64(b * Float64(t * i));
	elseif (x <= 6.8e-307)
		tmp = t_1;
	elseif (x <= 3.9e-250)
		tmp = Float64(t * Float64(b * i));
	elseif (x <= 5.5e-197)
		tmp = t_2;
	elseif (x <= 4.5e+120)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * b) * -c;
	t_2 = a * (c * j);
	tmp = 0.0;
	if (x <= -5.8e+218)
		tmp = y * (x * z);
	elseif (x <= -7.4e-57)
		tmp = x * (t * -a);
	elseif (x <= -3.7e-240)
		tmp = t_2;
	elseif (x <= -2.6e-268)
		tmp = b * (t * i);
	elseif (x <= 6.8e-307)
		tmp = t_1;
	elseif (x <= 3.9e-250)
		tmp = t * (b * i);
	elseif (x <= 5.5e-197)
		tmp = t_2;
	elseif (x <= 4.5e+120)
		tmp = t_1;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e+218], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.4e-57], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.7e-240], t$95$2, If[LessEqual[x, -2.6e-268], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e-307], t$95$1, If[LessEqual[x, 3.9e-250], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e-197], t$95$2, If[LessEqual[x, 4.5e+120], t$95$1, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -5.7999999999999999e218

   1. Initial program 64.2%

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

   3. Taylor expanded in y around inf 79.4%

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

      1. +-commutative 79.4%

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

      2. mul-1-neg 79.4%

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

      3. unsub-neg 79.4%

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

      4. *-commutative 79.4%

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

      5. *-commutative 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in z around inf 72.5%

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

   if -5.7999999999999999e218 < x < -7.4e-57

   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 x around inf 61.1%

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

   4. Taylor expanded in y around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. distribute-lft-neg-out 41.2%

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

      3. *-commutative 41.2%

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

   6. Simplified 41.2%

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

   if -7.4e-57 < x < -3.7000000000000002e-240 or 3.90000000000000027e-250 < x < 5.50000000000000037e-197

   1. Initial program 75.0%

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

   3. Taylor expanded in a around inf 54.1%

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

      1. +-commutative 54.1%

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

      2. mul-1-neg 54.1%

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

      3. unsub-neg 54.1%

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

      4. *-commutative 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in j around inf 48.1%

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

   if -3.7000000000000002e-240 < x < -2.60000000000000002e-268

   1. Initial program 66.4%

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

   3. Taylor expanded in j around 0 66.4%

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

   4. Taylor expanded in i around inf 99.7%

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

   if -2.60000000000000002e-268 < x < 6.79999999999999978e-307 or 5.50000000000000037e-197 < x < 4.49999999999999977e120

   1. Initial program 76.9%

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

   3. Taylor expanded in j around 0 62.1%

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

   4. Taylor expanded in c around inf 40.7%

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

      1. associate-*r* 40.7%

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

      2. neg-mul-1 40.7%

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

   6. Simplified 40.7%

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

   7. Taylor expanded in b around 0 40.7%

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

      1. neg-mul-1 40.7%

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

      2. distribute-lft-neg-in 40.7%

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

      3. *-commutative 40.7%

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

      4. associate-*l* 42.9%

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

   9. Simplified 42.9%

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

   if 6.79999999999999978e-307 < x < 3.90000000000000027e-250

   1. Initial program 86.0%

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

   3. Taylor expanded in j around 0 62.7%

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

   4. Taylor expanded in i around inf 58.4%

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

      1. associate-*r* 71.7%

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

   6. Simplified 71.7%

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

   if 4.49999999999999977e120 < x

   1. Initial program 70.1%

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

   3. Taylor expanded in z around inf 53.0%

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

      1. *-commutative 53.0%

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

      2. *-commutative 53.0%

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

   5. Simplified 53.0%

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

   6. Taylor expanded in y around inf 37.7%

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

      1. *-commutative 37.7%

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

   8. Simplified 37.7%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+218}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-240}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-268}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-307}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-197}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+120}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 30.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+219}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-237}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-267}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-305}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* b (- c)))) (t_2 (* a (* c j))))
   (if (<= x -1.5e+219)
     (* y (* x z))
     (if (<= x -9.5e-54)
       (* x (* t (- a)))
       (if (<= x -4e-237)
         t_2
         (if (<= x -4e-267)
           (* b (* t i))
           (if (<= x 2.3e-305)
             t_1
             (if (<= x 1.2e-249)
               (* t (* b i))
               (if (<= x 2.7e-209)
                 t_2
                 (if (<= x 5.2e+131) t_1 (* z (* x y))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (b * -c);
	double t_2 = a * (c * j);
	double tmp;
	if (x <= -1.5e+219) {
		tmp = y * (x * z);
	} else if (x <= -9.5e-54) {
		tmp = x * (t * -a);
	} else if (x <= -4e-237) {
		tmp = t_2;
	} else if (x <= -4e-267) {
		tmp = b * (t * i);
	} else if (x <= 2.3e-305) {
		tmp = t_1;
	} else if (x <= 1.2e-249) {
		tmp = t * (b * i);
	} else if (x <= 2.7e-209) {
		tmp = t_2;
	} else if (x <= 5.2e+131) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	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 = z * (b * -c)
    t_2 = a * (c * j)
    if (x <= (-1.5d+219)) then
        tmp = y * (x * z)
    else if (x <= (-9.5d-54)) then
        tmp = x * (t * -a)
    else if (x <= (-4d-237)) then
        tmp = t_2
    else if (x <= (-4d-267)) then
        tmp = b * (t * i)
    else if (x <= 2.3d-305) then
        tmp = t_1
    else if (x <= 1.2d-249) then
        tmp = t * (b * i)
    else if (x <= 2.7d-209) then
        tmp = t_2
    else if (x <= 5.2d+131) then
        tmp = t_1
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (b * -c);
	double t_2 = a * (c * j);
	double tmp;
	if (x <= -1.5e+219) {
		tmp = y * (x * z);
	} else if (x <= -9.5e-54) {
		tmp = x * (t * -a);
	} else if (x <= -4e-237) {
		tmp = t_2;
	} else if (x <= -4e-267) {
		tmp = b * (t * i);
	} else if (x <= 2.3e-305) {
		tmp = t_1;
	} else if (x <= 1.2e-249) {
		tmp = t * (b * i);
	} else if (x <= 2.7e-209) {
		tmp = t_2;
	} else if (x <= 5.2e+131) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (b * -c)
	t_2 = a * (c * j)
	tmp = 0
	if x <= -1.5e+219:
		tmp = y * (x * z)
	elif x <= -9.5e-54:
		tmp = x * (t * -a)
	elif x <= -4e-237:
		tmp = t_2
	elif x <= -4e-267:
		tmp = b * (t * i)
	elif x <= 2.3e-305:
		tmp = t_1
	elif x <= 1.2e-249:
		tmp = t * (b * i)
	elif x <= 2.7e-209:
		tmp = t_2
	elif x <= 5.2e+131:
		tmp = t_1
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(b * Float64(-c)))
	t_2 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (x <= -1.5e+219)
		tmp = Float64(y * Float64(x * z));
	elseif (x <= -9.5e-54)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (x <= -4e-237)
		tmp = t_2;
	elseif (x <= -4e-267)
		tmp = Float64(b * Float64(t * i));
	elseif (x <= 2.3e-305)
		tmp = t_1;
	elseif (x <= 1.2e-249)
		tmp = Float64(t * Float64(b * i));
	elseif (x <= 2.7e-209)
		tmp = t_2;
	elseif (x <= 5.2e+131)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (b * -c);
	t_2 = a * (c * j);
	tmp = 0.0;
	if (x <= -1.5e+219)
		tmp = y * (x * z);
	elseif (x <= -9.5e-54)
		tmp = x * (t * -a);
	elseif (x <= -4e-237)
		tmp = t_2;
	elseif (x <= -4e-267)
		tmp = b * (t * i);
	elseif (x <= 2.3e-305)
		tmp = t_1;
	elseif (x <= 1.2e-249)
		tmp = t * (b * i);
	elseif (x <= 2.7e-209)
		tmp = t_2;
	elseif (x <= 5.2e+131)
		tmp = t_1;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e+219], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.5e-54], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4e-237], t$95$2, If[LessEqual[x, -4e-267], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e-305], t$95$1, If[LessEqual[x, 1.2e-249], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e-209], t$95$2, If[LessEqual[x, 5.2e+131], t$95$1, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -1.4999999999999999e219

   1. Initial program 64.2%

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

   3. Taylor expanded in y around inf 79.4%

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

      1. +-commutative 79.4%

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

      2. mul-1-neg 79.4%

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

      3. unsub-neg 79.4%

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

      4. *-commutative 79.4%

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

      5. *-commutative 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in z around inf 72.5%

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

   if -1.4999999999999999e219 < x < -9.4999999999999994e-54

   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 x around inf 61.1%

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

   4. Taylor expanded in y around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. distribute-lft-neg-out 41.2%

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

      3. *-commutative 41.2%

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

   6. Simplified 41.2%

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

   if -9.4999999999999994e-54 < x < -4e-237 or 1.20000000000000006e-249 < x < 2.69999999999999998e-209

   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 a around inf 54.5%

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

      1. +-commutative 54.5%

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

      2. mul-1-neg 54.5%

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

      3. unsub-neg 54.5%

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

      4. *-commutative 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in j around inf 47.8%

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

   if -4e-237 < x < -3.9999999999999999e-267

   1. Initial program 66.4%

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

   3. Taylor expanded in j around 0 66.4%

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

   4. Taylor expanded in i around inf 99.7%

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

   if -3.9999999999999999e-267 < x < 2.3e-305 or 2.69999999999999998e-209 < x < 5.2e131

   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 z around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in y around 0 43.6%

