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

Percentage Accurate: 72.8% → 81.6%

Time: 24.7s

Alternatives: 20

Speedup: 0.5×

• 58.6% 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: 72.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((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 = c * ((a * j) - (z * b));
	}
	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 = c * ((a * j) - (z * b))
	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(c * Float64(Float64(a * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((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 = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.5%

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

   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 c around inf 55.7%

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

      1. *-commutative 55.7%

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

   6. Simplified 55.7%

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

4. Final simplification 82.4%

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

Alternative 2: 70.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + \left(j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -6e+145)
     t_1
     (if (<= x 1.35e+90)
       (+
        (* y (* x z))
        (- (* j (- (* a c) (* y i))) (* b (- (* z c) (* t i)))))
       (+ t_1 (* c (* a j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -6e+145) {
		tmp = t_1;
	} else if (x <= 1.35e+90) {
		tmp = (y * (x * z)) + ((j * ((a * c) - (y * i))) - (b * ((z * c) - (t * i))));
	} else {
		tmp = t_1 + (c * (a * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-6d+145)) then
        tmp = t_1
    else if (x <= 1.35d+90) then
        tmp = (y * (x * z)) + ((j * ((a * c) - (y * i))) - (b * ((z * c) - (t * i))))
    else
        tmp = t_1 + (c * (a * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -6e+145) {
		tmp = t_1;
	} else if (x <= 1.35e+90) {
		tmp = (y * (x * z)) + ((j * ((a * c) - (y * i))) - (b * ((z * c) - (t * i))));
	} else {
		tmp = t_1 + (c * (a * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -6e+145:
		tmp = t_1
	elif x <= 1.35e+90:
		tmp = (y * (x * z)) + ((j * ((a * c) - (y * i))) - (b * ((z * c) - (t * i))))
	else:
		tmp = t_1 + (c * (a * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -6e+145)
		tmp = t_1;
	elseif (x <= 1.35e+90)
		tmp = Float64(Float64(y * Float64(x * z)) + Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(b * Float64(Float64(z * c) - Float64(t * i)))));
	else
		tmp = Float64(t_1 + Float64(c * Float64(a * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -6e+145)
		tmp = t_1;
	elseif (x <= 1.35e+90)
		tmp = (y * (x * z)) + ((j * ((a * c) - (y * i))) - (b * ((z * c) - (t * i))));
	else
		tmp = t_1 + (c * (a * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+145], t$95$1, If[LessEqual[x, 1.35e+90], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.0000000000000005e145

   1. Initial program 68.4%

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

      1. associate-+l- 68.4%

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

      2. *-commutative 68.4%

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

      3. sub-neg 68.4%

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

      4. sub-neg 68.4%

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

      5. *-commutative 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in x around inf 77.1%

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

   if -6.0000000000000005e145 < x < 1.35e90

   1. Initial program 73.2%

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

      1. associate-+l- 73.2%

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

      2. *-commutative 73.2%

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

      3. sub-neg 73.2%

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

      4. sub-neg 73.2%

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

      5. *-commutative 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in y around inf 70.2%

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

      1. *-commutative 70.2%

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

      2. associate-*r* 71.9%

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

   6. Simplified 71.9%

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

   if 1.35e90 < x

   1. Initial program 54.5%

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

      1. associate-+l- 54.5%

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

      2. *-commutative 54.5%

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

      3. sub-neg 54.5%

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

      4. sub-neg 54.5%

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

      5. *-commutative 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in b around 0 61.4%

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

   5. Taylor expanded in a around inf 61.5%

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

   6. Taylor expanded in j around 0 65.3%

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

      1. associate-*r* 61.5%

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

      2. *-commutative 61.5%

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

      3. associate-*l* 65.3%

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

   8. Simplified 65.3%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+145}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + \left(j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 3: 63.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.8 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.16 \cdot 10^{-46}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.85 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t_1 - i \cdot \left(y \cdot j\right)\right) + b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -1.8e+93)
     t_1
     (if (<= c -1.16e-46)
       (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
       (if (<= c 3.85e+118)
         (+ (* y (- (* x z) (* i j))) (* b (- (* t i) (* z c))))
         (+ (- t_1 (* i (* y j))) (* b (* t i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.8e+93) {
		tmp = t_1;
	} else if (c <= -1.16e-46) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (c <= 3.85e+118) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (t_1 - (i * (y * j))) + (b * (t * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    if (c <= (-1.8d+93)) then
        tmp = t_1
    else if (c <= (-1.16d-46)) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else if (c <= 3.85d+118) then
        tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
    else
        tmp = (t_1 - (i * (y * j))) + (b * (t * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.8e+93) {
		tmp = t_1;
	} else if (c <= -1.16e-46) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (c <= 3.85e+118) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (t_1 - (i * (y * j))) + (b * (t * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -1.8e+93:
		tmp = t_1
	elif c <= -1.16e-46:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	elif c <= 3.85e+118:
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
	else:
		tmp = (t_1 - (i * (y * j))) + (b * (t * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.8e+93)
		tmp = t_1;
	elseif (c <= -1.16e-46)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (c <= 3.85e+118)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(t_1 - Float64(i * Float64(y * j))) + Float64(b * Float64(t * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.8e+93)
		tmp = t_1;
	elseif (c <= -1.16e-46)
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	elseif (c <= 3.85e+118)
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	else
		tmp = (t_1 - (i * (y * j))) + (b * (t * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.8e+93], t$95$1, If[LessEqual[c, -1.16e-46], 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[c, 3.85e+118], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.8e93

   1. Initial program 58.8%

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

      1. associate-+l- 58.8%

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

      2. *-commutative 58.8%

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

      3. sub-neg 58.8%

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

      4. sub-neg 58.8%

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

      5. *-commutative 58.8%

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

   3. Simplified 58.8%

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

   4. Taylor expanded in c around inf 72.9%

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

      1. *-commutative 72.9%

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

   6. Simplified 72.9%

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

   if -1.8e93 < c < -1.16e-46

   1. Initial program 74.0%

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

      1. associate-+l- 74.0%

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

      2. *-commutative 74.0%

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

      3. sub-neg 74.0%

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

      4. sub-neg 74.0%

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

      5. *-commutative 74.0%

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

   3. Simplified 74.0%

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

   4. Taylor expanded in b around 0 70.8%

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

   if -1.16e-46 < c < 3.8499999999999999e118

   1. Initial program 76.1%

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

      1. associate-+l- 76.1%

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

      2. *-commutative 76.1%

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

      3. sub-neg 76.1%

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

      4. sub-neg 76.1%

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

      5. *-commutative 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in a around 0 66.7%

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

      1. sub-neg 66.7%

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

      2. *-commutative 66.7%

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

      3. *-commutative 66.7%

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

      4. associate-*r* 67.4%

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

      5. associate-*r* 67.4%

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

      6. *-commutative 67.4%

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

      7. associate-*r* 69.0%

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

      8. distribute-rgt-in 72.0%

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

      9. +-commutative 72.0%

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

      10. mul-1-neg 72.0%

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

      11. unsub-neg 72.0%

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

      12. *-commutative 72.0%

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

      13. *-commutative 72.0%

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

      14. distribute-rgt-neg-in 72.0%

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

      15. neg-sub0 72.0%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \]

   6. Simplified 72.0%

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

   if 3.8499999999999999e118 < c

   1. Initial program 55.4%

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

      1. associate-+l- 55.4%

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

      2. *-commutative 55.4%

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

      3. sub-neg 55.4%

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

      4. sub-neg 55.4%

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

      5. *-commutative 55.4%

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

   3. Simplified 55.4%

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

   4. Taylor expanded in c around 0 83.1%

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

   5. Taylor expanded in c around inf 80.9%

      \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)}\right) - -1 \cdot \left(b \cdot \left(i \cdot t\right)\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+93}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.16 \cdot 10^{-46}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.85 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(a \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j\right)\right) + b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 4: 52.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -0.14:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-149}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-303}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -3e+118)
     t_1
     (if (<= j -0.14)
       (* a (- (* c j) (* x t)))
       (if (<= j -7.5e-149)
         (* z (- (* x y) (* b c)))
         (if (<= j 3.8e-303)
           (* b (- (* t i) (* z c)))
           (if (<= j 8e+147)
             (+ (* x (- (* y z) (* t a))) (* c (* a j)))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3e+118) {
		tmp = t_1;
	} else if (j <= -0.14) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -7.5e-149) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 3.8e-303) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 8e+147) {
		tmp = (x * ((y * z) - (t * a))) + (c * (a * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-3d+118)) then
        tmp = t_1
    else if (j <= (-0.14d0)) then
        tmp = a * ((c * j) - (x * t))
    else if (j <= (-7.5d-149)) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 3.8d-303) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 8d+147) then
        tmp = (x * ((y * z) - (t * a))) + (c * (a * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3e+118) {
		tmp = t_1;
	} else if (j <= -0.14) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -7.5e-149) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 3.8e-303) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 8e+147) {
		tmp = (x * ((y * z) - (t * a))) + (c * (a * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -3e+118:
		tmp = t_1
	elif j <= -0.14:
		tmp = a * ((c * j) - (x * t))
	elif j <= -7.5e-149:
		tmp = z * ((x * y) - (b * c))
	elif j <= 3.8e-303:
		tmp = b * ((t * i) - (z * c))
	elif j <= 8e+147:
		tmp = (x * ((y * z) - (t * a))) + (c * (a * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3e+118)
		tmp = t_1;
	elseif (j <= -0.14)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (j <= -7.5e-149)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 3.8e-303)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 8e+147)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(c * Float64(a * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -3e+118)
		tmp = t_1;
	elseif (j <= -0.14)
		tmp = a * ((c * j) - (x * t));
	elseif (j <= -7.5e-149)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 3.8e-303)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 8e+147)
		tmp = (x * ((y * z) - (t * a))) + (c * (a * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3e+118], t$95$1, If[LessEqual[j, -0.14], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7.5e-149], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.8e-303], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8e+147], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -3e118 or 7.9999999999999998e147 < j

