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

Percentage Accurate: 73.1% → 82.8%

Time: 18.8s

Alternatives: 22

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: 73.1% 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: 82.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(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]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(j * N[(N[(x * N[(z / j), $MachinePrecision]), $MachinePrecision] - i), $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 92.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 45.1%

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

      1. +-commutative 45.1%

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

      2. mul-1-neg 45.1%

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

      3. unsub-neg 45.1%

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

      4. *-commutative 45.1%

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

   5. Simplified 45.1%

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

   6. Taylor expanded in j around inf 46.9%

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

      1. associate-/l* 53.0%

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

   8. Simplified 53.0%

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

4. Final simplification 82.9%

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

Alternative 2: 66.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{-33}:\\ \;\;\;\;t\_3 + t\_2\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-214}:\\ \;\;\;\;t\_3 + t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-129}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) - b \cdot \left(z \cdot c\right)\right) + \left(a \cdot \left(c \cdot j\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= x -1.1e-33)
     (+ t_3 t_2)
     (if (<= x 1.32e-214)
       (+ t_3 t_1)
       (if (<= x 1.7e-129)
         (+ (- (* y (* x z)) (* b (* z c))) (- (* a (* c j)) (* i (* y j))))
         (+ t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (x <= -1.1e-33) {
		tmp = t_3 + t_2;
	} else if (x <= 1.32e-214) {
		tmp = t_3 + t_1;
	} else if (x <= 1.7e-129) {
		tmp = ((y * (x * z)) - (b * (z * c))) + ((a * (c * j)) - (i * (y * j)));
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((a * c) - (y * i))
    if (x <= (-1.1d-33)) then
        tmp = t_3 + t_2
    else if (x <= 1.32d-214) then
        tmp = t_3 + t_1
    else if (x <= 1.7d-129) then
        tmp = ((y * (x * z)) - (b * (z * c))) + ((a * (c * j)) - (i * (y * j)))
    else
        tmp = t_2 + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (x <= -1.1e-33) {
		tmp = t_3 + t_2;
	} else if (x <= 1.32e-214) {
		tmp = t_3 + t_1;
	} else if (x <= 1.7e-129) {
		tmp = ((y * (x * z)) - (b * (z * c))) + ((a * (c * j)) - (i * (y * j)));
	} else {
		tmp = t_2 + t_1;
	}
	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 x <= -1.1e-33:
		tmp = t_3 + t_2
	elif x <= 1.32e-214:
		tmp = t_3 + t_1
	elif x <= 1.7e-129:
		tmp = ((y * (x * z)) - (b * (z * c))) + ((a * (c * j)) - (i * (y * j)))
	else:
		tmp = t_2 + t_1
	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 (x <= -1.1e-33)
		tmp = Float64(t_3 + t_2);
	elseif (x <= 1.32e-214)
		tmp = Float64(t_3 + t_1);
	elseif (x <= 1.7e-129)
		tmp = Float64(Float64(Float64(y * Float64(x * z)) - Float64(b * Float64(z * c))) + Float64(Float64(a * Float64(c * j)) - Float64(i * Float64(y * j))));
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (x <= -1.1e-33)
		tmp = t_3 + t_2;
	elseif (x <= 1.32e-214)
		tmp = t_3 + t_1;
	elseif (x <= 1.7e-129)
		tmp = ((y * (x * z)) - (b * (z * c))) + ((a * (c * j)) - (i * (y * j)));
	else
		tmp = t_2 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(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[x, -1.1e-33], N[(t$95$3 + t$95$2), $MachinePrecision], If[LessEqual[x, 1.32e-214], N[(t$95$3 + t$95$1), $MachinePrecision], If[LessEqual[x, 1.7e-129], N[(N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.10000000000000003e-33

   1. Initial program 64.3%

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

   3. Taylor expanded in b around 0 73.9%

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

   if -1.10000000000000003e-33 < x < 1.3199999999999999e-214

   1. Initial program 69.0%

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

   3. Taylor expanded in x around 0 75.4%

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

      1. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   if 1.3199999999999999e-214 < x < 1.70000000000000007e-129

   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. *-commutative 61.3%

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

      2. *-commutative 61.3%

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

      3. fma-neg 61.3%

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

   3. Simplified 61.3%

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

   5. Taylor expanded in a around 0 61.1%

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

   6. Taylor expanded in y around inf 54.5%

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

      1. *-commutative 54.5%

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

      2. associate-*l* 80.2%

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

   8. Simplified 80.2%

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

   9. Taylor expanded in z around inf 86.9%

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

   if 1.70000000000000007e-129 < x

   1. Initial program 75.9%

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

   3. Taylor expanded in j around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. *-commutative 71.8%

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

   5. Simplified 71.8%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-33}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-214}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-129}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) - b \cdot \left(z \cdot c\right)\right) + \left(a \cdot \left(c \cdot j\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -26000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -4e+60)
     t_2
     (if (<= z -26000000.0)
       t_1
       (if (<= z -9.5e-106)
         (- (* x (- (* y z) (* t a))) (* z (* b c)))
         (if (<= z 1.1e-68)
           t_1
           (if (<= z 1.3e+52) (* a (- (* c j) (* x t))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -4e+60) {
		tmp = t_2;
	} else if (z <= -26000000.0) {
		tmp = t_1;
	} else if (z <= -9.5e-106) {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	} else if (z <= 1.1e-68) {
		tmp = t_1;
	} else if (z <= 1.3e+52) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-4d+60)) then
        tmp = t_2
    else if (z <= (-26000000.0d0)) then
        tmp = t_1
    else if (z <= (-9.5d-106)) then
        tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
    else if (z <= 1.1d-68) then
        tmp = t_1
    else if (z <= 1.3d+52) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -4e+60) {
		tmp = t_2;
	} else if (z <= -26000000.0) {
		tmp = t_1;
	} else if (z <= -9.5e-106) {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	} else if (z <= 1.1e-68) {
		tmp = t_1;
	} else if (z <= 1.3e+52) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -4e+60:
		tmp = t_2
	elif z <= -26000000.0:
		tmp = t_1
	elif z <= -9.5e-106:
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
	elif z <= 1.1e-68:
		tmp = t_1
	elif z <= 1.3e+52:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -4e+60)
		tmp = t_2;
	elseif (z <= -26000000.0)
		tmp = t_1;
	elseif (z <= -9.5e-106)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(z * Float64(b * c)));
	elseif (z <= 1.1e-68)
		tmp = t_1;
	elseif (z <= 1.3e+52)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -4e+60)
		tmp = t_2;
	elseif (z <= -26000000.0)
		tmp = t_1;
	elseif (z <= -9.5e-106)
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	elseif (z <= 1.1e-68)
		tmp = t_1;
	elseif (z <= 1.3e+52)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+60], t$95$2, If[LessEqual[z, -26000000.0], t$95$1, If[LessEqual[z, -9.5e-106], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-68], t$95$1, If[LessEqual[z, 1.3e+52], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.9999999999999998e60 or 1.3e52 < z