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

      1. mul-1-neg 43.6%

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

      2. *-commutative 43.6%

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

      3. distribute-rgt-neg-in 43.6%

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

   8. Simplified 43.6%

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

   if 2.3e-305 < x < 1.20000000000000006e-249

   1. Initial program 86.0%

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

   3. Taylor expanded in j around 0 62.7%

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

   4. Taylor expanded in i around inf 58.4%

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

      1. associate-*r* 71.7%

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

   6. Simplified 71.7%

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

   if 5.2e131 < x

   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 53.2%

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

      1. *-commutative 53.2%

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

      2. *-commutative 53.2%

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

   5. Simplified 53.2%

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

   6. Taylor expanded in y around inf 39.2%

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

      1. *-commutative 39.2%

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

   8. Simplified 39.2%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+219}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-237}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-267}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-305}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+131}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 29.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_3 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;x \leq -1.16 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -3.05 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-238}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-269}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-304}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-251}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-211}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))) (t_2 (* z (* b (- c)))) (t_3 (* a (* c j))))
   (if (<= x -1.16e+223)
     (* y (* x z))
     (if (<= x -3.05e-52)
       t_1
       (if (<= x -4.6e-238)
         t_3
         (if (<= x -4.8e-269)
           (* b (* t i))
           (if (<= x 5.5e-304)
             t_2
             (if (<= x 6.2e-251)
               (* t (* b i))
               (if (<= x 2.7e-211) t_3 (if (<= x 3.1e+143) 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 = z * (b * -c);
	double t_3 = a * (c * j);
	double tmp;
	if (x <= -1.16e+223) {
		tmp = y * (x * z);
	} else if (x <= -3.05e-52) {
		tmp = t_1;
	} else if (x <= -4.6e-238) {
		tmp = t_3;
	} else if (x <= -4.8e-269) {
		tmp = b * (t * i);
	} else if (x <= 5.5e-304) {
		tmp = t_2;
	} else if (x <= 6.2e-251) {
		tmp = t * (b * i);
	} else if (x <= 2.7e-211) {
		tmp = t_3;
	} else if (x <= 3.1e+143) {
		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) :: t_3
    real(8) :: tmp
    t_1 = a * (x * -t)
    t_2 = z * (b * -c)
    t_3 = a * (c * j)
    if (x <= (-1.16d+223)) then
        tmp = y * (x * z)
    else if (x <= (-3.05d-52)) then
        tmp = t_1
    else if (x <= (-4.6d-238)) then
        tmp = t_3
    else if (x <= (-4.8d-269)) then
        tmp = b * (t * i)
    else if (x <= 5.5d-304) then
        tmp = t_2
    else if (x <= 6.2d-251) then
        tmp = t * (b * i)
    else if (x <= 2.7d-211) then
        tmp = t_3
    else if (x <= 3.1d+143) 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 = z * (b * -c);
	double t_3 = a * (c * j);
	double tmp;
	if (x <= -1.16e+223) {
		tmp = y * (x * z);
	} else if (x <= -3.05e-52) {
		tmp = t_1;
	} else if (x <= -4.6e-238) {
		tmp = t_3;
	} else if (x <= -4.8e-269) {
		tmp = b * (t * i);
	} else if (x <= 5.5e-304) {
		tmp = t_2;
	} else if (x <= 6.2e-251) {
		tmp = t * (b * i);
	} else if (x <= 2.7e-211) {
		tmp = t_3;
	} else if (x <= 3.1e+143) {
		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 = z * (b * -c)
	t_3 = a * (c * j)
	tmp = 0
	if x <= -1.16e+223:
		tmp = y * (x * z)
	elif x <= -3.05e-52:
		tmp = t_1
	elif x <= -4.6e-238:
		tmp = t_3
	elif x <= -4.8e-269:
		tmp = b * (t * i)
	elif x <= 5.5e-304:
		tmp = t_2
	elif x <= 6.2e-251:
		tmp = t * (b * i)
	elif x <= 2.7e-211:
		tmp = t_3
	elif x <= 3.1e+143:
		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(z * Float64(b * Float64(-c)))
	t_3 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (x <= -1.16e+223)
		tmp = Float64(y * Float64(x * z));
	elseif (x <= -3.05e-52)
		tmp = t_1;
	elseif (x <= -4.6e-238)
		tmp = t_3;
	elseif (x <= -4.8e-269)
		tmp = Float64(b * Float64(t * i));
	elseif (x <= 5.5e-304)
		tmp = t_2;
	elseif (x <= 6.2e-251)
		tmp = Float64(t * Float64(b * i));
	elseif (x <= 2.7e-211)
		tmp = t_3;
	elseif (x <= 3.1e+143)
		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 = z * (b * -c);
	t_3 = a * (c * j);
	tmp = 0.0;
	if (x <= -1.16e+223)
		tmp = y * (x * z);
	elseif (x <= -3.05e-52)
		tmp = t_1;
	elseif (x <= -4.6e-238)
		tmp = t_3;
	elseif (x <= -4.8e-269)
		tmp = b * (t * i);
	elseif (x <= 5.5e-304)
		tmp = t_2;
	elseif (x <= 6.2e-251)
		tmp = t * (b * i);
	elseif (x <= 2.7e-211)
		tmp = t_3;
	elseif (x <= 3.1e+143)
		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[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.16e+223], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.05e-52], t$95$1, If[LessEqual[x, -4.6e-238], t$95$3, If[LessEqual[x, -4.8e-269], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e-304], t$95$2, If[LessEqual[x, 6.2e-251], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e-211], t$95$3, If[LessEqual[x, 3.1e+143], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.15999999999999993e223

   1. Initial program 64.2%

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

   3. Taylor expanded in y around inf 79.4%

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

      1. +-commutative 79.4%

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

      2. mul-1-neg 79.4%

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

      3. unsub-neg 79.4%

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

      4. *-commutative 79.4%

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

      5. *-commutative 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in z around inf 72.5%

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

   if -1.15999999999999993e223 < x < -3.04999999999999995e-52 or 3.0999999999999999e143 < x

   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 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. unsub-neg 49.9%

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

      4. *-commutative 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in j around 0 42.2%

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

      1. associate-*r* 42.2%

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

      2. neg-mul-1 42.2%

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

   8. Simplified 42.2%

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

   if -3.04999999999999995e-52 < x < -4.60000000000000009e-238 or 6.20000000000000006e-251 < x < 2.6999999999999999e-211

   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 a around inf 54.5%

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

      1. +-commutative 54.5%

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

      2. mul-1-neg 54.5%

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

      3. unsub-neg 54.5%

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

      4. *-commutative 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in j around inf 47.8%

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

   if -4.60000000000000009e-238 < x < -4.8000000000000002e-269

   1. Initial program 66.4%

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

   3. Taylor expanded in j around 0 66.4%

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

   4. Taylor expanded in i around inf 99.7%

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

   if -4.8000000000000002e-269 < x < 5.50000000000000035e-304 or 2.6999999999999999e-211 < x < 3.0999999999999999e143

   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 z around inf 50.8%

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

      1. *-commutative 50.8%

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

      2. *-commutative 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in y around 0 42.4%

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

      1. mul-1-neg 42.4%

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

      2. *-commutative 42.4%

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

      3. distribute-rgt-neg-in 42.4%

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

   8. Simplified 42.4%

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

   if 5.50000000000000035e-304 < x < 6.20000000000000006e-251

   1. Initial program 86.0%

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

   3. Taylor expanded in j around 0 62.7%

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

   4. Taylor expanded in i around inf 58.4%

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

      1. associate-*r* 71.7%

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

   6. Simplified 71.7%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -3.05 \cdot 10^{-52}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-238}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-269}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-304}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-251}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+143}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 28.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;x \leq -4.45 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-267}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-305}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+210}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= x -4.45e+223)
     (* y (* x z))
     (if (<= x -9.8e-54)
       (* a (* x (- t)))
       (if (<= x -2.4e-237)
         t_1
         (if (<= x -2.5e-267)
           (* b (* t i))
           (if (<= x 9e-305)
             (* z (* b (- c)))
             (if (<= x 1.45e-249)
               (* t (* b i))
               (if (<= x 2.7e-209)
                 t_1
                 (if (<= x 1.25e+210) (* b (* z (- c))) (* x (* y z))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (x <= -4.45e+223) {
		tmp = y * (x * z);
	} else if (x <= -9.8e-54) {
		tmp = a * (x * -t);
	} else if (x <= -2.4e-237) {
		tmp = t_1;
	} else if (x <= -2.5e-267) {
		tmp = b * (t * i);
	} else if (x <= 9e-305) {
		tmp = z * (b * -c);
	} else if (x <= 1.45e-249) {
		tmp = t * (b * i);
	} else if (x <= 2.7e-209) {
		tmp = t_1;
	} else if (x <= 1.25e+210) {
		tmp = b * (z * -c);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (x <= (-4.45d+223)) then
        tmp = y * (x * z)
    else if (x <= (-9.8d-54)) then
        tmp = a * (x * -t)
    else if (x <= (-2.4d-237)) then
        tmp = t_1
    else if (x <= (-2.5d-267)) then
        tmp = b * (t * i)
    else if (x <= 9d-305) then
        tmp = z * (b * -c)
    else if (x <= 1.45d-249) then
        tmp = t * (b * i)
    else if (x <= 2.7d-209) then
        tmp = t_1
    else if (x <= 1.25d+210) then
        tmp = b * (z * -c)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (x <= -4.45e+223) {
		tmp = y * (x * z);
	} else if (x <= -9.8e-54) {
		tmp = a * (x * -t);
	} else if (x <= -2.4e-237) {
		tmp = t_1;
	} else if (x <= -2.5e-267) {
		tmp = b * (t * i);
	} else if (x <= 9e-305) {
		tmp = z * (b * -c);
	} else if (x <= 1.45e-249) {
		tmp = t * (b * i);
	} else if (x <= 2.7e-209) {
		tmp = t_1;
	} else if (x <= 1.25e+210) {
		tmp = b * (z * -c);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if x <= -4.45e+223:
		tmp = y * (x * z)
	elif x <= -9.8e-54:
		tmp = a * (x * -t)
	elif x <= -2.4e-237:
		tmp = t_1
	elif x <= -2.5e-267:
		tmp = b * (t * i)
	elif x <= 9e-305:
		tmp = z * (b * -c)
	elif x <= 1.45e-249:
		tmp = t * (b * i)
	elif x <= 2.7e-209:
		tmp = t_1
	elif x <= 1.25e+210:
		tmp = b * (z * -c)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (x <= -4.45e+223)
		tmp = Float64(y * Float64(x * z));
	elseif (x <= -9.8e-54)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (x <= -2.4e-237)
		tmp = t_1;
	elseif (x <= -2.5e-267)
		tmp = Float64(b * Float64(t * i));
	elseif (x <= 9e-305)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (x <= 1.45e-249)
		tmp = Float64(t * Float64(b * i));
	elseif (x <= 2.7e-209)
		tmp = t_1;
	elseif (x <= 1.25e+210)
		tmp = Float64(b * Float64(z * Float64(-c)));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (x <= -4.45e+223)
		tmp = y * (x * z);
	elseif (x <= -9.8e-54)
		tmp = a * (x * -t);
	elseif (x <= -2.4e-237)
		tmp = t_1;
	elseif (x <= -2.5e-267)
		tmp = b * (t * i);
	elseif (x <= 9e-305)
		tmp = z * (b * -c);
	elseif (x <= 1.45e-249)
		tmp = t * (b * i);
	elseif (x <= 2.7e-209)
		tmp = t_1;
	elseif (x <= 1.25e+210)
		tmp = b * (z * -c);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.45e+223], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.8e-54], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.4e-237], t$95$1, If[LessEqual[x, -2.5e-267], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-305], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.45e-249], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e-209], t$95$1, If[LessEqual[x, 1.25e+210], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if x < -4.4499999999999999e223

