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

Percentage Accurate: 73.6% → 83.0%

Time: 20.6s

Alternatives: 17

Speedup: 0.5×

• 57.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.2%

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

   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. Step-by-step derivation

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. sub-neg 0.0%

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

      4. sub-neg 0.0%

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

      5. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in t around -inf 14.8%

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

   5. Taylor expanded in i around inf 56.4%

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

      1. +-commutative 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

   7. Simplified 56.4%

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

4. Final simplification 87.9%

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

Alternative 2: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+233}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3 \cdot 10^{+28}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-105}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* i (- (* t b) (* y j))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -2.8e+233)
     t_3
     (if (<= b -4.8e+48)
       t_2
       (if (<= b -3e+28)
         t_3
         (if (<= b -1.8e-90)
           t_1
           (if (<= b 5.5e-105)
             (* a (- (* c j) (* x t)))
             (if (<= b 1.02e-84)
               t_3
               (if (<= b 1.9e-33)
                 t_1
                 (if (<= b 1.4e+26) t_2 (if (<= b 1.05e+119) t_1 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.8e+233) {
		tmp = t_3;
	} else if (b <= -4.8e+48) {
		tmp = t_2;
	} else if (b <= -3e+28) {
		tmp = t_3;
	} else if (b <= -1.8e-90) {
		tmp = t_1;
	} else if (b <= 5.5e-105) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 1.02e-84) {
		tmp = t_3;
	} else if (b <= 1.9e-33) {
		tmp = t_1;
	} else if (b <= 1.4e+26) {
		tmp = t_2;
	} else if (b <= 1.05e+119) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = i * ((t * b) - (y * j))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-2.8d+233)) then
        tmp = t_3
    else if (b <= (-4.8d+48)) then
        tmp = t_2
    else if (b <= (-3d+28)) then
        tmp = t_3
    else if (b <= (-1.8d-90)) then
        tmp = t_1
    else if (b <= 5.5d-105) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 1.02d-84) then
        tmp = t_3
    else if (b <= 1.9d-33) then
        tmp = t_1
    else if (b <= 1.4d+26) then
        tmp = t_2
    else if (b <= 1.05d+119) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((t * b) - (y * j));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.8e+233) {
		tmp = t_3;
	} else if (b <= -4.8e+48) {
		tmp = t_2;
	} else if (b <= -3e+28) {
		tmp = t_3;
	} else if (b <= -1.8e-90) {
		tmp = t_1;
	} else if (b <= 5.5e-105) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 1.02e-84) {
		tmp = t_3;
	} else if (b <= 1.9e-33) {
		tmp = t_1;
	} else if (b <= 1.4e+26) {
		tmp = t_2;
	} else if (b <= 1.05e+119) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = i * ((t * b) - (y * j))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -2.8e+233:
		tmp = t_3
	elif b <= -4.8e+48:
		tmp = t_2
	elif b <= -3e+28:
		tmp = t_3
	elif b <= -1.8e-90:
		tmp = t_1
	elif b <= 5.5e-105:
		tmp = a * ((c * j) - (x * t))
	elif b <= 1.02e-84:
		tmp = t_3
	elif b <= 1.9e-33:
		tmp = t_1
	elif b <= 1.4e+26:
		tmp = t_2
	elif b <= 1.05e+119:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.8e+233)
		tmp = t_3;
	elseif (b <= -4.8e+48)
		tmp = t_2;
	elseif (b <= -3e+28)
		tmp = t_3;
	elseif (b <= -1.8e-90)
		tmp = t_1;
	elseif (b <= 5.5e-105)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 1.02e-84)
		tmp = t_3;
	elseif (b <= 1.9e-33)
		tmp = t_1;
	elseif (b <= 1.4e+26)
		tmp = t_2;
	elseif (b <= 1.05e+119)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = i * ((t * b) - (y * j));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.8e+233)
		tmp = t_3;
	elseif (b <= -4.8e+48)
		tmp = t_2;
	elseif (b <= -3e+28)
		tmp = t_3;
	elseif (b <= -1.8e-90)
		tmp = t_1;
	elseif (b <= 5.5e-105)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 1.02e-84)
		tmp = t_3;
	elseif (b <= 1.9e-33)
		tmp = t_1;
	elseif (b <= 1.4e+26)
		tmp = t_2;
	elseif (b <= 1.05e+119)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.8e+233], t$95$3, If[LessEqual[b, -4.8e+48], t$95$2, If[LessEqual[b, -3e+28], t$95$3, If[LessEqual[b, -1.8e-90], t$95$1, If[LessEqual[b, 5.5e-105], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.02e-84], t$95$3, If[LessEqual[b, 1.9e-33], t$95$1, If[LessEqual[b, 1.4e+26], t$95$2, If[LessEqual[b, 1.05e+119], t$95$1, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.8000000000000001e233 or -4.8000000000000002e48 < b < -3.0000000000000001e28 or 5.50000000000000029e-105 < b < 1.02000000000000004e-84 or 1.04999999999999991e119 < b

   1. Initial program 78.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 78.0%

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

      2. *-commutative 78.0%

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

      3. sub-neg 78.0%

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

      4. sub-neg 78.0%

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

      5. *-commutative 78.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in b around inf 89.9%

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

   if -2.8000000000000001e233 < b < -4.8000000000000002e48 or 1.89999999999999997e-33 < b < 1.4e26

   1. Initial program 71.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 71.3%

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

      2. *-commutative 71.3%

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

      3. sub-neg 71.3%

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

      4. sub-neg 71.3%

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

      5. *-commutative 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in a around -inf 65.3%

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

   6. Simplified 67.4%

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

   7. Taylor expanded in i around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. unsub-neg 62.1%

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

      4. *-commutative 62.1%

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

      5. *-commutative 62.1%

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

   9. Simplified 62.1%

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

   if -3.0000000000000001e28 < b < -1.7999999999999999e-90 or 1.02000000000000004e-84 < b < 1.89999999999999997e-33 or 1.4e26 < b < 1.04999999999999991e119

   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. Step-by-step derivation

      1. associate-+l- 76.9%

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

      2. *-commutative 76.9%

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

      3. sub-neg 76.9%

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

      4. sub-neg 76.9%

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

      5. *-commutative 76.9%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in x around inf 64.7%

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

   if -1.7999999999999999e-90 < b < 5.50000000000000029e-105

   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. Step-by-step derivation

      1. associate-+l- 80.2%

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

      2. *-commutative 80.2%

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

      3. sub-neg 80.2%

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

      4. sub-neg 80.2%

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

      5. *-commutative 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in a around inf 56.6%