   1. Initial program 58.7%

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

   3. Taylor expanded in z around inf 72.6%

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

      1. *-commutative 72.6%

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

   5. Simplified 72.6%

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

   if -3.9999999999999998e60 < z < -2.6e7 or -9.4999999999999994e-106 < z < 1.10000000000000001e-68

   1. Initial program 78.8%

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

   3. Taylor expanded in i around inf 61.3%

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

      1. distribute-lft-out-- 61.3%

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

      2. *-commutative 61.3%

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

   5. Simplified 61.3%

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

   if -2.6e7 < z < -9.4999999999999994e-106

   1. Initial program 80.9%

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

   3. Taylor expanded in j around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. *-commutative 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in c around inf 67.1%

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

      1. *-commutative 67.1%

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

      2. *-commutative 67.1%

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

      3. associate-*l* 67.2%

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

      4. *-commutative 67.2%

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

   8. Simplified 67.2%

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

   if 1.10000000000000001e-68 < z < 1.3e52

   1. Initial program 72.6%

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

   3. Taylor expanded in a around inf 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

   5. Simplified 69.2%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+60}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -26000000:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-68}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+24}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-177}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a))))
        (t_2 (* c (- (* a j) (* z b))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -9e+24)
     t_3
     (if (<= y -6e-111)
       t_2
       (if (<= y 1.3e-250)
         t_1
         (if (<= y 2.4e-177) t_2 (if (<= y 2.25e+27) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = c * ((a * j) - (z * b));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -9e+24) {
		tmp = t_3;
	} else if (y <= -6e-111) {
		tmp = t_2;
	} else if (y <= 1.3e-250) {
		tmp = t_1;
	} else if (y <= 2.4e-177) {
		tmp = t_2;
	} else if (y <= 2.25e+27) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    t_2 = c * ((a * j) - (z * b))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-9d+24)) then
        tmp = t_3
    else if (y <= (-6d-111)) then
        tmp = t_2
    else if (y <= 1.3d-250) then
        tmp = t_1
    else if (y <= 2.4d-177) then
        tmp = t_2
    else if (y <= 2.25d+27) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = c * ((a * j) - (z * b));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -9e+24) {
		tmp = t_3;
	} else if (y <= -6e-111) {
		tmp = t_2;
	} else if (y <= 1.3e-250) {
		tmp = t_1;
	} else if (y <= 2.4e-177) {
		tmp = t_2;
	} else if (y <= 2.25e+27) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = c * ((a * j) - (z * b))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -9e+24:
		tmp = t_3
	elif y <= -6e-111:
		tmp = t_2
	elif y <= 1.3e-250:
		tmp = t_1
	elif y <= 2.4e-177:
		tmp = t_2
	elif y <= 2.25e+27:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -9e+24)
		tmp = t_3;
	elseif (y <= -6e-111)
		tmp = t_2;
	elseif (y <= 1.3e-250)
		tmp = t_1;
	elseif (y <= 2.4e-177)
		tmp = t_2;
	elseif (y <= 2.25e+27)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	t_2 = c * ((a * j) - (z * b));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -9e+24)
		tmp = t_3;
	elseif (y <= -6e-111)
		tmp = t_2;
	elseif (y <= 1.3e-250)
		tmp = t_1;
	elseif (y <= 2.4e-177)
		tmp = t_2;
	elseif (y <= 2.25e+27)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+24], t$95$3, If[LessEqual[y, -6e-111], t$95$2, If[LessEqual[y, 1.3e-250], t$95$1, If[LessEqual[y, 2.4e-177], t$95$2, If[LessEqual[y, 2.25e+27], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.00000000000000039e24 or 2.25e27 < y

   1. Initial program 55.3%

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

   3. Taylor expanded in y around inf 68.5%

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

      1. +-commutative 68.5%

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

      2. mul-1-neg 68.5%

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

      3. unsub-neg 68.5%

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

      4. *-commutative 68.5%

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

   5. Simplified 68.5%

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

   if -9.00000000000000039e24 < y < -6.00000000000000016e-111 or 1.30000000000000004e-250 < y < 2.3999999999999999e-177

   1. Initial program 88.1%

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

   3. Taylor expanded in c around inf 66.5%

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

   if -6.00000000000000016e-111 < y < 1.30000000000000004e-250 or 2.3999999999999999e-177 < y < 2.25e27

   1. Initial program 83.4%

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

   3. Taylor expanded in t around inf 60.7%

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

      1. distribute-lft-out-- 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in t around 0 60.7%

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

      1. mul-1-neg 60.7%

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

      2. *-commutative 60.7%

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

      3. *-commutative 60.7%

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

      4. distribute-rgt-neg-out 60.7%

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

      5. neg-sub0 60.7%

         \[\leadsto t \cdot \color{blue}{\left(0 - \left(x \cdot a - i \cdot b\right)\right)} \]