   1. Initial program 64.2%

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

   3. Taylor expanded in y around inf 79.4%

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

      1. +-commutative 79.4%

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

      2. mul-1-neg 79.4%

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

      3. unsub-neg 79.4%

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

      4. *-commutative 79.4%

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

      5. *-commutative 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in z around inf 72.5%

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

   if -4.4499999999999999e223 < x < -9.80000000000000042e-54

   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 a around inf 50.7%

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

      1. +-commutative 50.7%

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

      2. mul-1-neg 50.7%

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

      3. unsub-neg 50.7%

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

      4. *-commutative 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in j around 0 41.3%

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

      1. associate-*r* 41.3%

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

      2. neg-mul-1 41.3%

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

   8. Simplified 41.3%

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

   if -9.80000000000000042e-54 < x < -2.4e-237 or 1.45000000000000011e-249 < x < 2.69999999999999998e-209

   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 a around inf 54.5%

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

      1. +-commutative 54.5%

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

      2. mul-1-neg 54.5%

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

      3. unsub-neg 54.5%

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

      4. *-commutative 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in j around inf 47.8%

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

   if -2.4e-237 < x < -2.5e-267

   1. Initial program 66.4%

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

   3. Taylor expanded in j around 0 66.4%

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

   4. Taylor expanded in i around inf 99.7%

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

   if -2.5e-267 < x < 9.0000000000000003e-305

   1. Initial program 75.4%

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

   3. Taylor expanded in z around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. *-commutative 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in y around 0 51.4%

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

      1. mul-1-neg 51.4%

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

      2. *-commutative 51.4%

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

      3. distribute-rgt-neg-in 51.4%

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

   8. Simplified 51.4%

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

   if 9.0000000000000003e-305 < x < 1.45000000000000011e-249

   1. Initial program 86.0%

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

   3. Taylor expanded in j around 0 62.7%

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

   4. Taylor expanded in i around inf 58.4%

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

      1. associate-*r* 71.7%

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

   6. Simplified 71.7%

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

   if 2.69999999999999998e-209 < x < 1.2499999999999999e210

   1. Initial program 75.2%

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

   3. Taylor expanded in j around 0 67.5%

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

   4. Taylor expanded in c around inf 40.7%

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

      1. associate-*r* 40.7%

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

      2. neg-mul-1 40.7%

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

   6. Simplified 40.7%

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

   if 1.2499999999999999e210 < x

   1. Initial program 63.2%

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

   3. Taylor expanded in x around inf 71.0%

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

   4. Taylor expanded in y around inf 45.5%

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

      1. *-commutative 45.5%

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

   6. Simplified 45.5%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.45 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-237}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-267}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-305}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+210}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(x \cdot \left(-a\right)\right)\\ t_2 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_3 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;x \leq -1.28 \cdot 10^{+222}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-237}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-268}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-307}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-208}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* x (- a)))) (t_2 (* z (* b (- c)))) (t_3 (* a (* c j))))
   (if (<= x -1.28e+222)
     (* y (* x z))
     (if (<= x -5.5e-53)
       t_1
       (if (<= x -2.45e-237)
         t_3
         (if (<= x -4.2e-268)
           (* b (* t i))
           (if (<= x 5.8e-307)
             t_2
             (if (<= x 3.6e-250)
               (* t (* b i))
               (if (<= x 7.4e-208) t_3 (if (<= x 2.9e+143) 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 = t * (x * -a);
	double t_2 = z * (b * -c);
	double t_3 = a * (c * j);
	double tmp;
	if (x <= -1.28e+222) {
		tmp = y * (x * z);
	} else if (x <= -5.5e-53) {
		tmp = t_1;
	} else if (x <= -2.45e-237) {
		tmp = t_3;
	} else if (x <= -4.2e-268) {
		tmp = b * (t * i);
	} else if (x <= 5.8e-307) {
		tmp = t_2;
	} else if (x <= 3.6e-250) {
		tmp = t * (b * i);
	} else if (x <= 7.4e-208) {
		tmp = t_3;
	} else if (x <= 2.9e+143) {
		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) :: t_3
    real(8) :: tmp
    t_1 = t * (x * -a)
    t_2 = z * (b * -c)
    t_3 = a * (c * j)
    if (x <= (-1.28d+222)) then
        tmp = y * (x * z)
    else if (x <= (-5.5d-53)) then
        tmp = t_1
    else if (x <= (-2.45d-237)) then
        tmp = t_3
    else if (x <= (-4.2d-268)) then
        tmp = b * (t * i)
    else if (x <= 5.8d-307) then
        tmp = t_2
    else if (x <= 3.6d-250) then
        tmp = t * (b * i)
    else if (x <= 7.4d-208) then
        tmp = t_3
    else if (x <= 2.9d+143) 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 = t * (x * -a);
	double t_2 = z * (b * -c);
	double t_3 = a * (c * j);
	double tmp;
	if (x <= -1.28e+222) {
		tmp = y * (x * z);
	} else if (x <= -5.5e-53) {
		tmp = t_1;
	} else if (x <= -2.45e-237) {
		tmp = t_3;
	} else if (x <= -4.2e-268) {
		tmp = b * (t * i);
	} else if (x <= 5.8e-307) {
		tmp = t_2;
	} else if (x <= 3.6e-250) {
		tmp = t * (b * i);
	} else if (x <= 7.4e-208) {
		tmp = t_3;
	} else if (x <= 2.9e+143) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (x * -a)
	t_2 = z * (b * -c)
	t_3 = a * (c * j)
	tmp = 0
	if x <= -1.28e+222:
		tmp = y * (x * z)
	elif x <= -5.5e-53:
		tmp = t_1
	elif x <= -2.45e-237:
		tmp = t_3
	elif x <= -4.2e-268:
		tmp = b * (t * i)
	elif x <= 5.8e-307:
		tmp = t_2
	elif x <= 3.6e-250:
		tmp = t * (b * i)
	elif x <= 7.4e-208:
		tmp = t_3
	elif x <= 2.9e+143:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(x * Float64(-a)))
	t_2 = Float64(z * Float64(b * Float64(-c)))
	t_3 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (x <= -1.28e+222)
		tmp = Float64(y * Float64(x * z));
	elseif (x <= -5.5e-53)
		tmp = t_1;
	elseif (x <= -2.45e-237)
		tmp = t_3;
	elseif (x <= -4.2e-268)
		tmp = Float64(b * Float64(t * i));
	elseif (x <= 5.8e-307)
		tmp = t_2;
	elseif (x <= 3.6e-250)
		tmp = Float64(t * Float64(b * i));
	elseif (x <= 7.4e-208)
		tmp = t_3;
	elseif (x <= 2.9e+143)
		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 = t * (x * -a);
	t_2 = z * (b * -c);
	t_3 = a * (c * j);
	tmp = 0.0;
	if (x <= -1.28e+222)
		tmp = y * (x * z);
	elseif (x <= -5.5e-53)
		tmp = t_1;
	elseif (x <= -2.45e-237)
		tmp = t_3;
	elseif (x <= -4.2e-268)
		tmp = b * (t * i);
	elseif (x <= 5.8e-307)
		tmp = t_2;
	elseif (x <= 3.6e-250)
		tmp = t * (b * i);
	elseif (x <= 7.4e-208)
		tmp = t_3;
	elseif (x <= 2.9e+143)
		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[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.28e+222], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.5e-53], t$95$1, If[LessEqual[x, -2.45e-237], t$95$3, If[LessEqual[x, -4.2e-268], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e-307], t$95$2, If[LessEqual[x, 3.6e-250], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e-208], t$95$3, If[LessEqual[x, 2.9e+143], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.28e222

   1. Initial program 64.2%

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

   3. Taylor expanded in y around inf 79.4%

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

      1. +-commutative 79.4%

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

      2. mul-1-neg 79.4%

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

      3. unsub-neg 79.4%

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

      4. *-commutative 79.4%

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

      5. *-commutative 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in z around inf 72.5%

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

   if -1.28e222 < x < -5.50000000000000023e-53 or 2.8999999999999998e143 < x

   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 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. unsub-neg 49.9%

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

      4. *-commutative 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in j around 0 42.2%

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

      1. associate-*r* 42.2%

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

      2. neg-mul-1 42.2%

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

   8. Simplified 42.2%

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

   9. Taylor expanded in a around 0 42.2%

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

       1. mul-1-neg 42.2%

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

       2. *-commutative 42.2%

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

       3. associate-*r* 45.4%

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

       4. distribute-rgt-neg-in 45.4%

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

   11. Simplified 45.4%

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

   if -5.50000000000000023e-53 < x < -2.45e-237 or 3.59999999999999982e-250 < x < 7.4000000000000004e-208

   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 a around inf 54.5%

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

      1. +-commutative 54.5%

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

      2. mul-1-neg 54.5%

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

      3. unsub-neg 54.5%

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

      4. *-commutative 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in j around inf 47.8%

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

   if -2.45e-237 < x < -4.19999999999999996e-268

   1. Initial program 66.4%

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

   3. Taylor expanded in j around 0 66.4%

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

   4. Taylor expanded in i around inf 99.7%

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

   if -4.19999999999999996e-268 < x < 5.8000000000000001e-307 or 7.4000000000000004e-208 < x < 2.8999999999999998e143

   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 z around inf 50.8%

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

      1. *-commutative 50.8%

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

      2. *-commutative 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in y around 0 42.4%