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

      1. +-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

      4. *-commutative 56.6%

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

   6. Simplified 56.6%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+233}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{+48}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-105}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-84}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+26}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 3: 66.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+159}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* i (- (* t b) (* y j))) (* b (* z c))))
        (t_2 (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))))
   (if (<= b -1.1e-41)
     t_1
     (if (<= b 5.4e-105)
       t_2
       (if (<= b 4.8e-84)
         t_1
         (if (<= b 2e+159) t_2 (* b (- (* t i) (* z c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * ((t * b) - (y * j))) - (b * (z * c));
	double t_2 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double tmp;
	if (b <= -1.1e-41) {
		tmp = t_1;
	} else if (b <= 5.4e-105) {
		tmp = t_2;
	} else if (b <= 4.8e-84) {
		tmp = t_1;
	} else if (b <= 2e+159) {
		tmp = t_2;
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (i * ((t * b) - (y * j))) - (b * (z * c))
    t_2 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    if (b <= (-1.1d-41)) then
        tmp = t_1
    else if (b <= 5.4d-105) then
        tmp = t_2
    else if (b <= 4.8d-84) then
        tmp = t_1
    else if (b <= 2d+159) then
        tmp = t_2
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * ((t * b) - (y * j))) - (b * (z * c));
	double t_2 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double tmp;
	if (b <= -1.1e-41) {
		tmp = t_1;
	} else if (b <= 5.4e-105) {
		tmp = t_2;
	} else if (b <= 4.8e-84) {
		tmp = t_1;
	} else if (b <= 2e+159) {
		tmp = t_2;
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * ((t * b) - (y * j))) - (b * (z * c))
	t_2 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	tmp = 0
	if b <= -1.1e-41:
		tmp = t_1
	elif b <= 5.4e-105:
		tmp = t_2
	elif b <= 4.8e-84:
		tmp = t_1
	elif b <= 2e+159:
		tmp = t_2
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * Float64(Float64(t * b) - Float64(y * j))) - Float64(b * Float64(z * c)))
	t_2 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	tmp = 0.0
	if (b <= -1.1e-41)
		tmp = t_1;
	elseif (b <= 5.4e-105)
		tmp = t_2;
	elseif (b <= 4.8e-84)
		tmp = t_1;
	elseif (b <= 2e+159)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (i * ((t * b) - (y * j))) - (b * (z * c));
	t_2 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	tmp = 0.0;
	if (b <= -1.1e-41)
		tmp = t_1;
	elseif (b <= 5.4e-105)
		tmp = t_2;
	elseif (b <= 4.8e-84)
		tmp = t_1;
	elseif (b <= 2e+159)
		tmp = t_2;
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, If[LessEqual[b, -1.1e-41], t$95$1, If[LessEqual[b, 5.4e-105], t$95$2, If[LessEqual[b, 4.8e-84], t$95$1, If[LessEqual[b, 2e+159], t$95$2, N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1e-41 or 5.39999999999999985e-105 < b < 4.80000000000000035e-84

   1. Initial program 71.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 71.7%

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

      2. *-commutative 71.7%

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

      3. sub-neg 71.7%

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

      4. sub-neg 71.7%

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

      5. *-commutative 71.7%

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

   3. Simplified 71.7%

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

   4. Taylor expanded in t around -inf 64.0%

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

   5. Taylor expanded in i around inf 76.1%

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

      1. +-commutative 76.1%

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

      2. mul-1-neg 76.1%

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

      3. unsub-neg 76.1%

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

   7. Simplified 76.1%

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

   if -1.1e-41 < b < 5.39999999999999985e-105 or 4.80000000000000035e-84 < b < 1.9999999999999999e159

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 79.4%

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

      2. *-commutative 79.4%

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

      3. sub-neg 79.4%

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

      4. sub-neg 79.4%

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

      5. *-commutative 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in b around 0 76.0%

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

   if 1.9999999999999999e159 < b

   1. Initial program 81.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 81.0%

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

      2. *-commutative 81.0%

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

      3. sub-neg 81.0%

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

      4. sub-neg 81.0%

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

      5. *-commutative 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in b around inf 94.5%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-41}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-105}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-84}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+159}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 4: 50.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -7.5 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-285}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-123}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{+70} \lor \neg \left(c \leq 4.3 \cdot 10^{+136}\right) \land c \leq 3.8 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -7.5e-57)
     t_2
     (if (<= c -1.3e-244)
       t_1
       (if (<= c 3.5e-285)
         (* i (- (* t b) (* y j)))
         (if (<= c 2.4e-123)
           (* y (- (* x z) (* i j)))
           (if (or (<= c 4.4e+70) (and (not (<= c 4.3e+136)) (<= c 3.8e+186)))
             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 = t * ((b * i) - (x * a));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -7.5e-57) {
		tmp = t_2;
	} else if (c <= -1.3e-244) {
		tmp = t_1;
	} else if (c <= 3.5e-285) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 2.4e-123) {
		tmp = y * ((x * z) - (i * j));
	} else if ((c <= 4.4e+70) || (!(c <= 4.3e+136) && (c <= 3.8e+186))) {
		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 = t * ((b * i) - (x * a))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-7.5d-57)) then
        tmp = t_2
    else if (c <= (-1.3d-244)) then
        tmp = t_1
    else if (c <= 3.5d-285) then
        tmp = i * ((t * b) - (y * j))
    else if (c <= 2.4d-123) then
        tmp = y * ((x * z) - (i * j))
    else if ((c <= 4.4d+70) .or. (.not. (c <= 4.3d+136)) .and. (c <= 3.8d+186)) 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 = t * ((b * i) - (x * a));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -7.5e-57) {
		tmp = t_2;
	} else if (c <= -1.3e-244) {
		tmp = t_1;
	} else if (c <= 3.5e-285) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 2.4e-123) {
		tmp = y * ((x * z) - (i * j));
	} else if ((c <= 4.4e+70) || (!(c <= 4.3e+136) && (c <= 3.8e+186))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -7.5e-57:
		tmp = t_2
	elif c <= -1.3e-244:
		tmp = t_1
	elif c <= 3.5e-285:
		tmp = i * ((t * b) - (y * j))
	elif c <= 2.4e-123:
		tmp = y * ((x * z) - (i * j))
	elif (c <= 4.4e+70) or (not (c <= 4.3e+136) and (c <= 3.8e+186)):
		tmp = t_1
	else:
		tmp = t_2
	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)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -7.5e-57)
		tmp = t_2;
	elseif (c <= -1.3e-244)
		tmp = t_1;
	elseif (c <= 3.5e-285)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (c <= 2.4e-123)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif ((c <= 4.4e+70) || (!(c <= 4.3e+136) && (c <= 3.8e+186)))
		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 = t * ((b * i) - (x * a));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -7.5e-57)
		tmp = t_2;
	elseif (c <= -1.3e-244)
		tmp = t_1;
	elseif (c <= 3.5e-285)
		tmp = i * ((t * b) - (y * j));
	elseif (c <= 2.4e-123)
		tmp = y * ((x * z) - (i * j));
	elseif ((c <= 4.4e+70) || (~((c <= 4.3e+136)) && (c <= 3.8e+186)))
		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[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.5e-57], t$95$2, If[LessEqual[c, -1.3e-244], t$95$1, If[LessEqual[c, 3.5e-285], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.4e-123], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 4.4e+70], And[N[Not[LessEqual[c, 4.3e+136]], $MachinePrecision], LessEqual[c, 3.8e+186]]], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -7.49999999999999973e-57 or 4.40000000000000001e70 < c < 4.2999999999999999e136 or 3.7999999999999998e186 < c