      6. associate--r- 60.7%

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

      7. neg-sub0 60.7%

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

      8. *-commutative 60.7%

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

      9. mul-1-neg 60.7%

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

      10. *-commutative 60.7%

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

      11. +-commutative 60.7%

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

      12. *-commutative 60.7%

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

      13. mul-1-neg 60.7%

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

      14. *-commutative 60.7%

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

      15. unsub-neg 60.7%

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

      16. *-commutative 60.7%

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

      17. *-commutative 60.7%

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

   8. Simplified 60.7%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-111}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-177}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{-29}:\\ \;\;\;\;t\_3 + t\_2\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-213}:\\ \;\;\;\;t\_3 + t\_1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-132}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) - b \cdot \left(z \cdot c\right)\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= x -7.2e-29)
     (+ t_3 t_2)
     (if (<= x 3.3e-213)
       (+ t_3 t_1)
       (if (<= x 3.8e-132)
         (- (- (* y (* x z)) (* b (* z c))) (* i (* y j)))
         (+ t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (x <= -7.2e-29) {
		tmp = t_3 + t_2;
	} else if (x <= 3.3e-213) {
		tmp = t_3 + t_1;
	} else if (x <= 3.8e-132) {
		tmp = ((y * (x * z)) - (b * (z * c))) - (i * (y * j));
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((a * c) - (y * i))
    if (x <= (-7.2d-29)) then
        tmp = t_3 + t_2
    else if (x <= 3.3d-213) then
        tmp = t_3 + t_1
    else if (x <= 3.8d-132) then
        tmp = ((y * (x * z)) - (b * (z * c))) - (i * (y * j))
    else
        tmp = t_2 + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (x <= -7.2e-29) {
		tmp = t_3 + t_2;
	} else if (x <= 3.3e-213) {
		tmp = t_3 + t_1;
	} else if (x <= 3.8e-132) {
		tmp = ((y * (x * z)) - (b * (z * c))) - (i * (y * j));
	} else {
		tmp = t_2 + t_1;
	}
	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 x <= -7.2e-29:
		tmp = t_3 + t_2
	elif x <= 3.3e-213:
		tmp = t_3 + t_1
	elif x <= 3.8e-132:
		tmp = ((y * (x * z)) - (b * (z * c))) - (i * (y * j))
	else:
		tmp = t_2 + t_1
	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 (x <= -7.2e-29)
		tmp = Float64(t_3 + t_2);
	elseif (x <= 3.3e-213)
		tmp = Float64(t_3 + t_1);
	elseif (x <= 3.8e-132)
		tmp = Float64(Float64(Float64(y * Float64(x * z)) - Float64(b * Float64(z * c))) - Float64(i * Float64(y * j)));
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (x <= -7.2e-29)
		tmp = t_3 + t_2;
	elseif (x <= 3.3e-213)
		tmp = t_3 + t_1;
	elseif (x <= 3.8e-132)
		tmp = ((y * (x * z)) - (b * (z * c))) - (i * (y * j));
	else
		tmp = t_2 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(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[x, -7.2e-29], N[(t$95$3 + t$95$2), $MachinePrecision], If[LessEqual[x, 3.3e-213], N[(t$95$3 + t$95$1), $MachinePrecision], If[LessEqual[x, 3.8e-132], N[(N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.19999999999999948e-29

   1. Initial program 64.3%

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

   3. Taylor expanded in b around 0 73.9%

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

   if -7.19999999999999948e-29 < x < 3.30000000000000031e-213

   1. Initial program 69.0%

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

   3. Taylor expanded in x around 0 75.4%

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

      1. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   if 3.30000000000000031e-213 < x < 3.7999999999999997e-132

   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. *-commutative 61.3%

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

      2. *-commutative 61.3%

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

      3. fma-neg 61.3%

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

   3. Simplified 61.3%

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

   5. Taylor expanded in a around 0 61.1%

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

   6. Taylor expanded in y around inf 54.5%

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

      1. *-commutative 54.5%

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

      2. associate-*l* 80.2%

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

   8. Simplified 80.2%

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

   9. Taylor expanded in z around inf 86.9%

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

   10. Taylor expanded in i around inf 81.3%

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

       1. neg-mul-1 81.3%

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

       2. distribute-rgt-neg-in 81.3%

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

       3. distribute-rgt-neg-in 81.3%

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

   12. Simplified 81.3%

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

   if 3.7999999999999997e-132 < x

   1. Initial program 75.9%

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

   3. Taylor expanded in j around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. *-commutative 71.8%

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

   5. Simplified 71.8%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-29}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-213}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-132}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) - b \cdot \left(z \cdot c\right)\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{-28} \lor \neg \left(x \leq 1.65 \cdot 10^{+87}\right):\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (or (<= x -9.5e-28) (not (<= x 1.65e+87)))
     (+ t_1 (* x (- (* y z) (* t a))))
     (+ t_1 (* b (- (* t i) (* z c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if ((x <= -9.5e-28) || !(x <= 1.65e+87)) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if ((x <= (-9.5d-28)) .or. (.not. (x <= 1.65d+87))) then
        tmp = t_1 + (x * ((y * z) - (t * a)))
    else
        tmp = t_1 + (b * ((t * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if ((x <= -9.5e-28) || !(x <= 1.65e+87)) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if (x <= -9.5e-28) or not (x <= 1.65e+87):
		tmp = t_1 + (x * ((y * z) - (t * a)))
	else:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if ((x <= -9.5e-28) || !(x <= 1.65e+87))
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if ((x <= -9.5e-28) || ~((x <= 1.65e+87)))
		tmp = t_1 + (x * ((y * z) - (t * a)));
	else
		tmp = t_1 + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -9.5e-28], N[Not[LessEqual[x, 1.65e+87]], $MachinePrecision]], N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000001e-28 or 1.6500000000000001e87 < x

   1. Initial program 70.6%

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

   3. Taylor expanded in b around 0 74.0%

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

   if -9.50000000000000001e-28 < x < 1.6500000000000001e87

   1. Initial program 69.1%

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

   3. Taylor expanded in x around 0 69.4%

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

      1. *-commutative 69.4%

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

   5. Simplified 69.4%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-28} \lor \neg \left(x \leq 1.65 \cdot 10^{+87}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+47} \lor \neg \left(b \leq 1.22 \cdot 10^{+113}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -4.8e+47) (not (<= b 1.22e+113)))
   (* 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 <= -4.8e+47) || !(b <= 1.22e+113)) {
		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 <= (-4.8d+47)) .or. (.not. (b <= 1.22d+113))) 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 <= -4.8e+47) || !(b <= 1.22e+113)) {
		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 <= -4.8e+47) or not (b <= 1.22e+113):
		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 <= -4.8e+47) || !(b <= 1.22e+113))
		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 <= -4.8e+47) || ~((b <= 1.22e+113)))
		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, -4.8e+47], N[Not[LessEqual[b, 1.22e+113]], $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 < -4.80000000000000037e47 or 1.2199999999999999e113 < b