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

      1. mul-1-neg 42.4%

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

      2. *-commutative 42.4%

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

      3. distribute-rgt-neg-in 42.4%

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

   8. Simplified 42.4%

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

   if 5.8000000000000001e-307 < x < 3.59999999999999982e-250

   1. Initial program 86.0%

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

   3. Taylor expanded in j around 0 62.7%

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

   4. Taylor expanded in i around inf 58.4%

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

      1. associate-*r* 71.7%

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

   6. Simplified 71.7%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.28 \cdot 10^{+222}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -2.45 \cdot 10^{-237}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-268}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-307}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-208}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+143}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;j \leq -2 \cdot 10^{+181}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -9.2 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot \frac{z}{a} - t\right)\right)\\ \mathbf{elif}\;j \leq -4.9 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -7.6 \cdot 10^{-256}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{-102}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+21}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (* t i)) (* j (- (* y i) (* a c)))))
        (t_2 (* z (- (* x y) (* b c)))))
   (if (<= j -2e+181)
     (* j (- (* a c) (* y i)))
     (if (<= j -9.2e+172)
       (* x (* a (- (* y (/ z a)) t)))
       (if (<= j -4.9e+26)
         t_1
         (if (<= j -7.6e-256)
           t_2
           (if (<= j 6.4e-102)
             (* t (- (* b i) (* x a)))
             (if (<= j 2.8e+21) 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 = (b * (t * i)) - (j * ((y * i) - (a * c)));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (j <= -2e+181) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -9.2e+172) {
		tmp = x * (a * ((y * (z / a)) - t));
	} else if (j <= -4.9e+26) {
		tmp = t_1;
	} else if (j <= -7.6e-256) {
		tmp = t_2;
	} else if (j <= 6.4e-102) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 2.8e+21) {
		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 = (b * (t * i)) - (j * ((y * i) - (a * c)))
    t_2 = z * ((x * y) - (b * c))
    if (j <= (-2d+181)) then
        tmp = j * ((a * c) - (y * i))
    else if (j <= (-9.2d+172)) then
        tmp = x * (a * ((y * (z / a)) - t))
    else if (j <= (-4.9d+26)) then
        tmp = t_1
    else if (j <= (-7.6d-256)) then
        tmp = t_2
    else if (j <= 6.4d-102) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 2.8d+21) 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 = (b * (t * i)) - (j * ((y * i) - (a * c)));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (j <= -2e+181) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -9.2e+172) {
		tmp = x * (a * ((y * (z / a)) - t));
	} else if (j <= -4.9e+26) {
		tmp = t_1;
	} else if (j <= -7.6e-256) {
		tmp = t_2;
	} else if (j <= 6.4e-102) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 2.8e+21) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * (t * i)) - (j * ((y * i) - (a * c)))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if j <= -2e+181:
		tmp = j * ((a * c) - (y * i))
	elif j <= -9.2e+172:
		tmp = x * (a * ((y * (z / a)) - t))
	elif j <= -4.9e+26:
		tmp = t_1
	elif j <= -7.6e-256:
		tmp = t_2
	elif j <= 6.4e-102:
		tmp = t * ((b * i) - (x * a))
	elif j <= 2.8e+21:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * Float64(t * i)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (j <= -2e+181)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (j <= -9.2e+172)
		tmp = Float64(x * Float64(a * Float64(Float64(y * Float64(z / a)) - t)));
	elseif (j <= -4.9e+26)
		tmp = t_1;
	elseif (j <= -7.6e-256)
		tmp = t_2;
	elseif (j <= 6.4e-102)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 2.8e+21)
		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 = (b * (t * i)) - (j * ((y * i) - (a * c)));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (j <= -2e+181)
		tmp = j * ((a * c) - (y * i));
	elseif (j <= -9.2e+172)
		tmp = x * (a * ((y * (z / a)) - t));
	elseif (j <= -4.9e+26)
		tmp = t_1;
	elseif (j <= -7.6e-256)
		tmp = t_2;
	elseif (j <= 6.4e-102)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 2.8e+21)
		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[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2e+181], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -9.2e+172], N[(x * N[(a * N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.9e+26], t$95$1, If[LessEqual[j, -7.6e-256], t$95$2, If[LessEqual[j, 6.4e-102], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.8e+21], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.9999999999999998e181

   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 j around inf 84.1%

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

   if -1.9999999999999998e181 < j < -9.2000000000000003e172

   1. Initial program 60.0%

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

   3. Taylor expanded in x around inf 81.0%

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

   4. Taylor expanded in a around inf 100.0%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if -9.2000000000000003e172 < j < -4.89999999999999974e26 or 2.8e21 < j

   1. Initial program 74.4%

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

   3. Taylor expanded in i around inf 69.5%

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

   if -4.89999999999999974e26 < j < -7.59999999999999953e-256 or 6.39999999999999973e-102 < j < 2.8e21

   1. Initial program 77.0%

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

   3. Taylor expanded in z around inf 62.8%

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

      1. *-commutative 62.8%

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

      2. *-commutative 62.8%

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

   5. Simplified 62.8%

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

   if -7.59999999999999953e-256 < j < 6.39999999999999973e-102

   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 t around -inf 61.0%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2 \cdot 10^{+181}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -9.2 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot \frac{z}{a} - t\right)\right)\\ \mathbf{elif}\;j \leq -4.9 \cdot 10^{+26}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq -7.6 \cdot 10^{-256}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{-102}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+21}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-137}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+17}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -3.8e+76)
     t_2
     (if (<= a -4.8e+25)
       t_1
       (if (<= a -1.1e-10)
         t_2
         (if (<= a -1.35e-137)
           (* b (- (* t i) (* z c)))
           (if (<= a 1.3e-193)
             t_1
             (if (<= a 2.05e+17)
               (* i (- (* t b) (* y j)))
               (if (<= a 4e+44) 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 = z * ((x * y) - (b * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.8e+76) {
		tmp = t_2;
	} else if (a <= -4.8e+25) {
		tmp = t_1;
	} else if (a <= -1.1e-10) {
		tmp = t_2;
	} else if (a <= -1.35e-137) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.3e-193) {
		tmp = t_1;
	} else if (a <= 2.05e+17) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 4e+44) {
		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 = z * ((x * y) - (b * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-3.8d+76)) then
        tmp = t_2
    else if (a <= (-4.8d+25)) then
        tmp = t_1
    else if (a <= (-1.1d-10)) then
        tmp = t_2
    else if (a <= (-1.35d-137)) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 1.3d-193) then
        tmp = t_1
    else if (a <= 2.05d+17) then
        tmp = i * ((t * b) - (y * j))
    else if (a <= 4d+44) 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 = z * ((x * y) - (b * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.8e+76) {
		tmp = t_2;
	} else if (a <= -4.8e+25) {
		tmp = t_1;
	} else if (a <= -1.1e-10) {
		tmp = t_2;
	} else if (a <= -1.35e-137) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.3e-193) {
		tmp = t_1;
	} else if (a <= 2.05e+17) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 4e+44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -3.8e+76:
		tmp = t_2
	elif a <= -4.8e+25:
		tmp = t_1
	elif a <= -1.1e-10:
		tmp = t_2
	elif a <= -1.35e-137:
		tmp = b * ((t * i) - (z * c))
	elif a <= 1.3e-193:
		tmp = t_1
	elif a <= 2.05e+17:
		tmp = i * ((t * b) - (y * j))
	elif a <= 4e+44:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.8e+76)
		tmp = t_2;
	elseif (a <= -4.8e+25)
		tmp = t_1;
	elseif (a <= -1.1e-10)
		tmp = t_2;
	elseif (a <= -1.35e-137)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 1.3e-193)
		tmp = t_1;
	elseif (a <= 2.05e+17)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (a <= 4e+44)
		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 = z * ((x * y) - (b * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -3.8e+76)
		tmp = t_2;
	elseif (a <= -4.8e+25)
		tmp = t_1;
	elseif (a <= -1.1e-10)
		tmp = t_2;
	elseif (a <= -1.35e-137)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 1.3e-193)
		tmp = t_1;
	elseif (a <= 2.05e+17)
		tmp = i * ((t * b) - (y * j));
	elseif (a <= 4e+44)
		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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e+76], t$95$2, If[LessEqual[a, -4.8e+25], t$95$1, If[LessEqual[a, -1.1e-10], t$95$2, If[LessEqual[a, -1.35e-137], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e-193], t$95$1, If[LessEqual[a, 2.05e+17], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+44], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.80000000000000024e76 or -4.79999999999999992e25 < a < -1.09999999999999995e-10 or 4.0000000000000004e44 < a

   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 a around inf 70.4%

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

      1. +-commutative 70.4%

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

      2. mul-1-neg 70.4%

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

      3. unsub-neg 70.4%

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

      4. *-commutative 70.4%

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

   5. Simplified 70.4%

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

   if -3.80000000000000024e76 < a < -4.79999999999999992e25 or -1.34999999999999996e-137 < a < 1.30000000000000004e-193 or 2.05e17 < a < 4.0000000000000004e44

   1. Initial program 77.1%

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

   3. Taylor expanded in z around inf 69.0%

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

      1. *-commutative 69.0%

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

      2. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   if -1.09999999999999995e-10 < a < -1.34999999999999996e-137