   1. Initial program 62.0%

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

      1. associate-+l- 62.0%

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

      2. *-commutative 62.0%

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

      3. sub-neg 62.0%

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

      4. sub-neg 62.0%

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

      5. *-commutative 62.0%

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

   3. Simplified 62.0%

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

   4. Taylor expanded in j around inf 69.6%

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

   if -3e118 < j < -0.14000000000000001

   1. Initial program 67.2%

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

      1. associate-+l- 67.2%

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

      2. *-commutative 67.2%

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

      3. sub-neg 67.2%

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

      4. sub-neg 67.2%

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

      5. *-commutative 67.2%

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

   3. Simplified 67.2%

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

   4. Taylor expanded in a around inf 65.2%

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

      1. +-commutative 65.2%

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

      2. mul-1-neg 65.2%

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

      3. unsub-neg 65.2%

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

      4. *-commutative 65.2%

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

   6. Simplified 65.2%

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

   if -0.14000000000000001 < j < -7.49999999999999995e-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 z around inf 71.2%

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

      1. *-commutative 71.2%

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

      2. *-commutative 71.2%

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

   6. Simplified 71.2%

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

   if -7.49999999999999995e-149 < j < 3.80000000000000009e-303

   1. Initial program 72.3%

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

      1. associate-+l- 72.3%

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

      2. *-commutative 72.3%

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

      3. sub-neg 72.3%

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

      4. sub-neg 72.3%

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

      5. *-commutative 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in b around inf 71.4%

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

   if 3.80000000000000009e-303 < j < 7.9999999999999998e147

   1. Initial program 66.6%

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

      1. associate-+l- 66.6%

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

      2. *-commutative 66.6%

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

      3. sub-neg 66.6%

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

      4. sub-neg 66.6%

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

      5. *-commutative 66.6%

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

   3. Simplified 66.6%

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

   4. Taylor expanded in b around 0 57.1%

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

   5. Taylor expanded in a around inf 55.8%

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

   6. Taylor expanded in j around 0 57.6%

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

      1. associate-*r* 55.8%

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

      2. *-commutative 55.8%

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

      3. associate-*l* 58.9%

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

   8. Simplified 58.9%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3 \cdot 10^{+118}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -0.14:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-149}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-303}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+147}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 5: 63.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.2 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-46}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{+133}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -4.2e+102)
     t_1
     (if (<= c -1.5e-46)
       (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
       (if (<= c 7e+133)
         (+ (* y (- (* x z) (* i j))) (* 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 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -4.2e+102) {
		tmp = t_1;
	} else if (c <= -1.5e-46) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (c <= 7e+133) {
		tmp = (y * ((x * z) - (i * j))) + (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 = c * ((a * j) - (z * b))
    if (c <= (-4.2d+102)) then
        tmp = t_1
    else if (c <= (-1.5d-46)) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else if (c <= 7d+133) then
        tmp = (y * ((x * z) - (i * j))) + (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 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -4.2e+102) {
		tmp = t_1;
	} else if (c <= -1.5e-46) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (c <= 7e+133) {
		tmp = (y * ((x * z) - (i * j))) + (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 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -4.2e+102:
		tmp = t_1
	elif c <= -1.5e-46:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	elif c <= 7e+133:
		tmp = (y * ((x * z) - (i * j))) + (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(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -4.2e+102)
		tmp = t_1;
	elseif (c <= -1.5e-46)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (c <= 7e+133)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + 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 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -4.2e+102)
		tmp = t_1;
	elseif (c <= -1.5e-46)
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	elseif (c <= 7e+133)
		tmp = (y * ((x * z) - (i * j))) + (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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.2e+102], t$95$1, If[LessEqual[c, -1.5e-46], 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[c, 7e+133], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.20000000000000003e102 or 6.9999999999999997e133 < c

   1. Initial program 57.0%

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

      1. associate-+l- 57.0%

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

      2. *-commutative 57.0%

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

      3. sub-neg 57.0%

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

      4. sub-neg 57.0%

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

      5. *-commutative 57.0%

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

   3. Simplified 57.0%

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

   4. Taylor expanded in c around inf 74.3%

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

      1. *-commutative 74.3%

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

   6. Simplified 74.3%

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

   if -4.20000000000000003e102 < c < -1.49999999999999994e-46

   1. Initial program 74.0%

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

      1. associate-+l- 74.0%

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

      2. *-commutative 74.0%

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

      3. sub-neg 74.0%

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

      4. sub-neg 74.0%

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

      5. *-commutative 74.0%

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

   3. Simplified 74.0%

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

   4. Taylor expanded in b around 0 70.8%

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

   if -1.49999999999999994e-46 < c < 6.9999999999999997e133

   1. Initial program 75.5%

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

      1. associate-+l- 75.5%

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

      2. *-commutative 75.5%

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

      3. sub-neg 75.5%

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

      4. sub-neg 75.5%

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

      5. *-commutative 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in a around 0 67.1%

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

      1. sub-neg 67.1%

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

      2. *-commutative 67.1%

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

      3. *-commutative 67.1%

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

      4. associate-*r* 67.9%

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

      5. associate-*r* 67.9%

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

      6. *-commutative 67.9%

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

      7. associate-*r* 69.5%

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

      8. distribute-rgt-in 72.4%

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

      9. +-commutative 72.4%

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

      10. mul-1-neg 72.4%

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

      11. unsub-neg 72.4%

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

      12. *-commutative 72.4%

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

      13. *-commutative 72.4%

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

      14. distribute-rgt-neg-in 72.4%

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

      15. neg-sub0 72.4%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \]

   6. Simplified 72.4%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+102}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-46}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{+133}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 6: 51.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -6 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-46}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.1 \cdot 10^{-264}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-37}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 0.056:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -6e+38)
     t_2
     (if (<= c -3e-46)
       (- (* j (* a c)) (* x (* t a)))
       (if (<= c -8e-129)
         t_1
         (if (<= c -4.1e-264)
           (* t (- (* b i) (* x a)))
           (if (<= c 4.6e-54)
             (* x (- (* y z) (* t a)))
             (if (<= c 3.2e-37)
               (* i (- (* t b) (* y j)))
               (if (<= c 0.056) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -6e+38) {
		tmp = t_2;
	} else if (c <= -3e-46) {
		tmp = (j * (a * c)) - (x * (t * a));
	} else if (c <= -8e-129) {
		tmp = t_1;
	} else if (c <= -4.1e-264) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 4.6e-54) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 3.2e-37) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 0.056) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-6d+38)) then
        tmp = t_2
    else if (c <= (-3d-46)) then
        tmp = (j * (a * c)) - (x * (t * a))
    else if (c <= (-8d-129)) then
        tmp = t_1
    else if (c <= (-4.1d-264)) then
        tmp = t * ((b * i) - (x * a))
    else if (c <= 4.6d-54) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 3.2d-37) then
        tmp = i * ((t * b) - (y * j))
    else if (c <= 0.056d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -6e+38) {
		tmp = t_2;
	} else if (c <= -3e-46) {
		tmp = (j * (a * c)) - (x * (t * a));
	} else if (c <= -8e-129) {
		tmp = t_1;
	} else if (c <= -4.1e-264) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 4.6e-54) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 3.2e-37) {
		tmp = i * ((t * b) - (y * j));
	} else if (c <= 0.056) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -6e+38:
		tmp = t_2
	elif c <= -3e-46:
		tmp = (j * (a * c)) - (x * (t * a))
	elif c <= -8e-129:
		tmp = t_1
	elif c <= -4.1e-264:
		tmp = t * ((b * i) - (x * a))
	elif c <= 4.6e-54:
		tmp = x * ((y * z) - (t * a))
	elif c <= 3.2e-37:
		tmp = i * ((t * b) - (y * j))
	elif c <= 0.056:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -6e+38)
		tmp = t_2;
	elseif (c <= -3e-46)
		tmp = Float64(Float64(j * Float64(a * c)) - Float64(x * Float64(t * a)));
	elseif (c <= -8e-129)
		tmp = t_1;
	elseif (c <= -4.1e-264)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (c <= 4.6e-54)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 3.2e-37)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (c <= 0.056)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -6e+38)
		tmp = t_2;
	elseif (c <= -3e-46)
		tmp = (j * (a * c)) - (x * (t * a));
	elseif (c <= -8e-129)
		tmp = t_1;
	elseif (c <= -4.1e-264)
		tmp = t * ((b * i) - (x * a));
	elseif (c <= 4.6e-54)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 3.2e-37)
		tmp = i * ((t * b) - (y * j));
	elseif (c <= 0.056)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6e+38], t$95$2, If[LessEqual[c, -3e-46], N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] - N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8e-129], t$95$1, If[LessEqual[c, -4.1e-264], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.6e-54], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.2e-37], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 0.056], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -6.0000000000000002e38 or 0.0560000000000000012 < c

   1. Initial program 61.6%

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

      1. associate-+l- 61.6%

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

      2. *-commutative 61.6%

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

      3. sub-neg 61.6%

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

      4. sub-neg 61.6%

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

      5. *-commutative 61.6%

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

   3. Simplified 61.6%

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

   4. Taylor expanded in c around inf 68.4%

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

      1. *-commutative 68.4%

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

   6. Simplified 68.4%

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

   if -6.0000000000000002e38 < c < -2.99999999999999987e-46

   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 0 79.9%

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

   5. Taylor expanded in a around inf 68.8%

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

   6. Taylor expanded in y around 0 56.6%

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

      1. mul-1-neg 35.2%

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

      2. associate-*r* 58.2%

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

      3. distribute-rgt-neg-in 58.2%

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

   8. Simplified 74.4%

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

   if -2.99999999999999987e-46 < c < -7.9999999999999994e-129 or 3.1999999999999999e-37 < c < 0.0560000000000000012

   1. Initial program 74.9%

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

      1. associate-+l- 74.9%

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

      2. *-commutative 74.9%

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

      3. sub-neg 74.9%

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

      4. sub-neg 74.9%

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

      5. *-commutative 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in z around inf 77.2%