   1. Initial program 71.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 71.0%

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

      2. *-commutative 71.0%

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

      3. sub-neg 71.0%

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

      4. sub-neg 71.0%

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

      5. *-commutative 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in c around inf 69.7%

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

      1. *-commutative 69.7%

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

   6. Simplified 69.7%

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

   if -7.49999999999999973e-57 < c < -1.3000000000000001e-244 or 2.4e-123 < c < 4.40000000000000001e70 or 4.2999999999999999e136 < c < 3.7999999999999998e186

   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. Step-by-step derivation

      1. associate-+l- 80.7%

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

      2. *-commutative 80.7%

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

      3. sub-neg 80.7%

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

      4. sub-neg 80.7%

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

      5. *-commutative 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in a around -inf 85.8%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in t around inf 58.2%

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

      1. *-commutative 58.2%

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

      2. *-commutative 58.2%

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

   9. Simplified 58.2%

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

   if -1.3000000000000001e-244 < c < 3.5000000000000004e-285

   1. Initial program 81.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 81.2%

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

      2. *-commutative 81.2%

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

      3. sub-neg 81.2%

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

      4. sub-neg 81.2%

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

      5. *-commutative 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in a around -inf 83.2%

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

   6. Simplified 79.4%

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

   7. Taylor expanded in i around inf 63.4%

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

      1. +-commutative 63.4%

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

      2. mul-1-neg 63.4%

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

      3. unsub-neg 63.4%

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

      4. *-commutative 63.4%

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

      5. *-commutative 63.4%

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

   9. Simplified 63.4%

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

   if 3.5000000000000004e-285 < c < 2.4e-123

   1. Initial program 88.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 88.1%

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

      2. *-commutative 88.1%

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

      3. sub-neg 88.1%

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

      4. sub-neg 88.1%

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

      5. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in y around inf 64.7%

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

      1. +-commutative 64.7%

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

      2. mul-1-neg 64.7%

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

      3. unsub-neg 64.7%

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

      4. *-commutative 64.7%

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

      5. *-commutative 64.7%

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

   6. Simplified 64.7%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{-57}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-244}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-285}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-123}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{+70} \lor \neg \left(c \leq 4.3 \cdot 10^{+136}\right) \land c \leq 3.8 \cdot 10^{+186}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 5: 57.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+215}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* i (- (* t b) (* y j))) (* b (* z c))))
        (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -9.5e+215)
     t_2
     (if (<= x -5.6e+68)
       t_1
       (if (<= x -4.5e-30)
         (* z (- (* x y) (* b c)))
         (if (<= x 5.8e+16) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * ((t * b) - (y * j))) - (b * (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -9.5e+215) {
		tmp = t_2;
	} else if (x <= -5.6e+68) {
		tmp = t_1;
	} else if (x <= -4.5e-30) {
		tmp = z * ((x * y) - (b * c));
	} else if (x <= 5.8e+16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (i * ((t * b) - (y * j))) - (b * (z * c))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-9.5d+215)) then
        tmp = t_2
    else if (x <= (-5.6d+68)) then
        tmp = t_1
    else if (x <= (-4.5d-30)) then
        tmp = z * ((x * y) - (b * c))
    else if (x <= 5.8d+16) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * ((t * b) - (y * j))) - (b * (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -9.5e+215) {
		tmp = t_2;
	} else if (x <= -5.6e+68) {
		tmp = t_1;
	} else if (x <= -4.5e-30) {
		tmp = z * ((x * y) - (b * c));
	} else if (x <= 5.8e+16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * ((t * b) - (y * j))) - (b * (z * c))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -9.5e+215:
		tmp = t_2
	elif x <= -5.6e+68:
		tmp = t_1
	elif x <= -4.5e-30:
		tmp = z * ((x * y) - (b * c))
	elif x <= 5.8e+16:
		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(i * Float64(Float64(t * b) - Float64(y * j))) - Float64(b * Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -9.5e+215)
		tmp = t_2;
	elseif (x <= -5.6e+68)
		tmp = t_1;
	elseif (x <= -4.5e-30)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (x <= 5.8e+16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (i * ((t * b) - (y * j))) - (b * (z * c));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -9.5e+215)
		tmp = t_2;
	elseif (x <= -5.6e+68)
		tmp = t_1;
	elseif (x <= -4.5e-30)
		tmp = z * ((x * y) - (b * c));
	elseif (x <= 5.8e+16)
		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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.5e+215], t$95$2, If[LessEqual[x, -5.6e+68], t$95$1, If[LessEqual[x, -4.5e-30], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e+16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.50000000000000036e215 or 5.8e16 < x

   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. Step-by-step derivation

      1. associate-+l- 74.7%

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

      2. *-commutative 74.7%

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

      3. sub-neg 74.7%

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

      4. sub-neg 74.7%

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

      5. *-commutative 74.7%

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

   3. Simplified 74.7%

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

   4. Taylor expanded in x around inf 71.1%

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

   if -9.50000000000000036e215 < x < -5.6e68 or -4.49999999999999967e-30 < x < 5.8e16

   1. Initial program 78.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 78.4%

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

      2. *-commutative 78.4%

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

      3. sub-neg 78.4%

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

      4. sub-neg 78.4%

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

      5. *-commutative 78.4%

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

   3. Simplified 78.4%

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

   4. Taylor expanded in t around -inf 78.1%

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

   5. Taylor expanded in i around inf 65.9%

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

      1. +-commutative 65.9%

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

      2. mul-1-neg 65.9%

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

      3. unsub-neg 65.9%

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

   7. Simplified 65.9%

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

   if -5.6e68 < x < -4.49999999999999967e-30

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 77.8%

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

      2. *-commutative 77.8%

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

      3. sub-neg 77.8%

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

      4. sub-neg 77.8%

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

      5. *-commutative 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in z around inf 58.9%