   1. Initial program 96.2%

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

   3. Taylor expanded in b around inf 60.6%

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

   if 1.30000000000000004e-193 < a < 2.05e17

   1. Initial program 80.7%

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

   3. Taylor expanded in i around inf 52.6%

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

   4. Taylor expanded in i around inf 65.1%

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

      1. +-commutative 65.1%

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

      2. mul-1-neg 65.1%

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

      3. unsub-neg 65.1%

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

      4. *-commutative 65.1%

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

      5. *-commutative 65.1%

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

   6. Simplified 65.1%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{+25}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-10}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-137}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-193}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+17}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+44}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t\_2 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -3.7 \cdot 10^{+181}:\\ \;\;\;\;b \cdot \left(t \cdot i + \frac{t\_1}{b}\right)\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{+145}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{+26}:\\ \;\;\;\;t\_1 + t\_2\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-27}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (+ t_2 (* b (- (* t i) (* z c))))))
   (if (<= j -3.7e+181)
     (* b (+ (* t i) (/ t_1 b)))
     (if (<= j -3.8e+145)
       t_3
       (if (<= j -3.2e+26)
         (+ t_1 t_2)
         (if (<= j 3.4e-27) t_3 (- t_1 (* b (* z c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -3.7e+181) {
		tmp = b * ((t * i) + (t_1 / b));
	} else if (j <= -3.8e+145) {
		tmp = t_3;
	} else if (j <= -3.2e+26) {
		tmp = t_1 + t_2;
	} else if (j <= 3.4e-27) {
		tmp = t_3;
	} else {
		tmp = t_1 - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    t_3 = t_2 + (b * ((t * i) - (z * c)))
    if (j <= (-3.7d+181)) then
        tmp = b * ((t * i) + (t_1 / b))
    else if (j <= (-3.8d+145)) then
        tmp = t_3
    else if (j <= (-3.2d+26)) then
        tmp = t_1 + t_2
    else if (j <= 3.4d-27) then
        tmp = t_3
    else
        tmp = t_1 - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -3.7e+181) {
		tmp = b * ((t * i) + (t_1 / b));
	} else if (j <= -3.8e+145) {
		tmp = t_3;
	} else if (j <= -3.2e+26) {
		tmp = t_1 + t_2;
	} else if (j <= 3.4e-27) {
		tmp = t_3;
	} else {
		tmp = t_1 - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	t_3 = t_2 + (b * ((t * i) - (z * c)))
	tmp = 0
	if j <= -3.7e+181:
		tmp = b * ((t * i) + (t_1 / b))
	elif j <= -3.8e+145:
		tmp = t_3
	elif j <= -3.2e+26:
		tmp = t_1 + t_2
	elif j <= 3.4e-27:
		tmp = t_3
	else:
		tmp = t_1 - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(t_2 + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (j <= -3.7e+181)
		tmp = Float64(b * Float64(Float64(t * i) + Float64(t_1 / b)));
	elseif (j <= -3.8e+145)
		tmp = t_3;
	elseif (j <= -3.2e+26)
		tmp = Float64(t_1 + t_2);
	elseif (j <= 3.4e-27)
		tmp = t_3;
	else
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	t_3 = t_2 + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (j <= -3.7e+181)
		tmp = b * ((t * i) + (t_1 / b));
	elseif (j <= -3.8e+145)
		tmp = t_3;
	elseif (j <= -3.2e+26)
		tmp = t_1 + t_2;
	elseif (j <= 3.4e-27)
		tmp = t_3;
	else
		tmp = t_1 - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.7e+181], N[(b * N[(N[(t * i), $MachinePrecision] + N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.8e+145], t$95$3, If[LessEqual[j, -3.2e+26], N[(t$95$1 + t$95$2), $MachinePrecision], If[LessEqual[j, 3.4e-27], t$95$3, N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.7000000000000004e181

   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 i around inf 80.3%

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

   4. Taylor expanded in b around inf 90.2%

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

   if -3.7000000000000004e181 < j < -3.80000000000000012e145 or -3.20000000000000029e26 < j < 3.3999999999999997e-27

   1. Initial program 75.0%

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

   3. Taylor expanded in j around 0 76.4%

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

   if -3.80000000000000012e145 < j < -3.20000000000000029e26

   1. Initial program 78.2%

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

   3. Taylor expanded in b around 0 78.2%

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

   if 3.3999999999999997e-27 < j

   1. Initial program 72.7%

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

   3. Taylor expanded in c around inf 72.6%

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

      1. associate-*r* 72.6%

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

      2. neg-mul-1 72.6%

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

   5. Simplified 72.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.7 \cdot 10^{+181}:\\ \;\;\;\;b \cdot \left(t \cdot i + \frac{j \cdot \left(a \cdot c - y \cdot i\right)}{b}\right)\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{+145}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{+26}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;j \leq -1.32 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(t \cdot i + \frac{t\_1}{b}\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-256}:\\ \;\;\;\;t\_2 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{-302}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-27}:\\ \;\;\;\;t\_2 + b \cdot \left(i \cdot \left(t - \frac{z \cdot c}{i}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* x (* y z))))
   (if (<= j -1.32e+27)
     (* b (+ (* t i) (/ t_1 b)))
     (if (<= j -5e-256)
       (+ t_2 (* b (- (* t i) (* z c))))
       (if (<= j -2.6e-302)
         (* t (- (* b i) (* x a)))
         (if (<= j 2.8e-27)
           (+ t_2 (* b (* i (- t (/ (* z c) i)))))
           (- t_1 (* b (* z c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * (y * z);
	double tmp;
	if (j <= -1.32e+27) {
		tmp = b * ((t * i) + (t_1 / b));
	} else if (j <= -5e-256) {
		tmp = t_2 + (b * ((t * i) - (z * c)));
	} else if (j <= -2.6e-302) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 2.8e-27) {
		tmp = t_2 + (b * (i * (t - ((z * c) / i))));
	} else {
		tmp = t_1 - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = x * (y * z)
    if (j <= (-1.32d+27)) then
        tmp = b * ((t * i) + (t_1 / b))
    else if (j <= (-5d-256)) then
        tmp = t_2 + (b * ((t * i) - (z * c)))
    else if (j <= (-2.6d-302)) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 2.8d-27) then
        tmp = t_2 + (b * (i * (t - ((z * c) / i))))
    else
        tmp = t_1 - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * (y * z);
	double tmp;
	if (j <= -1.32e+27) {
		tmp = b * ((t * i) + (t_1 / b));
	} else if (j <= -5e-256) {
		tmp = t_2 + (b * ((t * i) - (z * c)));
	} else if (j <= -2.6e-302) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 2.8e-27) {
		tmp = t_2 + (b * (i * (t - ((z * c) / i))));
	} else {
		tmp = t_1 - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = x * (y * z)
	tmp = 0
	if j <= -1.32e+27:
		tmp = b * ((t * i) + (t_1 / b))
	elif j <= -5e-256:
		tmp = t_2 + (b * ((t * i) - (z * c)))
	elif j <= -2.6e-302:
		tmp = t * ((b * i) - (x * a))
	elif j <= 2.8e-27:
		tmp = t_2 + (b * (i * (t - ((z * c) / i))))
	else:
		tmp = t_1 - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (j <= -1.32e+27)
		tmp = Float64(b * Float64(Float64(t * i) + Float64(t_1 / b)));
	elseif (j <= -5e-256)
		tmp = Float64(t_2 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (j <= -2.6e-302)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 2.8e-27)
		tmp = Float64(t_2 + Float64(b * Float64(i * Float64(t - Float64(Float64(z * c) / i)))));
	else
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = x * (y * z);
	tmp = 0.0;
	if (j <= -1.32e+27)
		tmp = b * ((t * i) + (t_1 / b));
	elseif (j <= -5e-256)
		tmp = t_2 + (b * ((t * i) - (z * c)));
	elseif (j <= -2.6e-302)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 2.8e-27)
		tmp = t_2 + (b * (i * (t - ((z * c) / i))));
	else
		tmp = t_1 - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.32e+27], N[(b * N[(N[(t * i), $MachinePrecision] + N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5e-256], N[(t$95$2 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.6e-302], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.8e-27], N[(t$95$2 + N[(b * N[(i * N[(t - N[(N[(z * c), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.31999999999999997e27

   1. Initial program 76.1%

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

   3. Taylor expanded in i around inf 68.9%

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

   4. Taylor expanded in b around inf 73.5%

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

   if -1.31999999999999997e27 < j < -5e-256

   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 j around 0 76.3%

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

   4. Taylor expanded in y around inf 69.7%

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

      1. *-commutative 31.8%

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

   6. Simplified 69.7%

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

   if -5e-256 < j < -2.60000000000000011e-302

   1. Initial program 70.5%

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

   3. Taylor expanded in t around -inf 81.0%

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

   if -2.60000000000000011e-302 < j < 2.8e-27

   1. Initial program 73.5%

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

   3. Taylor expanded in j around 0 77.9%

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

   4. Taylor expanded in y around inf 66.5%

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

      1. *-commutative 23.2%

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

   6. Simplified 66.5%

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

   7. Taylor expanded in i around inf 66.6%

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

   if 2.8e-27 < j

   1. Initial program 72.7%

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

   3. Taylor expanded in c around inf 72.6%

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

      1. associate-*r* 72.6%

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

      2. neg-mul-1 72.6%

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

   5. Simplified 72.6%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.32 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(t \cdot i + \frac{j \cdot \left(a \cdot c - y \cdot i\right)}{b}\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{-302}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(i \cdot \left(t - \frac{z \cdot c}{i}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot b\right) \cdot \left(-c\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -5.6 \cdot 10^{+63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -2.35 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-257}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 4.1 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z b) (- c))) (t_2 (* a (* c j))))
   (if (<= j -5.6e+63)
     t_2
     (if (<= j -2.35e-52)
       t_1
       (if (<= j -6.5e-257)
         (* y (* x z))
         (if (<= j 3.8e-256)
           t_1
           (if (<= j 4.1e-128) (* b (* t i)) (if (<= j 1.5e+27) 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 = (z * b) * -c;
	double t_2 = a * (c * j);
	double tmp;
	if (j <= -5.6e+63) {
		tmp = t_2;
	} else if (j <= -2.35e-52) {
		tmp = t_1;
	} else if (j <= -6.5e-257) {
		tmp = y * (x * z);
	} else if (j <= 3.8e-256) {
		tmp = t_1;
	} else if (j <= 4.1e-128) {
		tmp = b * (t * i);
	} else if (j <= 1.5e+27) {
		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 = (z * b) * -c
    t_2 = a * (c * j)
    if (j <= (-5.6d+63)) then
        tmp = t_2
    else if (j <= (-2.35d-52)) then
        tmp = t_1
    else if (j <= (-6.5d-257)) then
        tmp = y * (x * z)
    else if (j <= 3.8d-256) then
        tmp = t_1
    else if (j <= 4.1d-128) then
        tmp = b * (t * i)
    else if (j <= 1.5d+27) 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 = (z * b) * -c;
	double t_2 = a * (c * j);
	double tmp;
	if (j <= -5.6e+63) {
		tmp = t_2;
	} else if (j <= -2.35e-52) {
		tmp = t_1;
	} else if (j <= -6.5e-257) {
		tmp = y * (x * z);
	} else if (j <= 3.8e-256) {
		tmp = t_1;
	} else if (j <= 4.1e-128) {
		tmp = b * (t * i);
	} else if (j <= 1.5e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * b) * -c
	t_2 = a * (c * j)
	tmp = 0
	if j <= -5.6e+63:
		tmp = t_2
	elif j <= -2.35e-52:
		tmp = t_1
	elif j <= -6.5e-257:
		tmp = y * (x * z)
	elif j <= 3.8e-256:
		tmp = t_1
	elif j <= 4.1e-128:
		tmp = b * (t * i)
	elif j <= 1.5e+27:
		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(z * b) * Float64(-c))
	t_2 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (j <= -5.6e+63)
		tmp = t_2;
	elseif (j <= -2.35e-52)
		tmp = t_1;
	elseif (j <= -6.5e-257)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 3.8e-256)
		tmp = t_1;
	elseif (j <= 4.1e-128)
		tmp = Float64(b * Float64(t * i));
	elseif (j <= 1.5e+27)
		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 = (z * b) * -c;
	t_2 = a * (c * j);
	tmp = 0.0;
	if (j <= -5.6e+63)
		tmp = t_2;
	elseif (j <= -2.35e-52)
		tmp = t_1;
	elseif (j <= -6.5e-257)
		tmp = y * (x * z);
	elseif (j <= 3.8e-256)
		tmp = t_1;
	elseif (j <= 4.1e-128)
		tmp = b * (t * i);
	elseif (j <= 1.5e+27)
		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[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.6e+63], t$95$2, If[LessEqual[j, -2.35e-52], t$95$1, If[LessEqual[j, -6.5e-257], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.8e-256], t$95$1, If[LessEqual[j, 4.1e-128], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.5e+27], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -5.59999999999999974e63 or 1.49999999999999988e27 < j