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

      1. *-commutative 77.2%

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

      2. *-commutative 77.2%

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

   6. Simplified 77.2%

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

   if -7.9999999999999994e-129 < c < -4.10000000000000023e-264

   1. Initial program 67.3%

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

      1. associate-+l- 67.3%

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

      2. *-commutative 67.3%

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

      3. sub-neg 67.3%

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

      4. sub-neg 67.3%

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

      5. *-commutative 67.3%

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

   3. Simplified 67.3%

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

   4. Taylor expanded in t around inf 68.4%

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

      1. distribute-lft-out-- 68.4%

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

      2. *-commutative 68.4%

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

   6. Simplified 68.4%

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

   if -4.10000000000000023e-264 < c < 4.5999999999999998e-54

   1. Initial program 82.5%

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

      1. associate-+l- 82.5%

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

      2. *-commutative 82.5%

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

      3. sub-neg 82.5%

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

      4. sub-neg 82.5%

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

      5. *-commutative 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in x around inf 57.2%

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

   if 4.5999999999999998e-54 < c < 3.1999999999999999e-37

   1. Initial program 50.0%

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

      1. associate-+l- 50.0%

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

      2. *-commutative 50.0%

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

      3. sub-neg 50.0%

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

      4. sub-neg 50.0%

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

      5. *-commutative 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in a around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*r* 100.0%

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

      5. associate-*r* 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-*r* 100.0%

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

      8. distribute-rgt-in 100.0%

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

      9. +-commutative 100.0%

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

      10. mul-1-neg 100.0%

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

      11. unsub-neg 100.0%

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

      12. *-commutative 100.0%

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

      13. *-commutative 100.0%

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

      14. distribute-rgt-neg-in 100.0%

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

      15. neg-sub0 100.0%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \]

   6. Simplified 100.0%

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

   7. Taylor expanded in z around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*r* 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*r* 100.0%

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

      5. distribute-rgt-in 100.0%

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

      6. +-commutative 100.0%

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

      7. mul-1-neg 100.0%

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

      8. sub-neg 100.0%

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

      9. *-commutative 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-46}:\\ \;\;\;\;j \cdot \left(a \cdot c\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-129}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -4.1 \cdot 10^{-264}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-37}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 0.056:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 7: 65.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+189} \lor \neg \left(b \leq 3.5 \cdot 10^{+57}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.65e+189) (not (<= b 3.5e+57)))
   (* b (- (* t i) (* z c)))
   (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.65e+189) || !(b <= 3.5e+57)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.65d+189)) .or. (.not. (b <= 3.5d+57))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.65e+189) || !(b <= 3.5e+57)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.65e+189) or not (b <= 3.5e+57):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.65e+189) || !(b <= 3.5e+57))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.65e+189) || ~((b <= 3.5e+57)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.65e+189], N[Not[LessEqual[b, 3.5e+57]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if b < -1.6500000000000001e189 or 3.4999999999999997e57 < b

   1. Initial program 70.6%

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

      1. associate-+l- 70.6%

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

      2. *-commutative 70.6%

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

      3. sub-neg 70.6%

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

      4. sub-neg 70.6%

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

      5. *-commutative 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in b around inf 80.5%

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

   if -1.6500000000000001e189 < b < 3.4999999999999997e57

   1. Initial program 68.7%

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

      1. associate-+l- 68.7%

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

      2. *-commutative 68.7%

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

      3. sub-neg 68.7%

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

      4. sub-neg 68.7%

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

      5. *-commutative 68.7%

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

   3. Simplified 68.7%

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

   4. Taylor expanded in b around 0 63.6%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+189} \lor \neg \left(b \leq 3.5 \cdot 10^{+57}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 8: 51.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -7.6 \cdot 10^{+118}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -34:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -7.6e+118)
     t_3
     (if (<= j -34.0)
       (* a (- (* c j) (* x t)))
       (if (<= j -8.5e-109)
         t_1
         (if (<= j -9.5e-149)
           t_2
           (if (<= j 1e-276) t_1 (if (<= j 1.4e+90) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -7.6e+118) {
		tmp = t_3;
	} else if (j <= -34.0) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -8.5e-109) {
		tmp = t_1;
	} else if (j <= -9.5e-149) {
		tmp = t_2;
	} else if (j <= 1e-276) {
		tmp = t_1;
	} else if (j <= 1.4e+90) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-7.6d+118)) then
        tmp = t_3
    else if (j <= (-34.0d0)) then
        tmp = a * ((c * j) - (x * t))
    else if (j <= (-8.5d-109)) then
        tmp = t_1
    else if (j <= (-9.5d-149)) then
        tmp = t_2
    else if (j <= 1d-276) then
        tmp = t_1
    else if (j <= 1.4d+90) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -7.6e+118) {
		tmp = t_3;
	} else if (j <= -34.0) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -8.5e-109) {
		tmp = t_1;
	} else if (j <= -9.5e-149) {
		tmp = t_2;
	} else if (j <= 1e-276) {
		tmp = t_1;
	} else if (j <= 1.4e+90) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -7.6e+118:
		tmp = t_3
	elif j <= -34.0:
		tmp = a * ((c * j) - (x * t))
	elif j <= -8.5e-109:
		tmp = t_1
	elif j <= -9.5e-149:
		tmp = t_2
	elif j <= 1e-276:
		tmp = t_1
	elif j <= 1.4e+90:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -7.6e+118)
		tmp = t_3;
	elseif (j <= -34.0)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (j <= -8.5e-109)
		tmp = t_1;
	elseif (j <= -9.5e-149)
		tmp = t_2;
	elseif (j <= 1e-276)
		tmp = t_1;
	elseif (j <= 1.4e+90)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -7.6e+118)
		tmp = t_3;
	elseif (j <= -34.0)
		tmp = a * ((c * j) - (x * t));
	elseif (j <= -8.5e-109)
		tmp = t_1;
	elseif (j <= -9.5e-149)
		tmp = t_2;
	elseif (j <= 1e-276)
		tmp = t_1;
	elseif (j <= 1.4e+90)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.6e+118], t$95$3, If[LessEqual[j, -34.0], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.5e-109], t$95$1, If[LessEqual[j, -9.5e-149], t$95$2, If[LessEqual[j, 1e-276], t$95$1, If[LessEqual[j, 1.4e+90], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -7.60000000000000033e118 or 1.4e90 < j

   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 j around inf 65.0%

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

   if -7.60000000000000033e118 < j < -34

   1. Initial program 67.2%

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

      1. associate-+l- 67.2%

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

      2. *-commutative 67.2%

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

      3. sub-neg 67.2%

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

      4. sub-neg 67.2%

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

      5. *-commutative 67.2%

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

   3. Simplified 67.2%

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

   4. Taylor expanded in a around inf 65.2%

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

      1. +-commutative 65.2%

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

      2. mul-1-neg 65.2%

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

      3. unsub-neg 65.2%

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

      4. *-commutative 65.2%

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

   6. Simplified 65.2%

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

   if -34 < j < -8.50000000000000005e-109 or -9.50000000000000034e-149 < j < 1e-276

   1. Initial program 74.2%

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

      1. associate-+l- 74.2%

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

      2. *-commutative 74.2%

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

      3. sub-neg 74.2%

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

      4. sub-neg 74.2%

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

      5. *-commutative 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in b around inf 64.4%

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

   if -8.50000000000000005e-109 < j < -9.50000000000000034e-149 or 1e-276 < j < 1.4e90

   1. Initial program 73.5%

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

      1. associate-+l- 73.5%

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

      2. *-commutative 73.5%

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

      3. sub-neg 73.5%

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

      4. sub-neg 73.5%

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

      5. *-commutative 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in x around inf 58.7%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.6 \cdot 10^{+118}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -34:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-149}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 10^{-276}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 9: 48.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{+183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-126}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -2.7e+183)
     t_2
     (if (<= b -1e+50)
       t_1
       (if (<= b -1.35e-13)
         t_2
         (if (<= b 5e-304)
           t_1
           (if (<= b 1.5e-126) (* j (- (* a c) (* y i))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.7e+183) {
		tmp = t_2;
	} else if (b <= -1e+50) {
		tmp = t_1;
	} else if (b <= -1.35e-13) {
		tmp = t_2;
	} else if (b <= 5e-304) {
		tmp = t_1;
	} else if (b <= 1.5e-126) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-2.7d+183)) then
        tmp = t_2
    else if (b <= (-1d+50)) then
        tmp = t_1
    else if (b <= (-1.35d-13)) then
        tmp = t_2
    else if (b <= 5d-304) then
        tmp = t_1
    else if (b <= 1.5d-126) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.7e+183) {
		tmp = t_2;
	} else if (b <= -1e+50) {
		tmp = t_1;
	} else if (b <= -1.35e-13) {
		tmp = t_2;
	} else if (b <= 5e-304) {
		tmp = t_1;
	} else if (b <= 1.5e-126) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -2.7e+183:
		tmp = t_2
	elif b <= -1e+50:
		tmp = t_1
	elif b <= -1.35e-13:
		tmp = t_2
	elif b <= 5e-304:
		tmp = t_1
	elif b <= 1.5e-126:
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.7e+183)
		tmp = t_2;
	elseif (b <= -1e+50)
		tmp = t_1;
	elseif (b <= -1.35e-13)
		tmp = t_2;
	elseif (b <= 5e-304)
		tmp = t_1;
	elseif (b <= 1.5e-126)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.7e+183)
		tmp = t_2;
	elseif (b <= -1e+50)
		tmp = t_1;
	elseif (b <= -1.35e-13)
		tmp = t_2;
	elseif (b <= 5e-304)
		tmp = t_1;
	elseif (b <= 1.5e-126)
		tmp = j * ((a * c) - (y * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.7e+183], t$95$2, If[LessEqual[b, -1e+50], t$95$1, If[LessEqual[b, -1.35e-13], t$95$2, If[LessEqual[b, 5e-304], t$95$1, If[LessEqual[b, 1.5e-126], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.69999999999999982e183 or -1.0000000000000001e50 < b < -1.35000000000000005e-13 or 1.5000000000000001e-126 < b

   1. Initial program 69.1%

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

      1. associate-+l- 69.1%

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

      2. *-commutative 69.1%

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

      3. sub-neg 69.1%

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

      4. sub-neg 69.1%

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

      5. *-commutative 69.1%

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

   3. Simplified 69.1%

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

   4. Taylor expanded in b around inf 68.1%

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

   if -2.69999999999999982e183 < b < -1.0000000000000001e50 or -1.35000000000000005e-13 < b < 4.99999999999999965e-304