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

      1. *-commutative 58.9%

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

      2. *-commutative 58.9%

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

   6. Simplified 58.9%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+215}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+68}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+16}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 6: 38.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-245}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* z (* b (- c)))))
   (if (<= b -1.15e+137)
     t_2
     (if (<= b -4.5e-84)
       (* z (* x y))
       (if (<= b -2.2e-297)
         t_1
         (if (<= b 2.2e-245)
           (* j (* y (- i)))
           (if (<= b 2.2e+89) 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 = a * ((c * j) - (x * t));
	double t_2 = z * (b * -c);
	double tmp;
	if (b <= -1.15e+137) {
		tmp = t_2;
	} else if (b <= -4.5e-84) {
		tmp = z * (x * y);
	} else if (b <= -2.2e-297) {
		tmp = t_1;
	} else if (b <= 2.2e-245) {
		tmp = j * (y * -i);
	} else if (b <= 2.2e+89) {
		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 = a * ((c * j) - (x * t))
    t_2 = z * (b * -c)
    if (b <= (-1.15d+137)) then
        tmp = t_2
    else if (b <= (-4.5d-84)) then
        tmp = z * (x * y)
    else if (b <= (-2.2d-297)) then
        tmp = t_1
    else if (b <= 2.2d-245) then
        tmp = j * (y * -i)
    else if (b <= 2.2d+89) 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 = a * ((c * j) - (x * t));
	double t_2 = z * (b * -c);
	double tmp;
	if (b <= -1.15e+137) {
		tmp = t_2;
	} else if (b <= -4.5e-84) {
		tmp = z * (x * y);
	} else if (b <= -2.2e-297) {
		tmp = t_1;
	} else if (b <= 2.2e-245) {
		tmp = j * (y * -i);
	} else if (b <= 2.2e+89) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = z * (b * -c)
	tmp = 0
	if b <= -1.15e+137:
		tmp = t_2
	elif b <= -4.5e-84:
		tmp = z * (x * y)
	elif b <= -2.2e-297:
		tmp = t_1
	elif b <= 2.2e-245:
		tmp = j * (y * -i)
	elif b <= 2.2e+89:
		tmp = t_1
	else:
		tmp = t_2
	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(z * Float64(b * Float64(-c)))
	tmp = 0.0
	if (b <= -1.15e+137)
		tmp = t_2;
	elseif (b <= -4.5e-84)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= -2.2e-297)
		tmp = t_1;
	elseif (b <= 2.2e-245)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (b <= 2.2e+89)
		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 = a * ((c * j) - (x * t));
	t_2 = z * (b * -c);
	tmp = 0.0;
	if (b <= -1.15e+137)
		tmp = t_2;
	elseif (b <= -4.5e-84)
		tmp = z * (x * y);
	elseif (b <= -2.2e-297)
		tmp = t_1;
	elseif (b <= 2.2e-245)
		tmp = j * (y * -i);
	elseif (b <= 2.2e+89)
		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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.15e+137], t$95$2, If[LessEqual[b, -4.5e-84], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.2e-297], t$95$1, If[LessEqual[b, 2.2e-245], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e+89], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.15e137 or 2.2e89 < b

   1. Initial program 76.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 76.8%

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

      2. *-commutative 76.8%

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

      3. sub-neg 76.8%

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

      4. sub-neg 76.8%

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

      5. *-commutative 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in z around inf 63.6%

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

      1. *-commutative 63.6%

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

      2. *-commutative 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in y around 0 52.2%

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

      1. mul-1-neg 52.2%

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

      2. *-commutative 52.2%

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

      3. distribute-rgt-neg-in 52.2%

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

   9. Simplified 52.2%

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

   if -1.15e137 < b < -4.50000000000000016e-84

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 71.1%

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

      2. *-commutative 71.1%

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

      3. sub-neg 71.1%

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

      4. sub-neg 71.1%

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

      5. *-commutative 71.1%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in z around inf 60.7%

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

      1. *-commutative 60.7%

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

      2. *-commutative 60.7%

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

   6. Simplified 60.7%

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

   7. Taylor expanded in y around inf 42.8%

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

      1. *-commutative 42.8%

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

   9. Simplified 42.8%

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

   if -4.50000000000000016e-84 < b < -2.1999999999999998e-297 or 2.19999999999999993e-245 < b < 2.2e89

   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. Step-by-step derivation

      1. associate-+l- 79.6%

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

      2. *-commutative 79.6%

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

      3. sub-neg 79.6%

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

      4. sub-neg 79.6%

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

      5. *-commutative 79.6%

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

   3. Simplified 79.6%

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

   4. Taylor expanded in a around inf 54.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. 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%

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

   6. Simplified 54.5%

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

   if -2.1999999999999998e-297 < b < 2.19999999999999993e-245

   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. Step-by-step derivation

      1. associate-+l- 77.7%

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

      2. *-commutative 77.7%

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

      3. sub-neg 77.7%

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

      4. sub-neg 77.7%

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

      5. *-commutative 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in j around inf 58.0%

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

   5. Taylor expanded in a around 0 45.1%

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

      1. mul-1-neg 45.1%

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

      2. distribute-lft-neg-out 45.1%

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

      3. *-commutative 45.1%

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

   7. Simplified 45.1%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+137}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-297}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-245}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \]

Alternative 7: 50.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -9 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.22 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-148}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -9e+106)
     t_2
     (if (<= i -1.22e-21)
       (* j (- (* a c) (* y i)))
       (if (<= i -1.15e-28)
         t_1
         (if (<= i 1.1e-148)
           (* c (- (* a j) (* z b)))
           (if (<= i 3.2e+51) 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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -9e+106) {
		tmp = t_2;
	} else if (i <= -1.22e-21) {
		tmp = j * ((a * c) - (y * i));
	} else if (i <= -1.15e-28) {
		tmp = t_1;
	} else if (i <= 1.1e-148) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 3.2e+51) {
		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 = i * ((t * b) - (y * j))
    if (i <= (-9d+106)) then
        tmp = t_2
    else if (i <= (-1.22d-21)) then
        tmp = j * ((a * c) - (y * i))
    else if (i <= (-1.15d-28)) then
        tmp = t_1
    else if (i <= 1.1d-148) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 3.2d+51) 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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -9e+106) {
		tmp = t_2;
	} else if (i <= -1.22e-21) {
		tmp = j * ((a * c) - (y * i));
	} else if (i <= -1.15e-28) {
		tmp = t_1;
	} else if (i <= 1.1e-148) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 3.2e+51) {
		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 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -9e+106:
		tmp = t_2
	elif i <= -1.22e-21:
		tmp = j * ((a * c) - (y * i))
	elif i <= -1.15e-28:
		tmp = t_1
	elif i <= 1.1e-148:
		tmp = c * ((a * j) - (z * b))
	elif i <= 3.2e+51:
		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(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -9e+106)
		tmp = t_2;
	elseif (i <= -1.22e-21)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (i <= -1.15e-28)
		tmp = t_1;
	elseif (i <= 1.1e-148)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 3.2e+51)
		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 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -9e+106)
		tmp = t_2;
	elseif (i <= -1.22e-21)
		tmp = j * ((a * c) - (y * i));
	elseif (i <= -1.15e-28)
		tmp = t_1;
	elseif (i <= 1.1e-148)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 3.2e+51)
		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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9e+106], t$95$2, If[LessEqual[i, -1.22e-21], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.15e-28], t$95$1, If[LessEqual[i, 1.1e-148], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.2e+51], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -8.9999999999999994e106 or 3.2000000000000002e51 < i