   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 52.2%

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

      1. +-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

      4. *-commutative 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in j around inf 44.5%

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

   if -5.59999999999999974e63 < j < -2.3499999999999999e-52 or -6.5000000000000002e-257 < j < 3.79999999999999977e-256 or 4.1e-128 < j < 1.49999999999999988e27

   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 j around 0 71.8%

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

   4. Taylor expanded in c around inf 40.8%

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

      1. associate-*r* 40.8%

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

      2. neg-mul-1 40.8%

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

   6. Simplified 40.8%

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

   7. Taylor expanded in b around 0 40.8%

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

      1. neg-mul-1 40.8%

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

      2. distribute-lft-neg-in 40.8%

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

      3. *-commutative 40.8%

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

      4. associate-*l* 40.9%

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

   9. Simplified 40.9%

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

   if -2.3499999999999999e-52 < j < -6.5000000000000002e-257

   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 y around inf 45.6%

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

      1. +-commutative 45.6%

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

      2. mul-1-neg 45.6%

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

      3. unsub-neg 45.6%

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

      4. *-commutative 45.6%

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

      5. *-commutative 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in z around inf 41.0%

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

   if 3.79999999999999977e-256 < j < 4.1e-128

   1. Initial program 74.2%

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

   3. Taylor expanded in j around 0 74.3%

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

   4. Taylor expanded in i around inf 40.7%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.6 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -2.35 \cdot 10^{-52}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-257}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-256}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;j \leq 4.1 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+27}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 61.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -7.6 \cdot 10^{+26}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-301}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (* y z)) (* b (- (* t i) (* z c))))))
   (if (<= j -7.6e+26)
     (- (* b (* t i)) (* j (- (* y i) (* a c))))
     (if (<= j -6.6e-256)
       t_1
       (if (<= j -1.55e-301)
         (* t (- (* b i) (* x a)))
         (if (<= j 3.4e-27)
           t_1
           (- (* j (- (* a c) (* y i))) (* b (* z c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * (y * z)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -7.6e+26) {
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	} else if (j <= -6.6e-256) {
		tmp = t_1;
	} else if (j <= -1.55e-301) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 3.4e-27) {
		tmp = t_1;
	} else {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (y * z)) + (b * ((t * i) - (z * c)))
    if (j <= (-7.6d+26)) then
        tmp = (b * (t * i)) - (j * ((y * i) - (a * c)))
    else if (j <= (-6.6d-256)) then
        tmp = t_1
    else if (j <= (-1.55d-301)) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 3.4d-27) then
        tmp = t_1
    else
        tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * (y * z)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -7.6e+26) {
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	} else if (j <= -6.6e-256) {
		tmp = t_1;
	} else if (j <= -1.55e-301) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 3.4e-27) {
		tmp = t_1;
	} else {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * (y * z)) + (b * ((t * i) - (z * c)))
	tmp = 0
	if j <= -7.6e+26:
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)))
	elif j <= -6.6e-256:
		tmp = t_1
	elif j <= -1.55e-301:
		tmp = t * ((b * i) - (x * a))
	elif j <= 3.4e-27:
		tmp = t_1
	else:
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (j <= -7.6e+26)
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	elseif (j <= -6.6e-256)
		tmp = t_1;
	elseif (j <= -1.55e-301)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 3.4e-27)
		tmp = t_1;
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * (y * z)) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (j <= -7.6e+26)
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	elseif (j <= -6.6e-256)
		tmp = t_1;
	elseif (j <= -1.55e-301)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 3.4e-27)
		tmp = t_1;
	else
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.6e+26], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.6e-256], t$95$1, If[LessEqual[j, -1.55e-301], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.4e-27], t$95$1, N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -7.6000000000000004e26

   1. Initial program 76.1%

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

   3. Taylor expanded in i around inf 68.9%

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

   if -7.6000000000000004e26 < j < -6.6e-256 or -1.55000000000000007e-301 < j < 3.3999999999999997e-27

   1. Initial program 74.7%

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

   3. Taylor expanded in j around 0 77.1%

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

   4. Taylor expanded in y around inf 68.1%

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

      1. *-commutative 27.4%

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

   6. Simplified 68.1%

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

   if -6.6e-256 < j < -1.55000000000000007e-301

   1. Initial program 70.5%

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

   3. Taylor expanded in t around -inf 81.0%

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

   if 3.3999999999999997e-27 < j

   1. Initial program 72.7%

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

   3. Taylor expanded in c around inf 72.6%

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

      1. associate-*r* 72.6%

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

      2. neg-mul-1 72.6%

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

   5. Simplified 72.6%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.6 \cdot 10^{+26}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-301}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 60.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.65 \cdot 10^{+181}:\\ \;\;\;\;b \cdot \left(\left(\frac{c}{b} \cdot \frac{a}{y} - \frac{i}{b}\right) \cdot \left(y \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.32 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot \frac{z}{a} - t\right)\right)\\ \mathbf{elif}\;j \leq -5.1 \cdot 10^{+26}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.65e+181)
   (* b (* (- (* (/ c b) (/ a y)) (/ i b)) (* y j)))
   (if (<= j -1.32e+174)
     (* x (* a (- (* y (/ z a)) t)))
     (if (<= j -5.1e+26)
       (- (* b (* t i)) (* j (- (* y i) (* a c))))
       (if (<= j 2.4e-27)
         (+ (* x (* y z)) (* b (- (* t i) (* z c))))
         (- (* j (- (* a c) (* y i))) (* b (* z c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.65e+181) {
		tmp = b * ((((c / b) * (a / y)) - (i / b)) * (y * j));
	} else if (j <= -1.32e+174) {
		tmp = x * (a * ((y * (z / a)) - t));
	} else if (j <= -5.1e+26) {
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	} else if (j <= 2.4e-27) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-1.65d+181)) then
        tmp = b * ((((c / b) * (a / y)) - (i / b)) * (y * j))
    else if (j <= (-1.32d+174)) then
        tmp = x * (a * ((y * (z / a)) - t))
    else if (j <= (-5.1d+26)) then
        tmp = (b * (t * i)) - (j * ((y * i) - (a * c)))
    else if (j <= 2.4d-27) then
        tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
    else
        tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.65e+181) {
		tmp = b * ((((c / b) * (a / y)) - (i / b)) * (y * j));
	} else if (j <= -1.32e+174) {
		tmp = x * (a * ((y * (z / a)) - t));
	} else if (j <= -5.1e+26) {
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	} else if (j <= 2.4e-27) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.65e+181:
		tmp = b * ((((c / b) * (a / y)) - (i / b)) * (y * j))
	elif j <= -1.32e+174:
		tmp = x * (a * ((y * (z / a)) - t))
	elif j <= -5.1e+26:
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)))
	elif j <= 2.4e-27:
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
	else:
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.65e+181)
		tmp = Float64(b * Float64(Float64(Float64(Float64(c / b) * Float64(a / y)) - Float64(i / b)) * Float64(y * j)));
	elseif (j <= -1.32e+174)
		tmp = Float64(x * Float64(a * Float64(Float64(y * Float64(z / a)) - t)));
	elseif (j <= -5.1e+26)
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	elseif (j <= 2.4e-27)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.65e+181)
		tmp = b * ((((c / b) * (a / y)) - (i / b)) * (y * j));
	elseif (j <= -1.32e+174)
		tmp = x * (a * ((y * (z / a)) - t));
	elseif (j <= -5.1e+26)
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	elseif (j <= 2.4e-27)
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	else
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.65e+181], N[(b * N[(N[(N[(N[(c / b), $MachinePrecision] * N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(i / b), $MachinePrecision]), $MachinePrecision] * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.32e+174], N[(x * N[(a * N[(N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.1e+26], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.4e-27], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.65000000000000008e181

   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 b around inf 75.7%

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

   4. Taylor expanded in y around inf 48.5%

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

      1. +-commutative 48.5%

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

      2. mul-1-neg 48.5%

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

      3. unsub-neg 48.5%

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

      4. associate-*r* 55.2%

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

      5. times-frac 55.0%

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

      6. associate-/l* 55.0%

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

      7. associate-/l* 51.9%

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

   6. Simplified 51.9%

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

   7. Taylor expanded in j around inf 87.0%

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

      1. associate-*r* 87.1%

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

      2. *-commutative 87.1%

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

      3. times-frac 87.1%

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

   9. Simplified 87.1%

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

   if -1.65000000000000008e181 < j < -1.31999999999999999e174

   1. Initial program 60.0%

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

   3. Taylor expanded in x around inf 81.0%

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

   4. Taylor expanded in a around inf 100.0%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if -1.31999999999999999e174 < j < -5.0999999999999997e26