   1. Initial program 70.9%

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

      1. associate-+l- 70.9%

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

      2. *-commutative 70.9%

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

      3. sub-neg 70.9%

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

      4. sub-neg 70.9%

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

      5. *-commutative 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in a around inf 47.5%

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

      1. +-commutative 47.5%

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

      2. mul-1-neg 47.5%

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

      3. unsub-neg 47.5%

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

      4. *-commutative 47.5%

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

   6. Simplified 47.5%

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

   if 4.99999999999999965e-304 < b < 1.5000000000000001e-126

   1. Initial program 66.0%

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

      1. associate-+l- 66.0%

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

      2. *-commutative 66.0%

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

      3. sub-neg 66.0%

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

      4. sub-neg 66.0%

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

      5. *-commutative 66.0%

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

   3. Simplified 66.0%

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

   4. Taylor expanded in j around inf 51.8%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+183}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{+50}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-304}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-126}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 10: 51.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.6 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -160:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-149}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-277}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -1.6e+122)
     t_1
     (if (<= j -160.0)
       (* a (- (* c j) (* x t)))
       (if (<= j -8.5e-149)
         (* z (- (* x y) (* b c)))
         (if (<= j 7.8e-277)
           (* b (- (* t i) (* z c)))
           (if (<= j 1.16e+91) (* x (- (* y z) (* t a))) 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.6e+122) {
		tmp = t_1;
	} else if (j <= -160.0) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -8.5e-149) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 7.8e-277) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 1.16e+91) {
		tmp = x * ((y * z) - (t * a));
	} 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 = j * ((a * c) - (y * i))
    if (j <= (-1.6d+122)) then
        tmp = t_1
    else if (j <= (-160.0d0)) then
        tmp = a * ((c * j) - (x * t))
    else if (j <= (-8.5d-149)) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 7.8d-277) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 1.16d+91) then
        tmp = x * ((y * z) - (t * a))
    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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.6e+122) {
		tmp = t_1;
	} else if (j <= -160.0) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -8.5e-149) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 7.8e-277) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 1.16e+91) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.6e+122:
		tmp = t_1
	elif j <= -160.0:
		tmp = a * ((c * j) - (x * t))
	elif j <= -8.5e-149:
		tmp = z * ((x * y) - (b * c))
	elif j <= 7.8e-277:
		tmp = b * ((t * i) - (z * c))
	elif j <= 1.16e+91:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.6e+122)
		tmp = t_1;
	elseif (j <= -160.0)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (j <= -8.5e-149)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 7.8e-277)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 1.16e+91)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.6e+122)
		tmp = t_1;
	elseif (j <= -160.0)
		tmp = a * ((c * j) - (x * t));
	elseif (j <= -8.5e-149)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 7.8e-277)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 1.16e+91)
		tmp = x * ((y * z) - (t * a));
	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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.6e+122], t$95$1, If[LessEqual[j, -160.0], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.5e-149], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.8e-277], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.16e+91], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.60000000000000006e122 or 1.1600000000000001e91 < j

   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 j around inf 65.0%

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

   if -1.60000000000000006e122 < j < -160

   1. Initial program 67.2%

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

      1. associate-+l- 67.2%

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

      2. *-commutative 67.2%

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

      3. sub-neg 67.2%

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

      4. sub-neg 67.2%

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

      5. *-commutative 67.2%

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

   3. Simplified 67.2%

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

   4. Taylor expanded in a around inf 65.2%

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

      1. +-commutative 65.2%

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

      2. mul-1-neg 65.2%

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

      3. unsub-neg 65.2%

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

      4. *-commutative 65.2%

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

   6. Simplified 65.2%

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

   if -160 < j < -8.5000000000000006e-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 z around inf 71.2%

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

      1. *-commutative 71.2%

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

      2. *-commutative 71.2%

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

   6. Simplified 71.2%

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

   if -8.5000000000000006e-149 < j < 7.79999999999999973e-277

   1. Initial program 67.2%

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

      1. associate-+l- 67.2%

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

      2. *-commutative 67.2%

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

      3. sub-neg 67.2%

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

      4. sub-neg 67.2%

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

      5. *-commutative 67.2%

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

   3. Simplified 67.2%

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

   4. Taylor expanded in b around inf 64.7%

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

   if 7.79999999999999973e-277 < j < 1.1600000000000001e91

   1. Initial program 71.8%

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

      1. associate-+l- 71.8%

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

      2. *-commutative 71.8%

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

      3. sub-neg 71.8%

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

      4. sub-neg 71.8%

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

      5. *-commutative 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in x around inf 56.5%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.6 \cdot 10^{+122}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -160:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-149}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-277}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 11: 30.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-b \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;c \leq -9.6 \cdot 10^{+215}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-221}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{-272}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* b c)))) (t_2 (* z (* x y))))
   (if (<= c -9.6e+215)
     (* a (* c j))
     (if (<= c -3.3e+40)
       t_1
       (if (<= c -4e-46)
         (* x (* t (- a)))
         (if (<= c -4.4e-221)
           t_2
           (if (<= c -2.1e-272)
             (* i (* t b))
             (if (<= c 1.35e-16) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * -(b * c);
	double t_2 = z * (x * y);
	double tmp;
	if (c <= -9.6e+215) {
		tmp = a * (c * j);
	} else if (c <= -3.3e+40) {
		tmp = t_1;
	} else if (c <= -4e-46) {
		tmp = x * (t * -a);
	} else if (c <= -4.4e-221) {
		tmp = t_2;
	} else if (c <= -2.1e-272) {
		tmp = i * (t * b);
	} else if (c <= 1.35e-16) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * -(b * c)
    t_2 = z * (x * y)
    if (c <= (-9.6d+215)) then
        tmp = a * (c * j)
    else if (c <= (-3.3d+40)) then
        tmp = t_1
    else if (c <= (-4d-46)) then
        tmp = x * (t * -a)
    else if (c <= (-4.4d-221)) then
        tmp = t_2
    else if (c <= (-2.1d-272)) then
        tmp = i * (t * b)
    else if (c <= 1.35d-16) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * -(b * c);
	double t_2 = z * (x * y);
	double tmp;
	if (c <= -9.6e+215) {
		tmp = a * (c * j);
	} else if (c <= -3.3e+40) {
		tmp = t_1;
	} else if (c <= -4e-46) {
		tmp = x * (t * -a);
	} else if (c <= -4.4e-221) {
		tmp = t_2;
	} else if (c <= -2.1e-272) {
		tmp = i * (t * b);
	} else if (c <= 1.35e-16) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * -(b * c)
	t_2 = z * (x * y)
	tmp = 0
	if c <= -9.6e+215:
		tmp = a * (c * j)
	elif c <= -3.3e+40:
		tmp = t_1
	elif c <= -4e-46:
		tmp = x * (t * -a)
	elif c <= -4.4e-221:
		tmp = t_2
	elif c <= -2.1e-272:
		tmp = i * (t * b)
	elif c <= 1.35e-16:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(-Float64(b * c)))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (c <= -9.6e+215)
		tmp = Float64(a * Float64(c * j));
	elseif (c <= -3.3e+40)
		tmp = t_1;
	elseif (c <= -4e-46)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (c <= -4.4e-221)
		tmp = t_2;
	elseif (c <= -2.1e-272)
		tmp = Float64(i * Float64(t * b));
	elseif (c <= 1.35e-16)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * -(b * c);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (c <= -9.6e+215)
		tmp = a * (c * j);
	elseif (c <= -3.3e+40)
		tmp = t_1;
	elseif (c <= -4e-46)
		tmp = x * (t * -a);
	elseif (c <= -4.4e-221)
		tmp = t_2;
	elseif (c <= -2.1e-272)
		tmp = i * (t * b);
	elseif (c <= 1.35e-16)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9.6e+215], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.3e+40], t$95$1, If[LessEqual[c, -4e-46], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.4e-221], t$95$2, If[LessEqual[c, -2.1e-272], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.35e-16], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -9.6000000000000003e215

   1. Initial program 52.4%

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

      1. associate-+l- 52.4%

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

      2. *-commutative 52.4%

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

      3. sub-neg 52.4%

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

      4. sub-neg 52.4%

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

      5. *-commutative 52.4%

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

   3. Simplified 52.4%

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

   4. Taylor expanded in a around inf 63.4%

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

      1. +-commutative 63.4%

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

      2. mul-1-neg 63.4%

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

      3. unsub-neg 63.4%

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

      4. *-commutative 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in j around inf 74.1%

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

   if -9.6000000000000003e215 < c < -3.2999999999999998e40 or 1.35e-16 < c

   1. Initial program 64.8%

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

      1. associate-+l- 64.8%

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

      2. *-commutative 64.8%

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

      3. sub-neg 64.8%

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

      4. sub-neg 64.8%

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

      5. *-commutative 64.8%

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

   3. Simplified 64.8%

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

   4. Taylor expanded in z around inf 54.8%

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

      1. *-commutative 54.8%

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

      2. *-commutative 54.8%

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

   6. Simplified 54.8%

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

   7. Taylor expanded in y around 0 45.9%

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

      1. mul-1-neg 45.9%

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

      2. *-commutative 45.9%

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

      3. distribute-rgt-neg-in 45.9%

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

   9. Simplified 45.9%

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

   if -3.2999999999999998e40 < c < -4.00000000000000009e-46

   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 x around inf 52.8%

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

   5. Taylor expanded in y around 0 35.2%

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

      1. mul-1-neg 35.2%

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

      2. associate-*r* 58.2%

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

      3. distribute-rgt-neg-in 58.2%

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

   7. Simplified 58.2%

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

   if -4.00000000000000009e-46 < c < -4.40000000000000003e-221 or -2.09999999999999987e-272 < c < 1.35e-16

   1. Initial program 76.2%

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

      1. associate-+l- 76.2%

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

      2. *-commutative 76.2%

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

      3. sub-neg 76.2%

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

      4. sub-neg 76.2%

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

      5. *-commutative 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in z around inf 43.8%