   1. Initial program 68.5%

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

   3. Taylor expanded in b around inf 66.2%

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

      1. *-commutative 66.2%

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

   5. Simplified 66.2%

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

   if -4.80000000000000037e47 < b < 1.2199999999999999e113

   1. Initial program 70.9%

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

   3. Taylor expanded in b around 0 72.3%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+47} \lor \neg \left(b \leq 1.22 \cdot 10^{+113}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+154}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-119}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) - b \cdot \left(z \cdot c\right)\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -2.65e+154)
   (* t (- (* b i) (* x a)))
   (if (<= t 5.8e-119)
     (- (- (* y (* x z)) (* b (* z c))) (* i (* y j)))
     (- (* x (- (* y z) (* t a))) (* z (* b c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -2.65e+154) {
		tmp = t * ((b * i) - (x * a));
	} else if (t <= 5.8e-119) {
		tmp = ((y * (x * z)) - (b * (z * c))) - (i * (y * j));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-2.65d+154)) then
        tmp = t * ((b * i) - (x * a))
    else if (t <= 5.8d-119) then
        tmp = ((y * (x * z)) - (b * (z * c))) - (i * (y * j))
    else
        tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -2.65e+154) {
		tmp = t * ((b * i) - (x * a));
	} else if (t <= 5.8e-119) {
		tmp = ((y * (x * z)) - (b * (z * c))) - (i * (y * j));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -2.65e+154:
		tmp = t * ((b * i) - (x * a))
	elif t <= 5.8e-119:
		tmp = ((y * (x * z)) - (b * (z * c))) - (i * (y * j))
	else:
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -2.65e+154)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (t <= 5.8e-119)
		tmp = Float64(Float64(Float64(y * Float64(x * z)) - Float64(b * Float64(z * c))) - Float64(i * Float64(y * j)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(z * Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -2.65e+154)
		tmp = t * ((b * i) - (x * a));
	elseif (t <= 5.8e-119)
		tmp = ((y * (x * z)) - (b * (z * c))) - (i * (y * j));
	else
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -2.65e+154], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e-119], N[(N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.65000000000000012e154

   1. Initial program 40.6%

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

   3. Taylor expanded in t around inf 86.6%

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

      1. distribute-lft-out-- 86.6%

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

   5. Simplified 86.6%

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

   6. Taylor expanded in t around 0 86.6%

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

      1. mul-1-neg 86.6%

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

      2. *-commutative 86.6%

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

      3. *-commutative 86.6%

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

      4. distribute-rgt-neg-out 86.6%

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

      5. neg-sub0 86.6%

         \[\leadsto t \cdot \color{blue}{\left(0 - \left(x \cdot a - i \cdot b\right)\right)} \]

      6. associate--r- 86.6%

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

      7. neg-sub0 86.6%

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

      8. *-commutative 86.6%

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

      9. mul-1-neg 86.6%

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

      10. *-commutative 86.6%

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

      11. +-commutative 86.6%

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

      12. *-commutative 86.6%

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

      13. mul-1-neg 86.6%

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

      14. *-commutative 86.6%

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

      15. unsub-neg 86.6%

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

      16. *-commutative 86.6%

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

      17. *-commutative 86.6%

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

   8. Simplified 86.6%

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

   if -2.65000000000000012e154 < t < 5.8e-119

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

      2. *-commutative 81.6%

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

      3. fma-neg 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in a around 0 78.3%

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

   6. Taylor expanded in y around inf 71.7%

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

      1. *-commutative 71.7%

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

      2. associate-*l* 76.5%

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

   8. Simplified 76.5%

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

   9. Taylor expanded in z around inf 69.8%

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

   10. Taylor expanded in i around inf 65.4%

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

       1. neg-mul-1 65.4%

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

       2. distribute-rgt-neg-in 65.4%

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

       3. distribute-rgt-neg-in 65.4%

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

   12. Simplified 65.4%

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

   if 5.8e-119 < t

   1. Initial program 59.2%

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

   3. Taylor expanded in j around 0 63.8%

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

      1. *-commutative 63.8%

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

      2. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in c around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. *-commutative 57.6%

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

      3. associate-*l* 58.6%

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

      4. *-commutative 58.6%

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

   8. Simplified 58.6%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+154}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-119}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) - b \cdot \left(z \cdot c\right)\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;b \leq -2.15 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-297}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-47}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 1.38 \cdot 10^{+118}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* b i))))
   (if (<= b -2.15e+46)
     t_1
     (if (<= b -3e-297)
       (* y (* x z))
       (if (<= b 3e-47)
         (* c (* a j))
         (if (<= b 1.38e+118) (* z (* x y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (b * i);
	double tmp;
	if (b <= -2.15e+46) {
		tmp = t_1;
	} else if (b <= -3e-297) {
		tmp = y * (x * z);
	} else if (b <= 3e-47) {
		tmp = c * (a * j);
	} else if (b <= 1.38e+118) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b * i)
    if (b <= (-2.15d+46)) then
        tmp = t_1
    else if (b <= (-3d-297)) then
        tmp = y * (x * z)
    else if (b <= 3d-47) then
        tmp = c * (a * j)
    else if (b <= 1.38d+118) then
        tmp = z * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (b * i);
	double tmp;
	if (b <= -2.15e+46) {
		tmp = t_1;
	} else if (b <= -3e-297) {
		tmp = y * (x * z);
	} else if (b <= 3e-47) {
		tmp = c * (a * j);
	} else if (b <= 1.38e+118) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (b * i)
	tmp = 0
	if b <= -2.15e+46:
		tmp = t_1
	elif b <= -3e-297:
		tmp = y * (x * z)
	elif b <= 3e-47:
		tmp = c * (a * j)
	elif b <= 1.38e+118:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (b <= -2.15e+46)
		tmp = t_1;
	elseif (b <= -3e-297)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 3e-47)
		tmp = Float64(c * Float64(a * j));
	elseif (b <= 1.38e+118)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (b * i);
	tmp = 0.0;
	if (b <= -2.15e+46)
		tmp = t_1;
	elseif (b <= -3e-297)
		tmp = y * (x * z);
	elseif (b <= 3e-47)
		tmp = c * (a * j);
	elseif (b <= 1.38e+118)
		tmp = z * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.15e+46], t$95$1, If[LessEqual[b, -3e-297], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e-47], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.38e+118], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.15000000000000002e46 or 1.3800000000000001e118 < b

   1. Initial program 69.6%

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

   3. Taylor expanded in t around inf 56.2%

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

      1. distribute-lft-out-- 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in a around 0 42.7%