   1. Initial program 64.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 64.7%

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

      2. *-commutative 64.7%

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

      3. sub-neg 64.7%

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

      4. sub-neg 64.7%

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

      5. *-commutative 64.7%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in a around -inf 70.5%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in i around inf 72.6%

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

      1. +-commutative 72.6%

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

      2. mul-1-neg 72.6%

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

      3. unsub-neg 72.6%

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

      4. *-commutative 72.6%

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

      5. *-commutative 72.6%

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

   9. Simplified 72.6%

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

   if -8.9999999999999994e106 < i < -1.21999999999999991e-21

   1. Initial program 68.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 68.5%

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

      2. *-commutative 68.5%

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

      3. sub-neg 68.5%

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

      4. sub-neg 68.5%

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

      5. *-commutative 68.5%

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

   3. Simplified 68.5%

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

   4. Taylor expanded in j around inf 64.2%

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

   if -1.21999999999999991e-21 < i < -1.14999999999999993e-28 or 1.10000000000000009e-148 < i < 3.2000000000000002e51

   1. Initial program 92.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 92.4%

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

      2. *-commutative 92.4%

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

      3. sub-neg 92.4%

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

      4. sub-neg 92.4%

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

      5. *-commutative 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in b around inf 50.1%

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

   if -1.14999999999999993e-28 < i < 1.10000000000000009e-148

   1. Initial program 83.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 83.1%

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

      2. *-commutative 83.1%

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

      3. sub-neg 83.1%

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

      4. sub-neg 83.1%

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

      5. *-commutative 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in c around inf 56.4%

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

      1. *-commutative 56.4%

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

   6. Simplified 56.4%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9 \cdot 10^{+106}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.22 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{-28}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-148}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 8: 51.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.4 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{-28}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -6.4 \cdot 10^{-160}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 5.4 \cdot 10^{+84}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -2.4e+104)
     t_1
     (if (<= i -2.3e-21)
       (* j (- (* a c) (* y i)))
       (if (<= i -1.15e-28)
         (* b (- (* t i) (* z c)))
         (if (<= i -6.4e-160)
           (* a (- (* c j) (* x t)))
           (if (<= i 5.4e+84) (* z (- (* x y) (* b c))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -2.4e+104) {
		tmp = t_1;
	} else if (i <= -2.3e-21) {
		tmp = j * ((a * c) - (y * i));
	} else if (i <= -1.15e-28) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= -6.4e-160) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 5.4e+84) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-2.4d+104)) then
        tmp = t_1
    else if (i <= (-2.3d-21)) then
        tmp = j * ((a * c) - (y * i))
    else if (i <= (-1.15d-28)) then
        tmp = b * ((t * i) - (z * c))
    else if (i <= (-6.4d-160)) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 5.4d+84) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -2.4e+104) {
		tmp = t_1;
	} else if (i <= -2.3e-21) {
		tmp = j * ((a * c) - (y * i));
	} else if (i <= -1.15e-28) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= -6.4e-160) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 5.4e+84) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -2.4e+104:
		tmp = t_1
	elif i <= -2.3e-21:
		tmp = j * ((a * c) - (y * i))
	elif i <= -1.15e-28:
		tmp = b * ((t * i) - (z * c))
	elif i <= -6.4e-160:
		tmp = a * ((c * j) - (x * t))
	elif i <= 5.4e+84:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.4e+104)
		tmp = t_1;
	elseif (i <= -2.3e-21)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (i <= -1.15e-28)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (i <= -6.4e-160)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 5.4e+84)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.4e+104)
		tmp = t_1;
	elseif (i <= -2.3e-21)
		tmp = j * ((a * c) - (y * i));
	elseif (i <= -1.15e-28)
		tmp = b * ((t * i) - (z * c));
	elseif (i <= -6.4e-160)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 5.4e+84)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.4e+104], t$95$1, If[LessEqual[i, -2.3e-21], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.15e-28], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6.4e-160], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.4e+84], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -2.4e104 or 5.4e84 < i

   1. Initial program 65.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 65.4%

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

      2. *-commutative 65.4%

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

      3. sub-neg 65.4%

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

      4. sub-neg 65.4%

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

      5. *-commutative 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in a around -inf 71.4%

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

   6. Simplified 67.9%

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

   7. Taylor expanded in i around inf 74.8%

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

      1. +-commutative 74.8%

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

      2. mul-1-neg 74.8%

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

      3. unsub-neg 74.8%

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

      4. *-commutative 74.8%

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

      5. *-commutative 74.8%

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

   9. Simplified 74.8%

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

   if -2.4e104 < i < -2.29999999999999999e-21

   1. Initial program 68.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 68.5%

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

      2. *-commutative 68.5%

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

      3. sub-neg 68.5%

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

      4. sub-neg 68.5%

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

      5. *-commutative 68.5%

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

   3. Simplified 68.5%

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

   4. Taylor expanded in j around inf 64.2%

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

   if -2.29999999999999999e-21 < i < -1.14999999999999993e-28

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in b around inf 100.0%

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

   if -1.14999999999999993e-28 < i < -6.40000000000000018e-160

   1. Initial program 86.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 86.9%

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

      2. *-commutative 86.9%

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

      3. sub-neg 86.9%

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

      4. sub-neg 86.9%

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

      5. *-commutative 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in a around inf 66.8%

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

      1. +-commutative 66.8%

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

      2. mul-1-neg 66.8%

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

      3. unsub-neg 66.8%

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

      4. *-commutative 66.8%

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

   6. Simplified 66.8%

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

   if -6.40000000000000018e-160 < i < 5.4e84

   1. Initial program 84.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 84.3%

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

      2. *-commutative 84.3%

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

      3. sub-neg 84.3%

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

      4. sub-neg 84.3%

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

      5. *-commutative 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in z around inf 63.6%