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

      1. *-commutative 43.8%

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

      2. *-commutative 43.8%

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

   6. Simplified 43.8%

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

   7. Taylor expanded in y around inf 36.1%

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

   if -4.40000000000000003e-221 < c < -2.09999999999999987e-272

   1. Initial program 66.8%

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

      1. associate-+l- 66.8%

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

      2. *-commutative 66.8%

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

      3. sub-neg 66.8%

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

      4. sub-neg 66.8%

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

      5. *-commutative 66.8%

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

   3. Simplified 66.8%

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

   4. Taylor expanded in a around 0 55.6%

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

      1. sub-neg 55.6%

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

      2. *-commutative 55.6%

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

      3. *-commutative 55.6%

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

      4. associate-*r* 55.6%

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

      5. associate-*r* 55.6%

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

      6. *-commutative 55.6%

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

      7. associate-*r* 66.8%

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

      8. distribute-rgt-in 66.8%

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

      9. +-commutative 66.8%

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

      10. mul-1-neg 66.8%

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

      11. unsub-neg 66.8%

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

      12. *-commutative 66.8%

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

      13. *-commutative 66.8%

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

      14. distribute-rgt-neg-in 66.8%

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

      15. neg-sub0 66.8%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \]

   6. Simplified 66.8%

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

   7. Taylor expanded in z around 0 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-*r* 66.8%

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

      3. *-commutative 66.8%

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

      4. associate-*r* 66.8%

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

      5. distribute-rgt-in 66.8%

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

      6. +-commutative 66.8%

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

      7. mul-1-neg 66.8%

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

      8. sub-neg 66.8%

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

      9. *-commutative 66.8%

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

   9. Simplified 66.8%

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

   10. Taylor expanded in b around inf 66.8%

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

       1. *-commutative 66.8%

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

   12. Simplified 66.8%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.6 \cdot 10^{+215}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-221}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{-272}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \end{array} \]

Alternative 12: 37.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := z \cdot \left(-b \cdot c\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-196}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.45 \cdot 10^{+202}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* z (- (* b c)))))
   (if (<= b -1.2e+199)
     t_2
     (if (<= b 5.3e-278)
       t_1
       (if (<= b 1.25e-196)
         (* (* i j) (- y))
         (if (<= b 5.5e-110) t_1 (if (<= b 3.45e+202) t_2 (* b (* t i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = z * -(b * c);
	double tmp;
	if (b <= -1.2e+199) {
		tmp = t_2;
	} else if (b <= 5.3e-278) {
		tmp = t_1;
	} else if (b <= 1.25e-196) {
		tmp = (i * j) * -y;
	} else if (b <= 5.5e-110) {
		tmp = t_1;
	} else if (b <= 3.45e+202) {
		tmp = t_2;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = z * -(b * c)
    if (b <= (-1.2d+199)) then
        tmp = t_2
    else if (b <= 5.3d-278) then
        tmp = t_1
    else if (b <= 1.25d-196) then
        tmp = (i * j) * -y
    else if (b <= 5.5d-110) then
        tmp = t_1
    else if (b <= 3.45d+202) then
        tmp = t_2
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = z * -(b * c);
	double tmp;
	if (b <= -1.2e+199) {
		tmp = t_2;
	} else if (b <= 5.3e-278) {
		tmp = t_1;
	} else if (b <= 1.25e-196) {
		tmp = (i * j) * -y;
	} else if (b <= 5.5e-110) {
		tmp = t_1;
	} else if (b <= 3.45e+202) {
		tmp = t_2;
	} else {
		tmp = b * (t * i);
	}
	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 <= -1.2e+199:
		tmp = t_2
	elif b <= 5.3e-278:
		tmp = t_1
	elif b <= 1.25e-196:
		tmp = (i * j) * -y
	elif b <= 5.5e-110:
		tmp = t_1
	elif b <= 3.45e+202:
		tmp = t_2
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(z * Float64(-Float64(b * c)))
	tmp = 0.0
	if (b <= -1.2e+199)
		tmp = t_2;
	elseif (b <= 5.3e-278)
		tmp = t_1;
	elseif (b <= 1.25e-196)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (b <= 5.5e-110)
		tmp = t_1;
	elseif (b <= 3.45e+202)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = z * -(b * c);
	tmp = 0.0;
	if (b <= -1.2e+199)
		tmp = t_2;
	elseif (b <= 5.3e-278)
		tmp = t_1;
	elseif (b <= 1.25e-196)
		tmp = (i * j) * -y;
	elseif (b <= 5.5e-110)
		tmp = t_1;
	elseif (b <= 3.45e+202)
		tmp = t_2;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(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, -1.2e+199], t$95$2, If[LessEqual[b, 5.3e-278], t$95$1, If[LessEqual[b, 1.25e-196], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[b, 5.5e-110], t$95$1, If[LessEqual[b, 3.45e+202], t$95$2, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.20000000000000007e199 or 5.4999999999999998e-110 < b < 3.4500000000000002e202

   1. Initial program 64.6%

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

      1. associate-+l- 64.6%

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

      2. *-commutative 64.6%

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

      3. sub-neg 64.6%

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

      4. sub-neg 64.6%

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

      5. *-commutative 64.6%

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

   3. Simplified 64.6%

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

   4. Taylor expanded in z around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. *-commutative 57.2%

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

   6. Simplified 57.2%

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

   7. Taylor expanded in y around 0 47.5%

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

      1. mul-1-neg 47.5%

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

      2. *-commutative 47.5%

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

      3. distribute-rgt-neg-in 47.5%

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

   9. Simplified 47.5%

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

   if -1.20000000000000007e199 < b < 5.3e-278 or 1.2500000000000001e-196 < b < 5.4999999999999998e-110

   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 a around inf 46.5%

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

      1. +-commutative 46.5%

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

      2. mul-1-neg 46.5%

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

      3. unsub-neg 46.5%

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

      4. *-commutative 46.5%

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

   6. Simplified 46.5%

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

   if 5.3e-278 < b < 1.2500000000000001e-196

   1. Initial program 66.7%

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

      1. associate-+l- 66.7%

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

      2. *-commutative 66.7%

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

      3. sub-neg 66.7%

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

      4. sub-neg 66.7%

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

      5. *-commutative 66.7%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in j around inf 56.0%

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

   5. Taylor expanded in a around 0 55.5%

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

      1. associate-*r* 55.5%

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

      2. associate-*r* 55.5%

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

      3. *-commutative 55.5%

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

      4. mul-1-neg 55.5%

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

      5. distribute-rgt-neg-in 55.5%

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

   7. Simplified 55.5%

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

   if 3.4500000000000002e202 < b

   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 a around 0 81.4%

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

      1. sub-neg 81.4%

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

      2. *-commutative 81.4%

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

      3. *-commutative 81.4%

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

      4. associate-*r* 77.7%

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

      5. associate-*r* 77.7%

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

      6. *-commutative 77.7%

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

      7. associate-*r* 77.7%

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

      8. distribute-rgt-in 77.7%

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

      9. +-commutative 77.7%

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

      10. mul-1-neg 77.7%

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

      11. unsub-neg 77.7%

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

      12. *-commutative 77.7%

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

      13. *-commutative 77.7%

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

      14. distribute-rgt-neg-in 77.7%

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

      15. neg-sub0 77.7%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \]

   6. Simplified 77.7%

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

   7. Taylor expanded in z around 0 63.4%

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

      1. *-commutative 63.4%

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

      2. associate-*r* 63.4%

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

      3. *-commutative 63.4%

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

      4. associate-*r* 63.3%

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

      5. distribute-rgt-in 63.3%

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

      6. +-commutative 63.3%

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

      7. mul-1-neg 63.3%

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

      8. sub-neg 63.3%

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

      9. *-commutative 63.3%

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

   9. Simplified 63.3%

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

   10. Taylor expanded in b around inf 63.5%

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

       1. *-commutative 63.5%

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

   12. Simplified 63.5%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+199}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-196}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-110}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.45 \cdot 10^{+202}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 13: 50.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{+127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-123}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -1.65e+127)
     t_2
     (if (<= a -3.8e-20)
       t_1
       (if (<= a -5.2e-123) (* z (* x y)) (if (<= a 3.1e+20) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.65e+127) {
		tmp = t_2;
	} else if (a <= -3.8e-20) {
		tmp = t_1;
	} else if (a <= -5.2e-123) {
		tmp = z * (x * y);
	} else if (a <= 3.1e+20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-1.65d+127)) then
        tmp = t_2
    else if (a <= (-3.8d-20)) then
        tmp = t_1
    else if (a <= (-5.2d-123)) then
        tmp = z * (x * y)
    else if (a <= 3.1d+20) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.65e+127) {
		tmp = t_2;
	} else if (a <= -3.8e-20) {
		tmp = t_1;
	} else if (a <= -5.2e-123) {
		tmp = z * (x * y);
	} else if (a <= 3.1e+20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.65e+127:
		tmp = t_2
	elif a <= -3.8e-20:
		tmp = t_1
	elif a <= -5.2e-123:
		tmp = z * (x * y)
	elif a <= 3.1e+20:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.65e+127)
		tmp = t_2;
	elseif (a <= -3.8e-20)
		tmp = t_1;
	elseif (a <= -5.2e-123)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 3.1e+20)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.65e+127)
		tmp = t_2;
	elseif (a <= -3.8e-20)
		tmp = t_1;
	elseif (a <= -5.2e-123)
		tmp = z * (x * y);
	elseif (a <= 3.1e+20)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e+127], t$95$2, If[LessEqual[a, -3.8e-20], t$95$1, If[LessEqual[a, -5.2e-123], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e+20], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.64999999999999988e127 or 3.1e20 < a

   1. Initial program 57.3%

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

      1. associate-+l- 57.3%

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

      2. *-commutative 57.3%

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

      3. sub-neg 57.3%

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

      4. sub-neg 57.3%

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

      5. *-commutative 57.3%

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

   3. Simplified 57.3%

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

   4. Taylor expanded in a around inf 68.0%

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

      1. +-commutative 68.0%

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

      2. mul-1-neg 68.0%

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

      3. unsub-neg 68.0%

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

      4. *-commutative 68.0%

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

   6. Simplified 68.0%

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

   if -1.64999999999999988e127 < a < -3.7999999999999998e-20 or -5.1999999999999999e-123 < a < 3.1e20