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

      1. associate-*r* 45.2%

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

   8. Simplified 45.2%

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

   if -2.15000000000000002e46 < b < -2.99999999999999995e-297

   1. Initial program 63.0%

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

   3. Taylor expanded in y around inf 54.3%

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

      1. +-commutative 54.3%

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

      2. mul-1-neg 54.3%

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

      3. unsub-neg 54.3%

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

      4. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in z around inf 34.0%

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

      1. *-commutative 34.0%

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

   8. Simplified 34.0%

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

   if -2.99999999999999995e-297 < b < 3.00000000000000017e-47

   1. Initial program 75.7%

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

   3. Taylor expanded in c around inf 47.0%

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

   4. Taylor expanded in a around inf 43.1%

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

   if 3.00000000000000017e-47 < b < 1.3800000000000001e118

   1. Initial program 74.3%

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

   3. Taylor expanded in z around inf 67.1%

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

      1. *-commutative 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in y around inf 52.9%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-297}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-47}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 1.38 \cdot 10^{+118}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-47}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+119}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= b -7.2e+42)
     t_1
     (if (<= b -6.5e-299)
       (* y (* x z))
       (if (<= b 6e-47)
         (* c (* a j))
         (if (<= b 1.12e+119) (* z (* x y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (b <= -7.2e+42) {
		tmp = t_1;
	} else if (b <= -6.5e-299) {
		tmp = y * (x * z);
	} else if (b <= 6e-47) {
		tmp = c * (a * j);
	} else if (b <= 1.12e+119) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t * i)
    if (b <= (-7.2d+42)) then
        tmp = t_1
    else if (b <= (-6.5d-299)) then
        tmp = y * (x * z)
    else if (b <= 6d-47) then
        tmp = c * (a * j)
    else if (b <= 1.12d+119) then
        tmp = z * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (b <= -7.2e+42) {
		tmp = t_1;
	} else if (b <= -6.5e-299) {
		tmp = y * (x * z);
	} else if (b <= 6e-47) {
		tmp = c * (a * j);
	} else if (b <= 1.12e+119) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if b <= -7.2e+42:
		tmp = t_1
	elif b <= -6.5e-299:
		tmp = y * (x * z)
	elif b <= 6e-47:
		tmp = c * (a * j)
	elif b <= 1.12e+119:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (b <= -7.2e+42)
		tmp = t_1;
	elseif (b <= -6.5e-299)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 6e-47)
		tmp = Float64(c * Float64(a * j));
	elseif (b <= 1.12e+119)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	tmp = 0.0;
	if (b <= -7.2e+42)
		tmp = t_1;
	elseif (b <= -6.5e-299)
		tmp = y * (x * z);
	elseif (b <= 6e-47)
		tmp = c * (a * j);
	elseif (b <= 1.12e+119)
		tmp = z * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+42], t$95$1, If[LessEqual[b, -6.5e-299], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e-47], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.12e+119], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.2000000000000002e42 or 1.11999999999999994e119 < b

   1. Initial program 69.6%

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

   3. Taylor expanded in t around inf 56.2%

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

      1. distribute-lft-out-- 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in a around 0 42.7%

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

   if -7.2000000000000002e42 < b < -6.4999999999999997e-299

   1. Initial program 63.0%

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

   3. Taylor expanded in y around inf 54.3%

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

      1. +-commutative 54.3%

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

      2. mul-1-neg 54.3%

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

      3. unsub-neg 54.3%

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

      4. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in z around inf 34.0%

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

      1. *-commutative 34.0%

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

   8. Simplified 34.0%

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

   if -6.4999999999999997e-299 < b < 6.00000000000000033e-47

   1. Initial program 75.7%

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

   3. Taylor expanded in c around inf 47.0%

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

   4. Taylor expanded in a around inf 43.1%

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

   if 6.00000000000000033e-47 < b < 1.11999999999999994e119

   1. Initial program 74.3%

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

   3. Taylor expanded in z around inf 67.1%

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

      1. *-commutative 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in y around inf 52.9%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-47}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+119}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-296}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-45}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 7.3 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= b -1.15e+45)
     t_1
     (if (<= b -4.3e-296)
       (* y (* x z))
       (if (<= b 1.8e-45)
         (* c (* a j))
         (if (<= b 7.3e+118) (* x (* y z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (b <= -1.15e+45) {
		tmp = t_1;
	} else if (b <= -4.3e-296) {
		tmp = y * (x * z);
	} else if (b <= 1.8e-45) {
		tmp = c * (a * j);
	} else if (b <= 7.3e+118) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t * i)
    if (b <= (-1.15d+45)) then
        tmp = t_1
    else if (b <= (-4.3d-296)) then
        tmp = y * (x * z)
    else if (b <= 1.8d-45) then
        tmp = c * (a * j)
    else if (b <= 7.3d+118) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (b <= -1.15e+45) {
		tmp = t_1;
	} else if (b <= -4.3e-296) {
		tmp = y * (x * z);
	} else if (b <= 1.8e-45) {
		tmp = c * (a * j);
	} else if (b <= 7.3e+118) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if b <= -1.15e+45:
		tmp = t_1
	elif b <= -4.3e-296:
		tmp = y * (x * z)
	elif b <= 1.8e-45:
		tmp = c * (a * j)
	elif b <= 7.3e+118:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (b <= -1.15e+45)
		tmp = t_1;
	elseif (b <= -4.3e-296)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 1.8e-45)
		tmp = Float64(c * Float64(a * j));
	elseif (b <= 7.3e+118)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	tmp = 0.0;
	if (b <= -1.15e+45)
		tmp = t_1;
	elseif (b <= -4.3e-296)
		tmp = y * (x * z);
	elseif (b <= 1.8e-45)
		tmp = c * (a * j);
	elseif (b <= 7.3e+118)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.15e+45], t$95$1, If[LessEqual[b, -4.3e-296], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e-45], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.3e+118], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.15000000000000006e45 or 7.3000000000000003e118 < b

   1. Initial program 69.6%

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

   3. Taylor expanded in t around inf 56.2%

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

      1. distribute-lft-out-- 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in a around 0 42.7%

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

   if -1.15000000000000006e45 < b < -4.29999999999999978e-296

   1. Initial program 63.0%

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

   3. Taylor expanded in y around inf 54.3%

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

      1. +-commutative 54.3%

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

      2. mul-1-neg 54.3%

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

      3. unsub-neg 54.3%

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

      4. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in z around inf 34.0%

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

      1. *-commutative 34.0%

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

   8. Simplified 34.0%

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

   if -4.29999999999999978e-296 < b < 1.8e-45

   1. Initial program 75.7%

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

   3. Taylor expanded in c around inf 47.0%

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

   4. Taylor expanded in a around inf 43.1%

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

   if 1.8e-45 < b < 7.3000000000000003e118

   1. Initial program 74.3%

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

   3. Taylor expanded in y around inf 60.5%

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

      1. +-commutative 60.5%

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

      2. mul-1-neg 60.5%

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

      3. unsub-neg 60.5%

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

      4. *-commutative 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in z around inf 49.4%