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

      1. *-commutative 63.6%

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

      2. *-commutative 63.6%

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

   6. Simplified 63.6%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.4 \cdot 10^{+104}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{-28}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -6.4 \cdot 10^{-160}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 5.4 \cdot 10^{+84}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 9: 50.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.2 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -0.3:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{-28}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-160}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -1.2e+106)
     t_1
     (if (<= i -0.3)
       (- (* a (* c j)) (* i (* y j)))
       (if (<= i -1.15e-28)
         (* b (- (* t i) (* z c)))
         (if (<= i -6e-160)
           (* a (- (* c j) (* x t)))
           (if (<= i 1.8e+85) (* z (- (* x y) (* b c))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.2e+106) {
		tmp = t_1;
	} else if (i <= -0.3) {
		tmp = (a * (c * j)) - (i * (y * j));
	} else if (i <= -1.15e-28) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= -6e-160) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.8e+85) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-1.2d+106)) then
        tmp = t_1
    else if (i <= (-0.3d0)) then
        tmp = (a * (c * j)) - (i * (y * j))
    else if (i <= (-1.15d-28)) then
        tmp = b * ((t * i) - (z * c))
    else if (i <= (-6d-160)) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 1.8d+85) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.2e+106) {
		tmp = t_1;
	} else if (i <= -0.3) {
		tmp = (a * (c * j)) - (i * (y * j));
	} else if (i <= -1.15e-28) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= -6e-160) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.8e+85) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.2e+106:
		tmp = t_1
	elif i <= -0.3:
		tmp = (a * (c * j)) - (i * (y * j))
	elif i <= -1.15e-28:
		tmp = b * ((t * i) - (z * c))
	elif i <= -6e-160:
		tmp = a * ((c * j) - (x * t))
	elif i <= 1.8e+85:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.2e+106)
		tmp = t_1;
	elseif (i <= -0.3)
		tmp = Float64(Float64(a * Float64(c * j)) - Float64(i * Float64(y * j)));
	elseif (i <= -1.15e-28)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (i <= -6e-160)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 1.8e+85)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.2e+106)
		tmp = t_1;
	elseif (i <= -0.3)
		tmp = (a * (c * j)) - (i * (y * j));
	elseif (i <= -1.15e-28)
		tmp = b * ((t * i) - (z * c));
	elseif (i <= -6e-160)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 1.8e+85)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.2e+106], t$95$1, If[LessEqual[i, -0.3], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.15e-28], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6e-160], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.8e+85], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.2e106 or 1.7999999999999999e85 < i

   1. Initial program 65.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 65.4%

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

      2. *-commutative 65.4%

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

      3. sub-neg 65.4%

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

      4. sub-neg 65.4%

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

      5. *-commutative 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in a around -inf 71.4%

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

   6. Simplified 67.9%

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

   7. Taylor expanded in i around inf 74.8%

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

      1. +-commutative 74.8%

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

      2. mul-1-neg 74.8%

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

      3. unsub-neg 74.8%

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

      4. *-commutative 74.8%

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

      5. *-commutative 74.8%

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

   9. Simplified 74.8%

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

   if -1.2e106 < i < -0.299999999999999989

   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. Step-by-step derivation

      1. associate-+l- 72.2%

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

      2. *-commutative 72.2%

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

      3. sub-neg 72.2%

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

      4. sub-neg 72.2%

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

      5. *-commutative 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in j around inf 72.7%

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

   5. Taylor expanded in a around 0 72.7%

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

   if -0.299999999999999989 < i < -1.14999999999999993e-28

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 72.5%

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

      2. *-commutative 72.5%

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

      3. sub-neg 72.5%

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

      4. sub-neg 72.5%

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

      5. *-commutative 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in b around inf 57.8%

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

   if -1.14999999999999993e-28 < i < -5.99999999999999993e-160

   1. Initial program 86.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 86.9%

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

      2. *-commutative 86.9%

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

      3. sub-neg 86.9%

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

      4. sub-neg 86.9%

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

      5. *-commutative 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in a around inf 66.8%

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

      1. +-commutative 66.8%

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

      2. mul-1-neg 66.8%

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

      3. unsub-neg 66.8%

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

      4. *-commutative 66.8%

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

   6. Simplified 66.8%

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

   if -5.99999999999999993e-160 < i < 1.7999999999999999e85

   1. Initial program 84.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 84.3%

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

      2. *-commutative 84.3%

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

      3. sub-neg 84.3%

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

      4. sub-neg 84.3%

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

      5. *-commutative 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in z around inf 63.6%

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

      1. *-commutative 63.6%

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

      2. *-commutative 63.6%

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

   6. Simplified 63.6%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.2 \cdot 10^{+106}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -0.3:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{-28}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -6 \cdot 10^{-160}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 10: 51.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.15 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-149}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -1.15e-28)
     t_1
     (if (<= i 3.6e-149)
       (* c (- (* a j) (* z b)))
       (if (<= i 8.2e+46) (* b (- (* t i) (* z c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.15e-28) {
		tmp = t_1;
	} else if (i <= 3.6e-149) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 8.2e+46) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-1.15d-28)) then
        tmp = t_1
    else if (i <= 3.6d-149) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 8.2d+46) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.15e-28) {
		tmp = t_1;
	} else if (i <= 3.6e-149) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 8.2e+46) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.15e-28:
		tmp = t_1
	elif i <= 3.6e-149:
		tmp = c * ((a * j) - (z * b))
	elif i <= 8.2e+46:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.15e-28)
		tmp = t_1;
	elseif (i <= 3.6e-149)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 8.2e+46)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.15e-28)
		tmp = t_1;
	elseif (i <= 3.6e-149)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 8.2e+46)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.15e-28], t$95$1, If[LessEqual[i, 3.6e-149], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.2e+46], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.14999999999999993e-28 or 8.19999999999999999e46 < i

   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. Step-by-step derivation

      1. associate-+l- 66.4%

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

      2. *-commutative 66.4%

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

      3. sub-neg 66.4%

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

      4. sub-neg 66.4%

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

      5. *-commutative 66.4%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in a around -inf 71.0%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in i around inf 66.8%

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

      1. +-commutative 66.8%

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

      2. mul-1-neg 66.8%

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

      3. unsub-neg 66.8%

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

      4. *-commutative 66.8%

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

      5. *-commutative 66.8%

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

   9. Simplified 66.8%

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

   if -1.14999999999999993e-28 < i < 3.6000000000000002e-149

   1. Initial program 83.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 83.1%

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

      2. *-commutative 83.1%

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

      3. sub-neg 83.1%

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

      4. sub-neg 83.1%

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

      5. *-commutative 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in c around inf 56.4%