   1. Initial program 82.7%

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

   3. Taylor expanded in i around inf 66.0%

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

   if -5.0999999999999997e26 < j < 2.40000000000000002e-27

   1. Initial program 74.4%

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

   3. Taylor expanded in j around 0 75.9%

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

   4. Taylor expanded in y around inf 64.4%

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

      1. *-commutative 25.4%

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

   6. Simplified 64.4%

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

   if 2.40000000000000002e-27 < j

   1. Initial program 72.7%

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

   3. Taylor expanded in c around inf 72.6%

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

      1. associate-*r* 72.6%

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

      2. neg-mul-1 72.6%

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

   5. Simplified 72.6%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.65 \cdot 10^{+181}:\\ \;\;\;\;b \cdot \left(\left(\frac{c}{b} \cdot \frac{a}{y} - \frac{i}{b}\right) \cdot \left(y \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -1.32 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \left(a \cdot \left(y \cdot \frac{z}{a} - t\right)\right)\\ \mathbf{elif}\;j \leq -5.1 \cdot 10^{+26}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 60.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -1.15 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(t \cdot i + \frac{t\_1}{b}\right)\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-256}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-307}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-27}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ (* x (* y z)) (* b (- (* t i) (* z c))))))
   (if (<= j -1.15e+27)
     (* b (+ (* t i) (/ t_1 b)))
     (if (<= j -8.6e-256)
       t_2
       (if (<= j 1.2e-307)
         (* t (- (* b i) (* x a)))
         (if (<= j 3.2e-27) t_2 (- t_1 (* b (* z c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = (x * (y * z)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -1.15e+27) {
		tmp = b * ((t * i) + (t_1 / b));
	} else if (j <= -8.6e-256) {
		tmp = t_2;
	} else if (j <= 1.2e-307) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 3.2e-27) {
		tmp = t_2;
	} else {
		tmp = t_1 - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = (x * (y * z)) + (b * ((t * i) - (z * c)))
    if (j <= (-1.15d+27)) then
        tmp = b * ((t * i) + (t_1 / b))
    else if (j <= (-8.6d-256)) then
        tmp = t_2
    else if (j <= 1.2d-307) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 3.2d-27) then
        tmp = t_2
    else
        tmp = t_1 - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = (x * (y * z)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -1.15e+27) {
		tmp = b * ((t * i) + (t_1 / b));
	} else if (j <= -8.6e-256) {
		tmp = t_2;
	} else if (j <= 1.2e-307) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 3.2e-27) {
		tmp = t_2;
	} else {
		tmp = t_1 - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = (x * (y * z)) + (b * ((t * i) - (z * c)))
	tmp = 0
	if j <= -1.15e+27:
		tmp = b * ((t * i) + (t_1 / b))
	elif j <= -8.6e-256:
		tmp = t_2
	elif j <= 1.2e-307:
		tmp = t * ((b * i) - (x * a))
	elif j <= 3.2e-27:
		tmp = t_2
	else:
		tmp = t_1 - (b * (z * c))
	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(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (j <= -1.15e+27)
		tmp = Float64(b * Float64(Float64(t * i) + Float64(t_1 / b)));
	elseif (j <= -8.6e-256)
		tmp = t_2;
	elseif (j <= 1.2e-307)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 3.2e-27)
		tmp = t_2;
	else
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = (x * (y * z)) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (j <= -1.15e+27)
		tmp = b * ((t * i) + (t_1 / b));
	elseif (j <= -8.6e-256)
		tmp = t_2;
	elseif (j <= 1.2e-307)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 3.2e-27)
		tmp = t_2;
	else
		tmp = t_1 - (b * (z * c));
	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[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.15e+27], N[(b * N[(N[(t * i), $MachinePrecision] + N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.6e-256], t$95$2, If[LessEqual[j, 1.2e-307], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e-27], t$95$2, N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.15e27

   1. Initial program 76.1%

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

   3. Taylor expanded in i around inf 68.9%

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

   4. Taylor expanded in b around inf 73.5%

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

   if -1.15e27 < j < -8.6000000000000002e-256 or 1.20000000000000009e-307 < j < 3.19999999999999991e-27

   1. Initial program 74.7%

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

   3. Taylor expanded in j around 0 77.1%

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

   4. Taylor expanded in y around inf 68.1%

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

      1. *-commutative 27.4%

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

   6. Simplified 68.1%

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

   if -8.6000000000000002e-256 < j < 1.20000000000000009e-307

   1. Initial program 70.5%

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

   3. Taylor expanded in t around -inf 81.0%

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

   if 3.19999999999999991e-27 < j

   1. Initial program 72.7%

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

   3. Taylor expanded in c around inf 72.6%

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

      1. associate-*r* 72.6%

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

      2. neg-mul-1 72.6%

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

   5. Simplified 72.6%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.15 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(t \cdot i + \frac{j \cdot \left(a \cdot c - y \cdot i\right)}{b}\right)\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-307}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 42.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -4 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-209}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-71}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -4e-73)
     t_1
     (if (<= a -7.6e-209)
       (* (* z b) (- c))
       (if (<= a -4.6e-273)
         (* y (* i (- j)))
         (if (<= a 3.5e-71) (* z (* b (- c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4e-73) {
		tmp = t_1;
	} else if (a <= -7.6e-209) {
		tmp = (z * b) * -c;
	} else if (a <= -4.6e-273) {
		tmp = y * (i * -j);
	} else if (a <= 3.5e-71) {
		tmp = z * (b * -c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-4d-73)) then
        tmp = t_1
    else if (a <= (-7.6d-209)) then
        tmp = (z * b) * -c
    else if (a <= (-4.6d-273)) then
        tmp = y * (i * -j)
    else if (a <= 3.5d-71) then
        tmp = z * (b * -c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4e-73) {
		tmp = t_1;
	} else if (a <= -7.6e-209) {
		tmp = (z * b) * -c;
	} else if (a <= -4.6e-273) {
		tmp = y * (i * -j);
	} else if (a <= 3.5e-71) {
		tmp = z * (b * -c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -4e-73:
		tmp = t_1
	elif a <= -7.6e-209:
		tmp = (z * b) * -c
	elif a <= -4.6e-273:
		tmp = y * (i * -j)
	elif a <= 3.5e-71:
		tmp = z * (b * -c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4e-73)
		tmp = t_1;
	elseif (a <= -7.6e-209)
		tmp = Float64(Float64(z * b) * Float64(-c));
	elseif (a <= -4.6e-273)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (a <= 3.5e-71)
		tmp = Float64(z * Float64(b * Float64(-c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -4e-73)
		tmp = t_1;
	elseif (a <= -7.6e-209)
		tmp = (z * b) * -c;
	elseif (a <= -4.6e-273)
		tmp = y * (i * -j);
	elseif (a <= 3.5e-71)
		tmp = z * (b * -c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e-73], t$95$1, If[LessEqual[a, -7.6e-209], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision], If[LessEqual[a, -4.6e-273], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-71], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.99999999999999999e-73 or 3.4999999999999999e-71 < a

   1. Initial program 70.6%

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

   3. Taylor expanded in a around inf 59.9%

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

      1. +-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

      4. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   if -3.99999999999999999e-73 < a < -7.5999999999999998e-209

   1. Initial program 92.9%

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

   3. Taylor expanded in j around 0 86.5%

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

   4. Taylor expanded in c around inf 45.0%

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

      1. associate-*r* 45.0%

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

      2. neg-mul-1 45.0%

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

   6. Simplified 45.0%

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

   7. Taylor expanded in b around 0 45.0%

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

      1. neg-mul-1 45.0%

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

      2. distribute-lft-neg-in 45.0%

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

      3. *-commutative 45.0%

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

      4. associate-*l* 48.3%

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

   9. Simplified 48.3%

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

   if -7.5999999999999998e-209 < a < -4.59999999999999961e-273

   1. Initial program 72.6%

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

   3. Taylor expanded in y around inf 82.4%

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

      1. +-commutative 82.4%

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

      2. mul-1-neg 82.4%

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

      3. unsub-neg 82.4%

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

      4. *-commutative 82.4%

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

      5. *-commutative 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in z around 0 64.7%

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

      1. neg-mul-1 64.7%

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

      2. *-commutative 64.7%

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

      3. distribute-rgt-neg-in 64.7%

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

   8. Simplified 64.7%

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

   if -4.59999999999999961e-273 < a < 3.4999999999999999e-71

   1. Initial program 76.7%

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

   3. Taylor expanded in z around inf 59.1%

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

      1. *-commutative 59.1%

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

      2. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in y around 0 40.9%

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

      1. mul-1-neg 40.9%

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

      2. *-commutative 40.9%

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

      3. distribute-rgt-neg-in 40.9%

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

   8. Simplified 40.9%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-73}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-209}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-71}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -5.8e-10)
     t_2
     (if (<= a -7.2e-209)
       t_1
       (if (<= a -6.2e-273) (* y (* i (- j))) (if (<= a 7.2e+44) 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 <= -5.8e-10) {
		tmp = t_2;
	} else if (a <= -7.2e-209) {
		tmp = t_1;
	} else if (a <= -6.2e-273) {
		tmp = y * (i * -j);
	} else if (a <= 7.2e+44) {
		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 <= (-5.8d-10)) then
        tmp = t_2
    else if (a <= (-7.2d-209)) then
        tmp = t_1
    else if (a <= (-6.2d-273)) then
        tmp = y * (i * -j)
    else if (a <= 7.2d+44) 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 <= -5.8e-10) {
		tmp = t_2;
	} else if (a <= -7.2e-209) {
		tmp = t_1;
	} else if (a <= -6.2e-273) {
		tmp = y * (i * -j);
	} else if (a <= 7.2e+44) {
		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 <= -5.8e-10:
		tmp = t_2
	elif a <= -7.2e-209:
		tmp = t_1
	elif a <= -6.2e-273:
		tmp = y * (i * -j)
	elif a <= 7.2e+44:
		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 <= -5.8e-10)
		tmp = t_2;
	elseif (a <= -7.2e-209)
		tmp = t_1;
	elseif (a <= -6.2e-273)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (a <= 7.2e+44)
		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 <= -5.8e-10)
		tmp = t_2;
	elseif (a <= -7.2e-209)
		tmp = t_1;
	elseif (a <= -6.2e-273)
		tmp = y * (i * -j);
	elseif (a <= 7.2e+44)
		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, -5.8e-10], t$95$2, If[LessEqual[a, -7.2e-209], t$95$1, If[LessEqual[a, -6.2e-273], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e+44], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.79999999999999962e-10 or 7.2e44 < a

   1. Initial program 66.8%

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

   3. Taylor expanded in a around inf 66.0%

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

      1. +-commutative 66.0%

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

      2. mul-1-neg 66.0%

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

      3. unsub-neg 66.0%

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

      4. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   if -5.79999999999999962e-10 < a < -7.20000000000000032e-209 or -6.19999999999999976e-273 < a < 7.2e44