   1. Initial program 75.7%

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

      1. associate-+l- 75.7%

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

      2. *-commutative 75.7%

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

      3. sub-neg 75.7%

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

      4. sub-neg 75.7%

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

      5. *-commutative 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in b around inf 52.6%

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

   if -3.7999999999999998e-20 < a < -5.1999999999999999e-123

   1. Initial program 79.1%

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

      1. associate-+l- 79.1%

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

      2. *-commutative 79.1%

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

      3. sub-neg 79.1%

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

      4. sub-neg 79.1%

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

      5. *-commutative 79.1%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in z around inf 62.0%

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

      1. *-commutative 62.0%

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

      2. *-commutative 62.0%

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

   6. Simplified 62.0%

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

   7. Taylor expanded in y around inf 57.2%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-123}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+20}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 14: 28.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;b \leq -3.9 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-31}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 0.3:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* t (* b i))))
   (if (<= b -3.9e-10)
     t_2
     (if (<= b -4.8e-31)
       (* j (* a c))
       (if (<= b 1.6e-82)
         t_1
         (if (<= b 0.3) t_2 (if (<= b 2.45e+67) t_1 (* b (* t i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = t * (b * i);
	double tmp;
	if (b <= -3.9e-10) {
		tmp = t_2;
	} else if (b <= -4.8e-31) {
		tmp = j * (a * c);
	} else if (b <= 1.6e-82) {
		tmp = t_1;
	} else if (b <= 0.3) {
		tmp = t_2;
	} else if (b <= 2.45e+67) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = t * (b * i)
    if (b <= (-3.9d-10)) then
        tmp = t_2
    else if (b <= (-4.8d-31)) then
        tmp = j * (a * c)
    else if (b <= 1.6d-82) then
        tmp = t_1
    else if (b <= 0.3d0) then
        tmp = t_2
    else if (b <= 2.45d+67) then
        tmp = t_1
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = t * (b * i);
	double tmp;
	if (b <= -3.9e-10) {
		tmp = t_2;
	} else if (b <= -4.8e-31) {
		tmp = j * (a * c);
	} else if (b <= 1.6e-82) {
		tmp = t_1;
	} else if (b <= 0.3) {
		tmp = t_2;
	} else if (b <= 2.45e+67) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = t * (b * i)
	tmp = 0
	if b <= -3.9e-10:
		tmp = t_2
	elif b <= -4.8e-31:
		tmp = j * (a * c)
	elif b <= 1.6e-82:
		tmp = t_1
	elif b <= 0.3:
		tmp = t_2
	elif b <= 2.45e+67:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (b <= -3.9e-10)
		tmp = t_2;
	elseif (b <= -4.8e-31)
		tmp = Float64(j * Float64(a * c));
	elseif (b <= 1.6e-82)
		tmp = t_1;
	elseif (b <= 0.3)
		tmp = t_2;
	elseif (b <= 2.45e+67)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = t * (b * i);
	tmp = 0.0;
	if (b <= -3.9e-10)
		tmp = t_2;
	elseif (b <= -4.8e-31)
		tmp = j * (a * c);
	elseif (b <= 1.6e-82)
		tmp = t_1;
	elseif (b <= 0.3)
		tmp = t_2;
	elseif (b <= 2.45e+67)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.9e-10], t$95$2, If[LessEqual[b, -4.8e-31], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e-82], t$95$1, If[LessEqual[b, 0.3], t$95$2, If[LessEqual[b, 2.45e+67], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.9e-10 or 1.6000000000000001e-82 < b < 0.299999999999999989

   1. Initial program 66.8%

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

      1. associate-+l- 66.8%

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

      2. *-commutative 66.8%

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

      3. sub-neg 66.8%

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

      4. sub-neg 66.8%

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

      5. *-commutative 66.8%

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

   3. Simplified 66.8%

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

   4. Taylor expanded in a around 0 62.0%

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

      1. sub-neg 62.0%

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

      2. *-commutative 62.0%

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

      3. *-commutative 62.0%

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

      4. associate-*r* 63.2%

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

      5. associate-*r* 63.2%

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

      6. *-commutative 63.2%

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

      7. associate-*r* 63.4%

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

      8. distribute-rgt-in 66.0%

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

      9. +-commutative 66.0%

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

      10. mul-1-neg 66.0%

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

      11. unsub-neg 66.0%

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

      12. *-commutative 66.0%

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

      13. *-commutative 66.0%

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

      14. distribute-rgt-neg-in 66.0%

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

      15. neg-sub0 66.0%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \]

   6. Simplified 66.0%

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

   7. Taylor expanded in z around 0 37.7%

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

      1. *-commutative 37.7%

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

      2. associate-*r* 37.7%

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

      3. *-commutative 37.7%

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

      4. associate-*r* 41.4%

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

      5. distribute-rgt-in 41.4%

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

      6. +-commutative 41.4%

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

      7. mul-1-neg 41.4%

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

      8. sub-neg 41.4%

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

      9. *-commutative 41.4%

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

   9. Simplified 41.4%

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

   10. Taylor expanded in b around inf 30.4%

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

       1. associate-*r* 36.4%

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

       2. *-commutative 36.4%

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

   12. Simplified 36.4%

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

   if -3.9e-10 < b < -4.8e-31

   1. Initial program 88.7%

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

      1. associate-+l- 88.7%

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

      2. *-commutative 88.7%

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

      3. sub-neg 88.7%

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

      4. sub-neg 88.7%

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

      5. *-commutative 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in j around inf 60.3%

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

   5. Taylor expanded in a around inf 60.4%

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

   if -4.8e-31 < b < 1.6000000000000001e-82 or 0.299999999999999989 < b < 2.44999999999999995e67

   1. Initial program 67.7%

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

      1. associate-+l- 67.7%

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

      2. *-commutative 67.7%

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

      3. sub-neg 67.7%

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

      4. sub-neg 67.7%

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

      5. *-commutative 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in x around inf 49.5%

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

   5. Taylor expanded in y around inf 34.4%

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

   if 2.44999999999999995e67 < b

   1. Initial program 73.0%

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

      1. associate-+l- 73.0%

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

      2. *-commutative 73.0%

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

      3. sub-neg 73.0%

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

      4. sub-neg 73.0%

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

      5. *-commutative 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in a around 0 76.6%

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

      1. sub-neg 76.6%

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

      2. *-commutative 76.6%

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

      3. *-commutative 76.6%

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

      4. associate-*r* 74.8%

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

      5. associate-*r* 74.8%

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

      6. *-commutative 74.8%

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

      7. associate-*r* 76.6%

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

      8. distribute-rgt-in 76.6%

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

      9. +-commutative 76.6%

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

      10. mul-1-neg 76.6%

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

      11. unsub-neg 76.6%

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

      12. *-commutative 76.6%

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

      13. *-commutative 76.6%

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

      14. distribute-rgt-neg-in 76.6%

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

      15. neg-sub0 76.6%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \]

   6. Simplified 76.6%

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

   7. Taylor expanded in z around 0 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-*r* 51.6%

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

      3. *-commutative 51.6%

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

      4. associate-*r* 50.0%

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

      5. distribute-rgt-in 50.0%

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

      6. +-commutative 50.0%

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

      7. mul-1-neg 50.0%

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

      8. sub-neg 50.0%

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

      9. *-commutative 50.0%

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

   9. Simplified 50.0%

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

   10. Taylor expanded in b around inf 48.5%

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

       1. *-commutative 48.5%

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

   12. Simplified 48.5%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-31}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 0.3:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 2.45 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 15: 29.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-154}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+94}:\\ \;\;\;\;a \cdot \left(-x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -7.2e+130)
   (* x (* y z))
   (if (<= z -2.35e-154)
     (* a (* c j))
     (if (<= z 5.2e-148)
       (* b (* t i))
       (if (<= z 6e+94) (* a (- (* x t))) (* z (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -7.2e+130) {
		tmp = x * (y * z);
	} else if (z <= -2.35e-154) {
		tmp = a * (c * j);
	} else if (z <= 5.2e-148) {
		tmp = b * (t * i);
	} else if (z <= 6e+94) {
		tmp = a * -(x * t);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-7.2d+130)) then
        tmp = x * (y * z)
    else if (z <= (-2.35d-154)) then
        tmp = a * (c * j)
    else if (z <= 5.2d-148) then
        tmp = b * (t * i)
    else if (z <= 6d+94) then
        tmp = a * -(x * t)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -7.2e+130) {
		tmp = x * (y * z);
	} else if (z <= -2.35e-154) {
		tmp = a * (c * j);
	} else if (z <= 5.2e-148) {
		tmp = b * (t * i);
	} else if (z <= 6e+94) {
		tmp = a * -(x * t);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -7.2e+130:
		tmp = x * (y * z)
	elif z <= -2.35e-154:
		tmp = a * (c * j)
	elif z <= 5.2e-148:
		tmp = b * (t * i)
	elif z <= 6e+94:
		tmp = a * -(x * t)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -7.2e+130)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -2.35e-154)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 5.2e-148)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= 6e+94)
		tmp = Float64(a * Float64(-Float64(x * t)));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -7.2e+130)
		tmp = x * (y * z);
	elseif (z <= -2.35e-154)
		tmp = a * (c * j);
	elseif (z <= 5.2e-148)
		tmp = b * (t * i);
	elseif (z <= 6e+94)
		tmp = a * -(x * t);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -7.2e+130], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.35e-154], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-148], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+94], N[(a * (-N[(x * t), $MachinePrecision])), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.2000000000000002e130

   1. Initial program 57.5%

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

      1. associate-+l- 57.5%

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

      2. *-commutative 57.5%

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

      3. sub-neg 57.5%

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

      4. sub-neg 57.5%

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

      5. *-commutative 57.5%

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

   3. Simplified 57.5%

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

   4. Taylor expanded in x around inf 44.3%

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

   5. Taylor expanded in y around inf 46.5%

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

   if -7.2000000000000002e130 < z < -2.3500000000000001e-154

   1. Initial program 82.1%

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

      1. associate-+l- 82.1%

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

      2. *-commutative 82.1%

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

      3. sub-neg 82.1%

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

      4. sub-neg 82.1%

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

      5. *-commutative 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in a around inf 50.0%