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

      1. *-commutative 56.4%

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

   6. Simplified 56.4%

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

   if 3.6000000000000002e-149 < i < 8.19999999999999999e46

   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. Step-by-step derivation

      1. associate-+l- 91.9%

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

      2. *-commutative 91.9%

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

      3. sub-neg 91.9%

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

      4. sub-neg 91.9%

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

      5. *-commutative 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in b around inf 46.7%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.15 \cdot 10^{-28}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-149}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 11: 29.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-105}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* c (* z (- b)))))
   (if (<= b -4.2e+134)
     t_2
     (if (<= b -2.9e-142)
       t_1
       (if (<= b 4e-105) (* a (* c j)) (if (<= b 5.8e+144) 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);
	double t_2 = c * (z * -b);
	double tmp;
	if (b <= -4.2e+134) {
		tmp = t_2;
	} else if (b <= -2.9e-142) {
		tmp = t_1;
	} else if (b <= 4e-105) {
		tmp = a * (c * j);
	} else if (b <= 5.8e+144) {
		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)
    t_2 = c * (z * -b)
    if (b <= (-4.2d+134)) then
        tmp = t_2
    else if (b <= (-2.9d-142)) then
        tmp = t_1
    else if (b <= 4d-105) then
        tmp = a * (c * j)
    else if (b <= 5.8d+144) 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);
	double t_2 = c * (z * -b);
	double tmp;
	if (b <= -4.2e+134) {
		tmp = t_2;
	} else if (b <= -2.9e-142) {
		tmp = t_1;
	} else if (b <= 4e-105) {
		tmp = a * (c * j);
	} else if (b <= 5.8e+144) {
		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)
	t_2 = c * (z * -b)
	tmp = 0
	if b <= -4.2e+134:
		tmp = t_2
	elif b <= -2.9e-142:
		tmp = t_1
	elif b <= 4e-105:
		tmp = a * (c * j)
	elif b <= 5.8e+144:
		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(x * y))
	t_2 = Float64(c * Float64(z * Float64(-b)))
	tmp = 0.0
	if (b <= -4.2e+134)
		tmp = t_2;
	elseif (b <= -2.9e-142)
		tmp = t_1;
	elseif (b <= 4e-105)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 5.8e+144)
		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);
	t_2 = c * (z * -b);
	tmp = 0.0;
	if (b <= -4.2e+134)
		tmp = t_2;
	elseif (b <= -2.9e-142)
		tmp = t_1;
	elseif (b <= 4e-105)
		tmp = a * (c * j);
	elseif (b <= 5.8e+144)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.2e+134], t$95$2, If[LessEqual[b, -2.9e-142], t$95$1, If[LessEqual[b, 4e-105], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e+144], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.2000000000000002e134 or 5.79999999999999996e144 < b

   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. Step-by-step derivation

      1. associate-+l- 76.9%

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

      2. *-commutative 76.9%

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

      3. sub-neg 76.9%

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

      4. sub-neg 76.9%

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

      5. *-commutative 76.9%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in c around inf 57.6%

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

      1. *-commutative 57.6%

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

   6. Simplified 57.6%

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

   7. Taylor expanded in j around 0 48.9%

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

      1. neg-mul-1 48.9%

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

      2. distribute-rgt-neg-in 48.9%

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

   9. Simplified 48.9%

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

   if -4.2000000000000002e134 < b < -2.8999999999999999e-142 or 3.99999999999999986e-105 < b < 5.79999999999999996e144

   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. Step-by-step derivation

      1. associate-+l- 77.1%

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

      2. *-commutative 77.1%

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

      3. sub-neg 77.1%

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

      4. sub-neg 77.1%

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

      5. *-commutative 77.1%

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

   3. Simplified 77.1%

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

   4. Taylor expanded in z around inf 48.8%

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

      1. *-commutative 48.8%

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

      2. *-commutative 48.8%

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

   6. Simplified 48.8%

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

   7. Taylor expanded in y around inf 36.2%

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

      1. *-commutative 36.2%

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

   9. Simplified 36.2%

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

   if -2.8999999999999999e-142 < b < 3.99999999999999986e-105

   1. Initial program 78.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 78.0%

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

      2. *-commutative 78.0%

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

      3. sub-neg 78.0%

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

      4. sub-neg 78.0%

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

      5. *-commutative 78.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in a around inf 56.3%

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

      1. +-commutative 56.3%

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

      2. mul-1-neg 56.3%

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

      3. unsub-neg 56.3%

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

      4. *-commutative 56.3%

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

   6. Simplified 56.3%

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

   7. Taylor expanded in j around inf 36.5%

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

      1. *-commutative 36.5%

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

   9. Simplified 36.5%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+134}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-142}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-105}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+144}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]

Alternative 12: 29.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* z (* b (- c)))))
   (if (<= b -4.2e+137)
     t_2
     (if (<= b -1.32e-142)
       t_1
       (if (<= b 5.2e-106) (* a (* c j)) (if (<= b 6e+144) 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);
	double t_2 = z * (b * -c);
	double tmp;
	if (b <= -4.2e+137) {
		tmp = t_2;
	} else if (b <= -1.32e-142) {
		tmp = t_1;
	} else if (b <= 5.2e-106) {
		tmp = a * (c * j);
	} else if (b <= 6e+144) {
		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)
    t_2 = z * (b * -c)
    if (b <= (-4.2d+137)) then
        tmp = t_2
    else if (b <= (-1.32d-142)) then
        tmp = t_1
    else if (b <= 5.2d-106) then
        tmp = a * (c * j)
    else if (b <= 6d+144) 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);
	double t_2 = z * (b * -c);
	double tmp;
	if (b <= -4.2e+137) {
		tmp = t_2;
	} else if (b <= -1.32e-142) {
		tmp = t_1;
	} else if (b <= 5.2e-106) {
		tmp = a * (c * j);
	} else if (b <= 6e+144) {
		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)
	t_2 = z * (b * -c)
	tmp = 0
	if b <= -4.2e+137:
		tmp = t_2
	elif b <= -1.32e-142:
		tmp = t_1
	elif b <= 5.2e-106:
		tmp = a * (c * j)
	elif b <= 6e+144:
		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(x * y))
	t_2 = Float64(z * Float64(b * Float64(-c)))
	tmp = 0.0
	if (b <= -4.2e+137)
		tmp = t_2;
	elseif (b <= -1.32e-142)
		tmp = t_1;
	elseif (b <= 5.2e-106)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 6e+144)
		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);
	t_2 = z * (b * -c);
	tmp = 0.0;
	if (b <= -4.2e+137)
		tmp = t_2;
	elseif (b <= -1.32e-142)
		tmp = t_1;
	elseif (b <= 5.2e-106)
		tmp = a * (c * j);
	elseif (b <= 6e+144)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.2e+137], t$95$2, If[LessEqual[b, -1.32e-142], t$95$1, If[LessEqual[b, 5.2e-106], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e+144], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.1999999999999998e137 or 5.9999999999999998e144 < b

   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. Step-by-step derivation

      1. associate-+l- 76.9%

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

      2. *-commutative 76.9%

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

      3. sub-neg 76.9%

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

      4. sub-neg 76.9%

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

      5. *-commutative 76.9%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in z around inf 62.4%

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

      1. *-commutative 62.4%

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

      2. *-commutative 62.4%

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

   6. Simplified 62.4%

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

   7. Taylor expanded in y around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. *-commutative 54.8%

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

      3. distribute-rgt-neg-in 54.8%

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

   9. Simplified 54.8%

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

   if -4.1999999999999998e137 < b < -1.32e-142 or 5.2000000000000001e-106 < b < 5.9999999999999998e144