   1. Initial program 83.8%

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

   3. Taylor expanded in b around inf 52.5%

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

   if -7.20000000000000032e-209 < a < -6.19999999999999976e-273

   1. Initial program 72.6%

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

   3. Taylor expanded in y around inf 82.4%

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

      1. +-commutative 82.4%

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

      2. mul-1-neg 82.4%

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

      3. unsub-neg 82.4%

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

      4. *-commutative 82.4%

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

      5. *-commutative 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in z around 0 64.7%

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

      1. neg-mul-1 64.7%

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

      2. *-commutative 64.7%

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

      3. distribute-rgt-neg-in 64.7%

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

   8. Simplified 64.7%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-10}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-209}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+105}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+149}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(i \cdot \left(t - \frac{z \cdot c}{i}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -8.5e+105)
   (* b (- (* t i) (* z c)))
   (if (<= b 2.7e+149)
     (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
     (+ (* x (* y z)) (* b (* i (- t (/ (* z c) i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -8.5e+105) {
		tmp = b * ((t * i) - (z * c));
	} else if (b <= 2.7e+149) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (x * (y * z)) + (b * (i * (t - ((z * c) / i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-8.5d+105)) then
        tmp = b * ((t * i) - (z * c))
    else if (b <= 2.7d+149) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = (x * (y * z)) + (b * (i * (t - ((z * c) / i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -8.5e+105) {
		tmp = b * ((t * i) - (z * c));
	} else if (b <= 2.7e+149) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (x * (y * z)) + (b * (i * (t - ((z * c) / i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -8.5e+105:
		tmp = b * ((t * i) - (z * c))
	elif b <= 2.7e+149:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = (x * (y * z)) + (b * (i * (t - ((z * c) / i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -8.5e+105)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (b <= 2.7e+149)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(i * Float64(t - Float64(Float64(z * c) / i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -8.5e+105)
		tmp = b * ((t * i) - (z * c));
	elseif (b <= 2.7e+149)
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = (x * (y * z)) + (b * (i * (t - ((z * c) / i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -8.5e+105], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e+149], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(i * N[(t - N[(N[(z * c), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.49999999999999986e105

   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 b around inf 71.9%

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

   if -8.49999999999999986e105 < b < 2.7000000000000001e149

   1. Initial program 76.4%

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

   3. Taylor expanded in b around 0 70.2%

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

   if 2.7000000000000001e149 < b

   1. Initial program 79.3%

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

   3. Taylor expanded in j around 0 73.8%

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

   4. Taylor expanded in y around inf 74.0%

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

      1. *-commutative 22.3%

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

   6. Simplified 74.0%

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

   7. Taylor expanded in i around inf 74.0%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+105}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+149}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(i \cdot \left(t - \frac{z \cdot c}{i}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 52.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 205000000:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -1.45e+65)
     t_1
     (if (<= t 205000000.0)
       (* c (- (* a j) (* z b)))
       (if (<= t 2e+112) (* z (- (* x y) (* b c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.45e+65) {
		tmp = t_1;
	} else if (t <= 205000000.0) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 2e+112) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (t <= (-1.45d+65)) then
        tmp = t_1
    else if (t <= 205000000.0d0) then
        tmp = c * ((a * j) - (z * b))
    else if (t <= 2d+112) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.45e+65) {
		tmp = t_1;
	} else if (t <= 205000000.0) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 2e+112) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.45e+65:
		tmp = t_1
	elif t <= 205000000.0:
		tmp = c * ((a * j) - (z * b))
	elif t <= 2e+112:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.45e+65)
		tmp = t_1;
	elseif (t <= 205000000.0)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (t <= 2e+112)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.45e+65)
		tmp = t_1;
	elseif (t <= 205000000.0)
		tmp = c * ((a * j) - (z * b));
	elseif (t <= 2e+112)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e+65], t$95$1, If[LessEqual[t, 205000000.0], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+112], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.45e65 or 1.9999999999999999e112 < t

   1. Initial program 67.2%

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

   3. Taylor expanded in t around -inf 68.6%

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

   if -1.45e65 < t < 2.05e8

   1. Initial program 80.2%

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

   3. Taylor expanded in c around inf 57.7%

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

      1. *-commutative 57.7%

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

   5. Simplified 57.7%

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

   if 2.05e8 < t < 1.9999999999999999e112

   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 z around inf 57.5%

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

      1. *-commutative 57.5%

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

      2. *-commutative 57.5%

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

   5. Simplified 57.5%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 205000000:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -1.75 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-258}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= j -1.75e-34)
     t_1
     (if (<= j -2.9e-258)
       (* x (* y z))
       (if (<= j 1.4e-25) (* b (* t i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (j <= -1.75e-34) {
		tmp = t_1;
	} else if (j <= -2.9e-258) {
		tmp = x * (y * z);
	} else if (j <= 1.4e-25) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (j <= (-1.75d-34)) then
        tmp = t_1
    else if (j <= (-2.9d-258)) then
        tmp = x * (y * z)
    else if (j <= 1.4d-25) then
        tmp = b * (t * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (j <= -1.75e-34) {
		tmp = t_1;
	} else if (j <= -2.9e-258) {
		tmp = x * (y * z);
	} else if (j <= 1.4e-25) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if j <= -1.75e-34:
		tmp = t_1
	elif j <= -2.9e-258:
		tmp = x * (y * z)
	elif j <= 1.4e-25:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (j <= -1.75e-34)
		tmp = t_1;
	elseif (j <= -2.9e-258)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 1.4e-25)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (j <= -1.75e-34)
		tmp = t_1;
	elseif (j <= -2.9e-258)
		tmp = x * (y * z);
	elseif (j <= 1.4e-25)
		tmp = b * (t * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.75e-34], t$95$1, If[LessEqual[j, -2.9e-258], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.4e-25], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.75e-34 or 1.39999999999999994e-25 < j

   1. Initial program 74.5%

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

   3. Taylor expanded in 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 40.9%

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

   if -1.75e-34 < j < -2.9e-258

   1. Initial program 76.1%

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

   3. Taylor expanded in x around inf 56.7%

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

   4. Taylor expanded in y around inf 37.3%

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

      1. *-commutative 37.3%

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

   6. Simplified 37.3%

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

   if -2.9e-258 < j < 1.39999999999999994e-25

   1. Initial program 73.1%

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

   3. Taylor expanded in j around 0 75.5%

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

   4. Taylor expanded in i around inf 30.2%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.75 \cdot 10^{-34}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-258}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -1.85 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-258}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-21}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= j -1.85e-50)
     t_1
     (if (<= j -5.8e-258)
       (* y (* x z))
       (if (<= j 3.3e-21) (* b (* t i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (j <= -1.85e-50) {
		tmp = t_1;
	} else if (j <= -5.8e-258) {
		tmp = y * (x * z);
	} else if (j <= 3.3e-21) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (j <= (-1.85d-50)) then
        tmp = t_1
    else if (j <= (-5.8d-258)) then
        tmp = y * (x * z)
    else if (j <= 3.3d-21) then
        tmp = b * (t * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (j <= -1.85e-50) {
		tmp = t_1;
	} else if (j <= -5.8e-258) {
		tmp = y * (x * z);
	} else if (j <= 3.3e-21) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if j <= -1.85e-50:
		tmp = t_1
	elif j <= -5.8e-258:
		tmp = y * (x * z)
	elif j <= 3.3e-21:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (j <= -1.85e-50)
		tmp = t_1;
	elseif (j <= -5.8e-258)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 3.3e-21)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (j <= -1.85e-50)
		tmp = t_1;
	elseif (j <= -5.8e-258)
		tmp = y * (x * z);
	elseif (j <= 3.3e-21)
		tmp = b * (t * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.85e-50], t$95$1, If[LessEqual[j, -5.8e-258], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.3e-21], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.85e-50 or 3.30000000000000009e-21 < j

   1. Initial program 74.1%

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

   3. Taylor expanded in 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 40.3%

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

   if -1.85e-50 < j < -5.7999999999999999e-258

   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 y around inf 45.6%

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

      1. +-commutative 45.6%

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

      2. mul-1-neg 45.6%

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

      3. unsub-neg 45.6%

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

      4. *-commutative 45.6%

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

      5. *-commutative 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in z around inf 41.0%

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

   if -5.7999999999999999e-258 < j < 3.30000000000000009e-21

   1. Initial program 73.1%

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

   3. Taylor expanded in j around 0 75.5%

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

   4. Taylor expanded in i around inf 30.2%

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

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.85 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-258}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.3 \cdot 10^{-21}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -9.2 \cdot 10^{+45} \lor \neg \left(j \leq 2.25 \cdot 10^{-21}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -9.2e+45) (not (<= j 2.25e-21))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -9.2e+45) || !(j <= 2.25e-21)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-9.2d+45)) .or. (.not. (j <= 2.25d-21))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -9.2e+45) || !(j <= 2.25e-21)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -9.2e+45) or not (j <= 2.25e-21):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -9.2e+45) || !(j <= 2.25e-21))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -9.2e+45) || ~((j <= 2.25e-21)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -9.2e+45], N[Not[LessEqual[j, 2.25e-21]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -9.20000000000000049e45 or 2.24999999999999984e-21 < j

   1. Initial program 73.9%

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

   3. Taylor expanded in a around inf 51.5%

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

      1. +-commutative 51.5%

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

      2. mul-1-neg 51.5%

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

      3. unsub-neg 51.5%

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

      4. *-commutative 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in j around inf 44.2%

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

   if -9.20000000000000049e45 < j < 2.24999999999999984e-21

   1. Initial program 74.8%

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

   3. Taylor expanded in j around 0 74.0%

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

   4. Taylor expanded in i around inf 26.0%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.2 \cdot 10^{+45} \lor \neg \left(j \leq 2.25 \cdot 10^{-21}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.3% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.4%

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

3. Taylor expanded in a around inf 42.0%

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

   1. +-commutative 42.0%

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

   2. mul-1-neg 42.0%

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

   3. unsub-neg 42.0%

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

   4. *-commutative 42.0%

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

5. Simplified 42.0%

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

6. Taylor expanded in j around inf 25.8%

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

7. Final simplification 25.8%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
8. Add Preprocessing

Developer target: 60.4% 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 2024079 
(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)))))