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

      1. *-commutative 49.4%

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

   8. Simplified 49.4%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+45}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-296}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-45}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 7.3 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-65}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -1.75e+61)
     t_1
     (if (<= z 1.25e-65)
       (* i (- (* t b) (* y j)))
       (if (<= z 5.9e+51) (* a (- (* c j) (* x t))) 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 * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.75e+61) {
		tmp = t_1;
	} else if (z <= 1.25e-65) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 5.9e+51) {
		tmp = a * ((c * j) - (x * t));
	} 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 = z * ((x * y) - (b * c))
    if (z <= (-1.75d+61)) then
        tmp = t_1
    else if (z <= 1.25d-65) then
        tmp = i * ((t * b) - (y * j))
    else if (z <= 5.9d+51) then
        tmp = a * ((c * j) - (x * t))
    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 * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.75e+61) {
		tmp = t_1;
	} else if (z <= 1.25e-65) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 5.9e+51) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -1.75e+61:
		tmp = t_1
	elif z <= 1.25e-65:
		tmp = i * ((t * b) - (y * j))
	elif z <= 5.9e+51:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (z <= -1.75e+61)
		tmp = t_1;
	elseif (z <= 1.25e-65)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (z <= 5.9e+51)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	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 * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -1.75e+61)
		tmp = t_1;
	elseif (z <= 1.25e-65)
		tmp = i * ((t * b) - (y * j));
	elseif (z <= 5.9e+51)
		tmp = a * ((c * j) - (x * t));
	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[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+61], t$95$1, If[LessEqual[z, 1.25e-65], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.9e+51], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.75000000000000009e61 or 5.89999999999999983e51 < z

   1. Initial program 58.7%

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

   3. Taylor expanded in z around inf 72.6%

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

      1. *-commutative 72.6%

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

   5. Simplified 72.6%

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

   if -1.75000000000000009e61 < z < 1.24999999999999996e-65

   1. Initial program 79.2%

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

   3. Taylor expanded in i around inf 55.2%

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

      1. distribute-lft-out-- 55.2%

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

      2. *-commutative 55.2%

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

   5. Simplified 55.2%

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

   if 1.24999999999999996e-65 < z < 5.89999999999999983e51

   1. Initial program 72.6%

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

   3. Taylor expanded in a around inf 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

   5. Simplified 69.2%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+61}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-65}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7.8 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -7.8e+41)
     t_1
     (if (<= b -2.2e-57)
       (* y (* x z))
       (if (<= b 1.2e+113) (* a (- (* c j) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7.8e+41) {
		tmp = t_1;
	} else if (b <= -2.2e-57) {
		tmp = y * (x * z);
	} else if (b <= 1.2e+113) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-7.8d+41)) then
        tmp = t_1
    else if (b <= (-2.2d-57)) then
        tmp = y * (x * z)
    else if (b <= 1.2d+113) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7.8e+41) {
		tmp = t_1;
	} else if (b <= -2.2e-57) {
		tmp = y * (x * z);
	} else if (b <= 1.2e+113) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -7.8e+41:
		tmp = t_1
	elif b <= -2.2e-57:
		tmp = y * (x * z)
	elif b <= 1.2e+113:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (b <= -7.8e+41)
		tmp = t_1;
	elseif (b <= -2.2e-57)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 1.2e+113)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -7.8e+41)
		tmp = t_1;
	elseif (b <= -2.2e-57)
		tmp = y * (x * z);
	elseif (b <= 1.2e+113)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.8e+41], t$95$1, If[LessEqual[b, -2.2e-57], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e+113], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.7999999999999994e41 or 1.19999999999999992e113 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 65.7%

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

      1. *-commutative 65.7%

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

   5. Simplified 65.7%

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

   if -7.7999999999999994e41 < b < -2.19999999999999999e-57

   1. Initial program 82.6%

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

   3. Taylor expanded in y around inf 76.8%

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

      1. +-commutative 76.8%

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

      2. mul-1-neg 76.8%

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

      3. unsub-neg 76.8%

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

      4. *-commutative 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in z around inf 53.5%

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

      1. *-commutative 53.5%

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

   8. Simplified 53.5%

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

   if -2.19999999999999999e-57 < b < 1.19999999999999992e113

   1. Initial program 69.0%

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

   3. Taylor expanded in a around inf 45.5%

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

      1. +-commutative 45.5%

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

      2. mul-1-neg 45.5%

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

      3. unsub-neg 45.5%

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

   5. Simplified 45.5%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-285}:\\ \;\;\;\;\left(-y\right) \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-80}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1.7e+34)
     t_1
     (if (<= a -1.5e-285)
       (* (- y) (* i j))
       (if (<= a 6.4e-80) (* c (* z (- b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.7e+34) {
		tmp = t_1;
	} else if (a <= -1.5e-285) {
		tmp = -y * (i * j);
	} else if (a <= 6.4e-80) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-1.7d+34)) then
        tmp = t_1
    else if (a <= (-1.5d-285)) then
        tmp = -y * (i * j)
    else if (a <= 6.4d-80) then
        tmp = c * (z * -b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.7e+34) {
		tmp = t_1;
	} else if (a <= -1.5e-285) {
		tmp = -y * (i * j);
	} else if (a <= 6.4e-80) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.7e+34:
		tmp = t_1
	elif a <= -1.5e-285:
		tmp = -y * (i * j)
	elif a <= 6.4e-80:
		tmp = c * (z * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.7e+34)
		tmp = t_1;
	elseif (a <= -1.5e-285)
		tmp = Float64(Float64(-y) * Float64(i * j));
	elseif (a <= 6.4e-80)
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.7e+34)
		tmp = t_1;
	elseif (a <= -1.5e-285)
		tmp = -y * (i * j);
	elseif (a <= 6.4e-80)
		tmp = c * (z * -b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+34], t$95$1, If[LessEqual[a, -1.5e-285], N[((-y) * N[(i * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.4e-80], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.7e34 or 6.3999999999999998e-80 < a

   1. Initial program 65.1%

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

   3. Taylor expanded in a around inf 56.8%

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

      1. +-commutative 56.8%

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

      2. mul-1-neg 56.8%

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

      3. unsub-neg 56.8%

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

   5. Simplified 56.8%

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

   if -1.7e34 < a < -1.50000000000000002e-285

   1. Initial program 69.8%

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

   3. Taylor expanded in y around inf 64.6%

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

      1. +-commutative 64.6%

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

      2. mul-1-neg 64.6%

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

      3. unsub-neg 64.6%

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

      4. *-commutative 64.6%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in z around 0 42.4%