   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. Step-by-step derivation

      1. associate-+l- 77.1%

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

      2. *-commutative 77.1%

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

      3. sub-neg 77.1%

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

      4. sub-neg 77.1%

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

      5. *-commutative 77.1%

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

   3. Simplified 77.1%

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

   4. Taylor expanded in z around inf 48.8%

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

      1. *-commutative 48.8%

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

      2. *-commutative 48.8%

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

   6. Simplified 48.8%

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

   7. Taylor expanded in y around inf 36.2%

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

      1. *-commutative 36.2%

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

   9. Simplified 36.2%

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

   if -1.32e-142 < b < 5.2000000000000001e-106

   1. Initial program 78.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 78.0%

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

      2. *-commutative 78.0%

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

      3. sub-neg 78.0%

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

      4. sub-neg 78.0%

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

      5. *-commutative 78.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in a around inf 56.3%

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

      1. +-commutative 56.3%

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

      2. mul-1-neg 56.3%

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

      3. unsub-neg 56.3%

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

      4. *-commutative 56.3%

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

   6. Simplified 56.3%

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

   7. Taylor expanded in j around inf 36.5%

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

      1. *-commutative 36.5%

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

   9. Simplified 36.5%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+137}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{-142}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+144}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \]

Alternative 13: 53.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+44} \lor \neg \left(a \leq 450000\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -4.6e+44) (not (<= a 450000.0)))
   (* a (- (* c j) (* x t)))
   (* b (- (* t i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -4.6e+44) || !(a <= 450000.0)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-4.6d+44)) .or. (.not. (a <= 450000.0d0))) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -4.6e+44) || !(a <= 450000.0)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -4.6e+44) or not (a <= 450000.0):
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -4.6e+44) || !(a <= 450000.0))
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -4.6e+44) || ~((a <= 450000.0)))
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -4.6e+44], N[Not[LessEqual[a, 450000.0]], $MachinePrecision]], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.60000000000000009e44 or 4.5e5 < a

   1. Initial program 61.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 61.3%

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

      2. *-commutative 61.3%

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

      3. sub-neg 61.3%

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

      4. sub-neg 61.3%

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

      5. *-commutative 61.3%

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

   3. Simplified 61.3%

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

   4. Taylor expanded in a around inf 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. *-commutative 62.9%

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

   6. Simplified 62.9%

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

   if -4.60000000000000009e44 < a < 4.5e5

   1. Initial program 88.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 88.1%

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

      2. *-commutative 88.1%

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

      3. sub-neg 88.1%

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

      4. sub-neg 88.1%

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

      5. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in b around inf 51.7%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+44} \lor \neg \left(a \leq 450000\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 14: 28.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.02 \cdot 10^{+65}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;c \leq 1.12 \cdot 10^{+98}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.02e+65)
   (* c (* a j))
   (if (<= c 1.12e+98) (* z (* x y)) (* j (* a c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.02e+65) {
		tmp = c * (a * j);
	} else if (c <= 1.12e+98) {
		tmp = z * (x * y);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-1.02d+65)) then
        tmp = c * (a * j)
    else if (c <= 1.12d+98) then
        tmp = z * (x * y)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.02e+65) {
		tmp = c * (a * j);
	} else if (c <= 1.12e+98) {
		tmp = z * (x * y);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.02e+65:
		tmp = c * (a * j)
	elif c <= 1.12e+98:
		tmp = z * (x * y)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.02e+65)
		tmp = Float64(c * Float64(a * j));
	elseif (c <= 1.12e+98)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -1.02e+65)
		tmp = c * (a * j);
	elseif (c <= 1.12e+98)
		tmp = z * (x * y);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.02e+65], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.12e+98], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.02000000000000005e65

   1. Initial program 70.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 70.8%

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

      2. *-commutative 70.8%

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

      3. sub-neg 70.8%

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

      4. sub-neg 70.8%

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

      5. *-commutative 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in c around inf 71.0%

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

      1. *-commutative 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in j around inf 43.6%

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

   if -1.02000000000000005e65 < c < 1.12e98

   1. Initial program 83.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 83.3%

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

      2. *-commutative 83.3%

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

      3. sub-neg 83.3%

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

      4. sub-neg 83.3%

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

      5. *-commutative 83.3%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in z around inf 41.9%

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

      1. *-commutative 41.9%

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

      2. *-commutative 41.9%

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

   6. Simplified 41.9%

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

   7. Taylor expanded in y around inf 30.6%

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

      1. *-commutative 30.6%

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

   9. Simplified 30.6%

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

   if 1.12e98 < 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. Step-by-step derivation

      1. associate-+l- 60.6%

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

      2. *-commutative 60.6%

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

      3. sub-neg 60.6%

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

      4. sub-neg 60.6%

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

      5. *-commutative 60.6%

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

   3. Simplified 60.6%

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

   4. Taylor expanded in j around inf 45.1%

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

   5. Taylor expanded in a around inf 45.1%

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

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.02 \cdot 10^{+65}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;c \leq 1.12 \cdot 10^{+98}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]

Alternative 15: 22.1% 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 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. Step-by-step derivation

   1. associate-+l- 77.3%

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

   2. *-commutative 77.3%

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

   3. sub-neg 77.3%

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

   4. sub-neg 77.3%

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

   5. *-commutative 77.3%

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

3. Simplified 77.3%

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

4. Taylor expanded in a around inf 37.3%

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

   1. +-commutative 37.3%

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

   2. mul-1-neg 37.3%

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

   3. unsub-neg 37.3%

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

   4. *-commutative 37.3%

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

6. Simplified 37.3%

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

7. Taylor expanded in j around inf 22.1%

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

   1. *-commutative 22.1%

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

9. Simplified 22.1%

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

10. Final simplification 22.1%

    \[\leadsto a \cdot \left(c \cdot j\right) \]

Alternative 16: 22.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ c \cdot \left(a \cdot j\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]

Derivation

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. Step-by-step derivation

   1. associate-+l- 77.3%

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

   2. *-commutative 77.3%

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

   3. sub-neg 77.3%

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

   4. sub-neg 77.3%

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

   5. *-commutative 77.3%

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

3. Simplified 77.3%

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

4. Taylor expanded in c around inf 41.0%

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

   1. *-commutative 41.0%

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

6. Simplified 41.0%

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

7. Taylor expanded in j around inf 22.1%

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

8. Final simplification 22.1%

   \[\leadsto c \cdot \left(a \cdot j\right) \]

Alternative 17: 21.8% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ j \cdot \left(a \cdot c\right) \end{array} \]

FPCore

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

C

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

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 = j * (a * c)
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 j * (a * c);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]

Derivation

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. Step-by-step derivation

   1. associate-+l- 77.3%

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

   2. *-commutative 77.3%

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

   3. sub-neg 77.3%

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

   4. sub-neg 77.3%

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

   5. *-commutative 77.3%

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

3. Simplified 77.3%

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

4. Taylor expanded in j around inf 36.0%

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

5. Taylor expanded in a around inf 22.2%

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

6. Final simplification 22.2%

   \[\leadsto j \cdot \left(a \cdot c\right) \]

Developer target: 59.8% 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 2023293 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))