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

      1. +-commutative 50.0%

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

      2. mul-1-neg 50.0%

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

      3. unsub-neg 50.0%

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

      4. *-commutative 50.0%

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

   6. Simplified 50.0%

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

   7. Taylor expanded in j around inf 40.0%

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

   if -2.3500000000000001e-154 < z < 5.20000000000000015e-148

   1. Initial program 69.2%

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

      1. associate-+l- 69.2%

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

      2. *-commutative 69.2%

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

      3. sub-neg 69.2%

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

      4. sub-neg 69.2%

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

      5. *-commutative 69.2%

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

   3. Simplified 69.2%

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

   4. Taylor expanded in a around 0 69.1%

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

      1. sub-neg 69.1%

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

      2. *-commutative 69.1%

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

      3. *-commutative 69.1%

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

      4. associate-*r* 70.7%

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

      5. associate-*r* 70.7%

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

      6. *-commutative 70.7%

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

      7. associate-*r* 70.7%

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

      8. distribute-rgt-in 70.7%

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

      9. +-commutative 70.7%

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

      10. mul-1-neg 70.7%

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

      11. unsub-neg 70.7%

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

      12. *-commutative 70.7%

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

      13. *-commutative 70.7%

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

      14. distribute-rgt-neg-in 70.7%

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

      15. neg-sub0 70.7%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \]

   6. Simplified 70.7%

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

   7. Taylor expanded in z around 0 58.9%

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

      1. *-commutative 58.9%

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

      2. associate-*r* 58.9%

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

      3. *-commutative 58.9%

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

      4. associate-*r* 57.3%

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

      5. distribute-rgt-in 57.3%

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

      6. +-commutative 57.3%

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

      7. mul-1-neg 57.3%

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

      8. sub-neg 57.3%

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

      9. *-commutative 57.3%

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

   9. Simplified 57.3%

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

   10. Taylor expanded in b around inf 45.5%

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

       1. *-commutative 45.5%

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

   12. Simplified 45.5%

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

   if 5.20000000000000015e-148 < z < 6.0000000000000001e94

   1. Initial program 79.7%

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

      1. associate-+l- 79.7%

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

      2. *-commutative 79.7%

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

      3. sub-neg 79.7%

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

      4. sub-neg 79.7%

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

      5. *-commutative 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in a around inf 40.0%

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

      1. +-commutative 40.0%

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

      2. mul-1-neg 40.0%

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

      3. unsub-neg 40.0%

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

      4. *-commutative 40.0%

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

   6. Simplified 40.0%

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

   7. Taylor expanded in j around 0 29.2%

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

      1. mul-1-neg 29.2%

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

      2. distribute-rgt-neg-in 29.2%

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

   9. Simplified 29.2%

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

   if 6.0000000000000001e94 < z

   1. Initial program 54.5%

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

      1. associate-+l- 54.5%

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

      2. *-commutative 54.5%

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

      3. sub-neg 54.5%

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

      4. sub-neg 54.5%

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

      5. *-commutative 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in z around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. *-commutative 67.0%

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

   6. Simplified 67.0%

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

   7. Taylor expanded in y around inf 34.2%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-154}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+94}:\\ \;\;\;\;a \cdot \left(-x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 16: 27.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-b \cdot c\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.9 \cdot 10^{-32}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-166}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+201}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* b c)))))
   (if (<= b -8e+198)
     t_1
     (if (<= b -4.9e-32)
       (* a (* c j))
       (if (<= b 1.4e-166)
         (* x (* y z))
         (if (<= b 4.3e+201) t_1 (* b (* t i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * -(b * c);
	double tmp;
	if (b <= -8e+198) {
		tmp = t_1;
	} else if (b <= -4.9e-32) {
		tmp = a * (c * j);
	} else if (b <= 1.4e-166) {
		tmp = x * (y * z);
	} else if (b <= 4.3e+201) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -(b * c)
    if (b <= (-8d+198)) then
        tmp = t_1
    else if (b <= (-4.9d-32)) then
        tmp = a * (c * j)
    else if (b <= 1.4d-166) then
        tmp = x * (y * z)
    else if (b <= 4.3d+201) then
        tmp = t_1
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * -(b * c);
	double tmp;
	if (b <= -8e+198) {
		tmp = t_1;
	} else if (b <= -4.9e-32) {
		tmp = a * (c * j);
	} else if (b <= 1.4e-166) {
		tmp = x * (y * z);
	} else if (b <= 4.3e+201) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * -(b * c)
	tmp = 0
	if b <= -8e+198:
		tmp = t_1
	elif b <= -4.9e-32:
		tmp = a * (c * j)
	elif b <= 1.4e-166:
		tmp = x * (y * z)
	elif b <= 4.3e+201:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(-Float64(b * c)))
	tmp = 0.0
	if (b <= -8e+198)
		tmp = t_1;
	elseif (b <= -4.9e-32)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 1.4e-166)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 4.3e+201)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * -(b * c);
	tmp = 0.0;
	if (b <= -8e+198)
		tmp = t_1;
	elseif (b <= -4.9e-32)
		tmp = a * (c * j);
	elseif (b <= 1.4e-166)
		tmp = x * (y * z);
	elseif (b <= 4.3e+201)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[b, -8e+198], t$95$1, If[LessEqual[b, -4.9e-32], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e-166], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.3e+201], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.00000000000000014e198 or 1.4e-166 < b < 4.2999999999999999e201

   1. Initial program 61.2%

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

      1. associate-+l- 61.2%

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

      2. *-commutative 61.2%

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

      3. sub-neg 61.2%

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

      4. sub-neg 61.2%

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

      5. *-commutative 61.2%

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

   3. Simplified 61.2%

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

   4. Taylor expanded in z around inf 55.5%

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

      1. *-commutative 55.5%

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

      2. *-commutative 55.5%

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

   6. Simplified 55.5%

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

   7. Taylor expanded in y around 0 44.8%

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

      1. mul-1-neg 44.8%

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

      2. *-commutative 44.8%

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

      3. distribute-rgt-neg-in 44.8%

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

   9. Simplified 44.8%

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

   if -8.00000000000000014e198 < b < -4.8999999999999998e-32

   1. Initial program 76.5%

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

      1. associate-+l- 76.5%

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

      2. *-commutative 76.5%

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

      3. sub-neg 76.5%

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

      4. sub-neg 76.5%

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

      5. *-commutative 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in a around inf 51.2%

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

      1. +-commutative 51.2%

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

      2. mul-1-neg 51.2%

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

      3. unsub-neg 51.2%

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

      4. *-commutative 51.2%

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

   6. Simplified 51.2%

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

   7. Taylor expanded in j around inf 34.5%

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

   if -4.8999999999999998e-32 < b < 1.4e-166

   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 x around inf 50.9%

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

   5. Taylor expanded in y around inf 36.1%

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

   if 4.2999999999999999e201 < b

   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 a around 0 81.4%

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

      1. sub-neg 81.4%

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

      2. *-commutative 81.4%

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

      3. *-commutative 81.4%

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

      4. associate-*r* 77.7%

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

      5. associate-*r* 77.7%

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

      6. *-commutative 77.7%

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

      7. associate-*r* 77.7%

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

      8. distribute-rgt-in 77.7%

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

      9. +-commutative 77.7%

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

      10. mul-1-neg 77.7%

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

      11. unsub-neg 77.7%

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

      12. *-commutative 77.7%

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

      13. *-commutative 77.7%

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

      14. distribute-rgt-neg-in 77.7%

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

      15. neg-sub0 77.7%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \]

   6. Simplified 77.7%

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

   7. Taylor expanded in z around 0 63.4%

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

      1. *-commutative 63.4%

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

      2. associate-*r* 63.4%

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

      3. *-commutative 63.4%

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

      4. associate-*r* 63.3%

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

      5. distribute-rgt-in 63.3%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      6. +-commutative 63.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      7. mul-1-neg 63.3%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      8. sub-neg 63.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      9. *-commutative 63.3%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   9. Simplified 63.3%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   10. Taylor expanded in b around inf 63.5%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   11. Step-by-step derivation

       1. *-commutative 63.5%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   12. Simplified 63.5%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+198}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;b \leq -4.9 \cdot 10^{-32}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-166}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+201}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 17: 29.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-156}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+72}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -3.8e+134)
   (* x (* y z))
   (if (<= z -2.3e-156)
     (* a (* c j))
     (if (<= z 2.45e+72) (* b (* t i)) (* z (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3.8e+134) {
		tmp = x * (y * z);
	} else if (z <= -2.3e-156) {
		tmp = a * (c * j);
	} else if (z <= 2.45e+72) {
		tmp = b * (t * i);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-3.8d+134)) then
        tmp = x * (y * z)
    else if (z <= (-2.3d-156)) then
        tmp = a * (c * j)
    else if (z <= 2.45d+72) then
        tmp = b * (t * i)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3.8e+134) {
		tmp = x * (y * z);
	} else if (z <= -2.3e-156) {
		tmp = a * (c * j);
	} else if (z <= 2.45e+72) {
		tmp = b * (t * i);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -3.8e+134:
		tmp = x * (y * z)
	elif z <= -2.3e-156:
		tmp = a * (c * j)
	elif z <= 2.45e+72:
		tmp = b * (t * i)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -3.8e+134)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -2.3e-156)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 2.45e+72)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -3.8e+134)
		tmp = x * (y * z);
	elseif (z <= -2.3e-156)
		tmp = a * (c * j);
	elseif (z <= 2.45e+72)
		tmp = b * (t * i);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -3.8e+134], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-156], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e+72], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.79999999999999998e134

   1. Initial program 57.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 57.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 57.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 57.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 57.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 57.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 57.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in x around inf 44.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in y around inf 46.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -3.79999999999999998e134 < z < -2.3e-156

   1. Initial program 82.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 82.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 82.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 82.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 82.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 82.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 50.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 50.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 50.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 40.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -2.3e-156 < z < 2.45000000000000003e72

   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 a around 0 64.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   5. Step-by-step derivation