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

      1. neg-mul-1 42.4%

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

      2. distribute-rgt-neg-in 42.4%

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

   8. Simplified 42.4%

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

   if -1.50000000000000002e-285 < a < 6.3999999999999998e-80

   1. Initial program 80.0%

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

   3. Taylor expanded in c around inf 38.3%

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

   4. Taylor expanded in a around 0 36.5%

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

      1. associate-*r* 36.5%

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

      2. neg-mul-1 36.5%

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

      3. *-commutative 36.5%

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

   6. Simplified 36.5%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+34}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-285}:\\ \;\;\;\;\left(-y\right) \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-80}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.6 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+21}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+269}:\\ \;\;\;\;\left(-y\right) \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -2.6e+100)
   (* a (* c j))
   (if (<= j 3.6e+21)
     (* z (* x y))
     (if (<= j 5.8e+269) (* (- y) (* i j)) (* c (* a j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.6e+100) {
		tmp = a * (c * j);
	} else if (j <= 3.6e+21) {
		tmp = z * (x * y);
	} else if (j <= 5.8e+269) {
		tmp = -y * (i * j);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-2.6d+100)) then
        tmp = a * (c * j)
    else if (j <= 3.6d+21) then
        tmp = z * (x * y)
    else if (j <= 5.8d+269) then
        tmp = -y * (i * j)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.6e+100) {
		tmp = a * (c * j);
	} else if (j <= 3.6e+21) {
		tmp = z * (x * y);
	} else if (j <= 5.8e+269) {
		tmp = -y * (i * j);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -2.6e+100:
		tmp = a * (c * j)
	elif j <= 3.6e+21:
		tmp = z * (x * y)
	elif j <= 5.8e+269:
		tmp = -y * (i * j)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -2.6e+100)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= 3.6e+21)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 5.8e+269)
		tmp = Float64(Float64(-y) * Float64(i * j));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -2.6e+100)
		tmp = a * (c * j);
	elseif (j <= 3.6e+21)
		tmp = z * (x * y);
	elseif (j <= 5.8e+269)
		tmp = -y * (i * j);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -2.6e+100], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.6e+21], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.8e+269], N[((-y) * N[(i * j), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.6000000000000002e100

   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. Add Preprocessing

   3. Taylor expanded in a around inf 61.8%

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

      1. +-commutative 61.8%

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

      2. mul-1-neg 61.8%

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

      3. unsub-neg 61.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in c around inf 52.5%

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

   if -2.6000000000000002e100 < j < 3.6e21

   1. Initial program 69.3%

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

   3. Taylor expanded in z around inf 51.9%

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

      1. *-commutative 51.9%

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

   5. Simplified 51.9%

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

   6. Taylor expanded in y around inf 36.3%

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

   if 3.6e21 < j < 5.80000000000000051e269

   1. Initial program 75.1%

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

   3. Taylor expanded in y around inf 53.2%

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

      1. +-commutative 53.2%

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

      2. mul-1-neg 53.2%

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

      3. unsub-neg 53.2%

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

      4. *-commutative 53.2%

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

   5. Simplified 53.2%

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

   6. Taylor expanded in z around 0 46.6%

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

      1. neg-mul-1 46.6%

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

      2. distribute-rgt-neg-in 46.6%

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

   8. Simplified 46.6%

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

   if 5.80000000000000051e269 < j

   1. Initial program 85.7%

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

   3. Taylor expanded in c around inf 88.5%

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

   4. Taylor expanded in a around inf 88.5%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.6 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+21}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+269}:\\ \;\;\;\;\left(-y\right) \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3400000:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 92:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -3400000.0)
   (* c (* z (- b)))
   (if (<= c 3.9e-271)
     (* y (* x z))
     (if (<= c 92.0) (* t (* b i)) (* j (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -3400000.0) {
		tmp = c * (z * -b);
	} else if (c <= 3.9e-271) {
		tmp = y * (x * z);
	} else if (c <= 92.0) {
		tmp = t * (b * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-3400000.0d0)) then
        tmp = c * (z * -b)
    else if (c <= 3.9d-271) then
        tmp = y * (x * z)
    else if (c <= 92.0d0) then
        tmp = t * (b * i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -3400000.0) {
		tmp = c * (z * -b);
	} else if (c <= 3.9e-271) {
		tmp = y * (x * z);
	} else if (c <= 92.0) {
		tmp = t * (b * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -3400000.0:
		tmp = c * (z * -b)
	elif c <= 3.9e-271:
		tmp = y * (x * z)
	elif c <= 92.0:
		tmp = t * (b * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -3400000.0)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (c <= 3.9e-271)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 92.0)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -3400000.0)
		tmp = c * (z * -b);
	elseif (c <= 3.9e-271)
		tmp = y * (x * z);
	elseif (c <= 92.0)
		tmp = t * (b * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -3400000.0], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.9e-271], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 92.0], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.4e6

   1. Initial program 60.1%

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

   3. Taylor expanded in c around inf 57.7%

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

   4. Taylor expanded in a around 0 43.0%

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

      1. associate-*r* 43.0%

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

      2. neg-mul-1 43.0%

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

      3. *-commutative 43.0%

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

   6. Simplified 43.0%

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

   if -3.4e6 < c < 3.89999999999999997e-271

   1. Initial program 79.4%

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

   3. Taylor expanded in y around inf 54.3%

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

      1. +-commutative 54.3%

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

      2. mul-1-neg 54.3%

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

      3. unsub-neg 54.3%

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

      4. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in z around inf 41.2%

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

      1. *-commutative 41.2%

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

   8. Simplified 41.2%

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

   if 3.89999999999999997e-271 < c < 92

   1. Initial program 72.9%

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

   3. Taylor expanded in t around inf 52.4%

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

      1. distribute-lft-out-- 52.4%

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

   5. Simplified 52.4%

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

   6. Taylor expanded in a around 0 32.2%

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

      1. associate-*r* 35.4%

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

   8. Simplified 35.4%

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

   if 92 < c

   1. Initial program 66.1%

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

   3. Taylor expanded in a around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. mul-1-neg 55.0%

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

      3. unsub-neg 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in c around inf 45.3%