      1. sub-neg 64.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      2. *-commutative 64.7%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      3. *-commutative 64.7%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

      4. associate-*r* 64.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      5. associate-*r* 64.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      6. *-commutative 64.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      7. associate-*r* 64.7%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      8. distribute-rgt-in 65.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      9. +-commutative 65.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      10. mul-1-neg 65.7%

          \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      11. unsub-neg 65.7%

          \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      12. *-commutative 65.7%

          \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      13. *-commutative 65.7%

          \[\leadsto y \cdot \left(z \cdot x - \color{blue}{j \cdot i}\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      14. distribute-rgt-neg-in 65.7%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + \color{blue}{b \cdot \left(-\left(z \cdot c - t \cdot i\right)\right)} \]

      15. neg-sub0 65.7%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \]

   6. Simplified 65.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in z around 0 48.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + b \cdot \left(i \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 48.4%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot y\right) \cdot i\right)} + b \cdot \left(i \cdot t\right) \]

      2. associate-*r* 48.4%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right) \cdot i} + b \cdot \left(i \cdot t\right) \]

      3. *-commutative 48.4%

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + b \cdot \color{blue}{\left(t \cdot i\right)} \]

      4. associate-*r* 49.5%

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + \color{blue}{\left(b \cdot t\right) \cdot i} \]

      5. distribute-rgt-in 49.5%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      6. +-commutative 49.5%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      7. mul-1-neg 49.5%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      8. sub-neg 49.5%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      9. *-commutative 49.5%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   9. Simplified 49.5%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   10. Taylor expanded in b around inf 33.6%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   11. Step-by-step derivation

       1. *-commutative 33.6%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   12. Simplified 33.6%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if 2.45000000000000003e72 < z

   1. Initial program 55.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 55.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 55.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 55.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 55.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 55.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 55.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 65.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 65.1%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 65.1%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   6. Simplified 65.1%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   7. Taylor expanded in y around inf 32.4%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-156}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+72}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 18: 29.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.00125 \lor \neg \left(t \leq 1.65 \cdot 10^{-66}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -0.00125) (not (<= t 1.65e-66))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -0.00125) || !(t <= 1.65e-66)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-0.00125d0)) .or. (.not. (t <= 1.65d-66))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -0.00125) || !(t <= 1.65e-66)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -0.00125) or not (t <= 1.65e-66):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -0.00125) || !(t <= 1.65e-66))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -0.00125) || ~((t <= 1.65e-66)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -0.00125], N[Not[LessEqual[t, 1.65e-66]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.00125000000000000003 or 1.6499999999999999e-66 < t

   1. Initial program 62.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 62.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 62.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 62.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 62.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 62.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 62.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around 0 52.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   5. Step-by-step derivation

      1. sub-neg 52.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      2. *-commutative 52.0%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      3. *-commutative 52.0%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

      4. associate-*r* 52.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      5. associate-*r* 52.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      6. *-commutative 52.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      7. associate-*r* 53.5%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      8. distribute-rgt-in 54.9%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      9. +-commutative 54.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      10. mul-1-neg 54.9%

          \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      11. unsub-neg 54.9%

          \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      12. *-commutative 54.9%

          \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      13. *-commutative 54.9%

          \[\leadsto y \cdot \left(z \cdot x - \color{blue}{j \cdot i}\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      14. distribute-rgt-neg-in 54.9%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + \color{blue}{b \cdot \left(-\left(z \cdot c - t \cdot i\right)\right)} \]

      15. neg-sub0 54.9%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \]

   6. Simplified 54.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in z around 0 35.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + b \cdot \left(i \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.8%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot y\right) \cdot i\right)} + b \cdot \left(i \cdot t\right) \]

      2. associate-*r* 35.8%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right) \cdot i} + b \cdot \left(i \cdot t\right) \]

      3. *-commutative 35.8%

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + b \cdot \color{blue}{\left(t \cdot i\right)} \]

      4. associate-*r* 38.7%

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + \color{blue}{\left(b \cdot t\right) \cdot i} \]

      5. distribute-rgt-in 39.4%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      6. +-commutative 39.4%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      7. mul-1-neg 39.4%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      8. sub-neg 39.4%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      9. *-commutative 39.4%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   9. Simplified 39.4%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   10. Taylor expanded in b around inf 35.7%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   11. Step-by-step derivation

       1. *-commutative 35.7%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   12. Simplified 35.7%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -0.00125000000000000003 < t < 1.6499999999999999e-66

   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 33.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 33.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 33.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 33.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 33.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 33.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 32.1%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.00125 \lor \neg \left(t \leq 1.65 \cdot 10^{-66}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 19: 29.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.027:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-66}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -0.027)
   (* i (* t b))
   (if (<= t 8.8e-66) (* a (* c j)) (* b (* t i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -0.027) {
		tmp = i * (t * b);
	} else if (t <= 8.8e-66) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-0.027d0)) then
        tmp = i * (t * b)
    else if (t <= 8.8d-66) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -0.027) {
		tmp = i * (t * b);
	} else if (t <= 8.8e-66) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -0.027:
		tmp = i * (t * b)
	elif t <= 8.8e-66:
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -0.027)
		tmp = Float64(i * Float64(t * b));
	elseif (t <= 8.8e-66)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -0.027)
		tmp = i * (t * b);
	elseif (t <= 8.8e-66)
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -0.027], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e-66], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.0269999999999999997

   1. Initial program 65.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 65.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 65.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 65.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 65.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 65.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 65.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around 0 50.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   5. Step-by-step derivation

      1. sub-neg 50.3%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      2. *-commutative 50.3%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      3. *-commutative 50.3%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

      4. associate-*r* 51.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      5. associate-*r* 51.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      6. *-commutative 51.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      7. associate-*r* 50.6%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      8. distribute-rgt-in 53.5%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      9. +-commutative 53.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      10. mul-1-neg 53.5%

          \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      11. unsub-neg 53.5%

          \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      12. *-commutative 53.5%

          \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      13. *-commutative 53.5%

          \[\leadsto y \cdot \left(z \cdot x - \color{blue}{j \cdot i}\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      14. distribute-rgt-neg-in 53.5%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + \color{blue}{b \cdot \left(-\left(z \cdot c - t \cdot i\right)\right)} \]

      15. neg-sub0 53.5%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \]

   6. Simplified 53.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in z around 0 33.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + b \cdot \left(i \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 33.6%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot y\right) \cdot i\right)} + b \cdot \left(i \cdot t\right) \]

      2. associate-*r* 33.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right) \cdot i} + b \cdot \left(i \cdot t\right) \]

      3. *-commutative 33.6%

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + b \cdot \color{blue}{\left(t \cdot i\right)} \]

      4. associate-*r* 37.8%

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + \color{blue}{\left(b \cdot t\right) \cdot i} \]

      5. distribute-rgt-in 39.3%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      6. +-commutative 39.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      7. mul-1-neg 39.3%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      8. sub-neg 39.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      9. *-commutative 39.3%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   9. Simplified 39.3%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   10. Taylor expanded in b around inf 39.2%

       \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
   11. Step-by-step derivation

       1. *-commutative 39.2%

          \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   12. Simplified 39.2%

       \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   if -0.0269999999999999997 < t < 8.8000000000000004e-66

   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 33.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 33.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 33.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 33.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 33.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   6. Simplified 33.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   7. Taylor expanded in j around inf 32.1%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   if 8.8000000000000004e-66 < t

   1. Initial program 60.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 60.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 60.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 60.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 60.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 60.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 60.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around 0 53.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   5. Step-by-step derivation

      1. sub-neg 53.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      2. *-commutative 53.5%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      3. *-commutative 53.5%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

      4. associate-*r* 53.5%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      5. associate-*r* 53.5%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + x \cdot \left(y \cdot z\right)\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      6. *-commutative 53.5%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)}\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      7. associate-*r* 56.2%

         \[\leadsto \left(\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y}\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      8. distribute-rgt-in 56.2%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      9. +-commutative 56.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      10. mul-1-neg 56.2%

          \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      11. unsub-neg 56.2%

          \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      12. *-commutative 56.2%

          \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      13. *-commutative 56.2%

          \[\leadsto y \cdot \left(z \cdot x - \color{blue}{j \cdot i}\right) + \left(-b \cdot \left(z \cdot c - t \cdot i\right)\right) \]

      14. distribute-rgt-neg-in 56.2%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + \color{blue}{b \cdot \left(-\left(z \cdot c - t \cdot i\right)\right)} \]

      15. neg-sub0 56.2%

          \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \]

   6. Simplified 56.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   7. Taylor expanded in z around 0 37.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + b \cdot \left(i \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 37.9%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(j \cdot y\right) \cdot i\right)} + b \cdot \left(i \cdot t\right) \]

      2. associate-*r* 37.9%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right) \cdot i} + b \cdot \left(i \cdot t\right) \]

      3. *-commutative 37.9%

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + b \cdot \color{blue}{\left(t \cdot i\right)} \]

      4. associate-*r* 39.5%

         \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i + \color{blue}{\left(b \cdot t\right) \cdot i} \]

      5. distribute-rgt-in 39.5%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      6. +-commutative 39.5%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      7. mul-1-neg 39.5%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      8. sub-neg 39.5%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      9. *-commutative 39.5%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   9. Simplified 39.5%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   10. Taylor expanded in b around inf 35.1%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   11. Step-by-step derivation

       1. *-commutative 35.1%

          \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   12. Simplified 35.1%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.027:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-66}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 20: 23.1% 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 69.3%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. associate-+l- 69.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

   2. *-commutative 69.3%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

   3. sub-neg 69.3%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

   4. sub-neg 69.3%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

   5. *-commutative 69.3%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

3. Simplified 69.3%

   \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

4. Taylor expanded in a around inf 36.7%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
5. Step-by-step derivation

   1. +-commutative 36.7%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 36.7%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 36.7%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 36.7%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

6. Simplified 36.7%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

7. Taylor expanded in j around inf 22.9%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

8. Final simplification 22.9%

   \[\leadsto a \cdot \left(c \cdot j\right) \]

Developer target: 59.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023271 
(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)))))