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

      1. associate-*r* 47.2%

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

      2. *-commutative 47.2%

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

      3. *-commutative 47.2%

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

   8. Simplified 47.2%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3400000:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 92:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{-101} \lor \neg \left(c \leq 280000000000\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -8e-101) (not (<= c 280000000000.0)))
   (* c (- (* a j) (* z b)))
   (* t (- (* b i) (* x a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -8e-101) || !(c <= 280000000000.0)) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-8d-101)) .or. (.not. (c <= 280000000000.0d0))) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t * ((b * i) - (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -8e-101) || !(c <= 280000000000.0)) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -8e-101) or not (c <= 280000000000.0):
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -8e-101) || !(c <= 280000000000.0))
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -8e-101) || ~((c <= 280000000000.0)))
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -8e-101], N[Not[LessEqual[c, 280000000000.0]], $MachinePrecision]], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -8.00000000000000041e-101 or 2.8e11 < c

   1. Initial program 65.9%

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

   3. Taylor expanded in c around inf 59.8%

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

   if -8.00000000000000041e-101 < c < 2.8e11

   1. Initial program 74.3%

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

   3. Taylor expanded in t around inf 51.4%

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

      1. distribute-lft-out-- 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in t around 0 51.4%

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

      1. mul-1-neg 51.4%

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

      2. *-commutative 51.4%

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

      3. *-commutative 51.4%

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

      4. distribute-rgt-neg-out 51.4%

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

      5. neg-sub0 51.4%

         \[\leadsto t \cdot \color{blue}{\left(0 - \left(x \cdot a - i \cdot b\right)\right)} \]

      6. associate--r- 51.4%

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

      7. neg-sub0 51.4%

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

      8. *-commutative 51.4%

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

      9. mul-1-neg 51.4%

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

      10. *-commutative 51.4%

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

      11. +-commutative 51.4%

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

      12. *-commutative 51.4%

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

      13. mul-1-neg 51.4%

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

      14. *-commutative 51.4%

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

      15. unsub-neg 51.4%

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

      16. *-commutative 51.4%

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

      17. *-commutative 51.4%

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

   8. Simplified 51.4%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{-101} \lor \neg \left(c \leq 280000000000\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 10^{+20}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -2.4e+100)
   (* a (* c j))
   (if (<= j 1e+20) (* z (* x y)) (* i (* y (- j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.4e+100) {
		tmp = a * (c * j);
	} else if (j <= 1e+20) {
		tmp = z * (x * y);
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-2.4d+100)) then
        tmp = a * (c * j)
    else if (j <= 1d+20) then
        tmp = z * (x * y)
    else
        tmp = i * (y * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.4e+100) {
		tmp = a * (c * j);
	} else if (j <= 1e+20) {
		tmp = z * (x * y);
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -2.4e+100:
		tmp = a * (c * j)
	elif j <= 1e+20:
		tmp = z * (x * y)
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -2.4e+100)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= 1e+20)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -2.4e+100)
		tmp = a * (c * j);
	elseif (j <= 1e+20)
		tmp = z * (x * y);
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -2.4e+100], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1e+20], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.40000000000000012e100

   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. Add Preprocessing

   3. Taylor expanded in a around inf 61.8%

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

      1. +-commutative 61.8%

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

      2. mul-1-neg 61.8%

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

      3. unsub-neg 61.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in c around inf 52.5%

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

   if -2.40000000000000012e100 < j < 1e20

   1. Initial program 69.3%

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

   3. Taylor expanded in z around inf 51.9%

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

      1. *-commutative 51.9%

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

   5. Simplified 51.9%

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

   6. Taylor expanded in y around inf 36.3%

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

   if 1e20 < j

   1. Initial program 76.3%

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

   3. Taylor expanded in y around inf 52.1%

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

      1. +-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

      4. *-commutative 52.1%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in z around 0 44.8%

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

      1. neg-mul-1 44.8%

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

      2. distribute-rgt-neg-in 44.8%

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

      3. distribute-lft-neg-in 44.8%

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

   8. Simplified 44.8%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 10^{+20}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 28.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.85 \cdot 10^{-56} \lor \neg \left(b \leq 4.4 \cdot 10^{+92}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -3.85e-56) (not (<= b 4.4e+92))) (* b (* t i)) (* c (* a j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.85e-56) || !(b <= 4.4e+92)) {
		tmp = b * (t * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-3.85d-56)) .or. (.not. (b <= 4.4d+92))) then
        tmp = b * (t * i)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.85e-56) || !(b <= 4.4e+92)) {
		tmp = b * (t * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -3.85e-56) or not (b <= 4.4e+92):
		tmp = b * (t * i)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -3.85e-56) || !(b <= 4.4e+92))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -3.85e-56) || ~((b <= 4.4e+92)))
		tmp = b * (t * i);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -3.85e-56], N[Not[LessEqual[b, 4.4e+92]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.85000000000000019e-56 or 4.39999999999999984e92 < b

   1. Initial program 71.5%

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

   3. Taylor expanded in t around inf 49.6%

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

      1. distribute-lft-out-- 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in a around 0 37.1%

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

   if -3.85000000000000019e-56 < b < 4.39999999999999984e92

   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. Add Preprocessing

   3. Taylor expanded in c around inf 36.0%

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

   4. Taylor expanded in a around inf 30.3%

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

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.85 \cdot 10^{-56} \lor \neg \left(b \leq 4.4 \cdot 10^{+92}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 28.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-56} \lor \neg \left(b \leq 5.8 \cdot 10^{+92}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -4e-56) (not (<= b 5.8e+92))) (* 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 ((b <= -4e-56) || !(b <= 5.8e+92)) {
		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 ((b <= (-4d-56)) .or. (.not. (b <= 5.8d+92))) 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 ((b <= -4e-56) || !(b <= 5.8e+92)) {
		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 (b <= -4e-56) or not (b <= 5.8e+92):
		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 ((b <= -4e-56) || !(b <= 5.8e+92))
		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 ((b <= -4e-56) || ~((b <= 5.8e+92)))
		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[b, -4e-56], N[Not[LessEqual[b, 5.8e+92]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.0000000000000002e-56 or 5.8000000000000001e92 < b

   1. Initial program 71.5%

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

   3. Taylor expanded in t around inf 49.6%

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

      1. distribute-lft-out-- 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in a around 0 37.1%

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

   if -4.0000000000000002e-56 < b < 5.8000000000000001e92

   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. Add Preprocessing

   3. Taylor expanded in a around inf 45.6%

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

      1. +-commutative 45.6%

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

      2. mul-1-neg 45.6%

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

      3. unsub-neg 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in c around inf 27.8%

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

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-56} \lor \neg \left(b \leq 5.8 \cdot 10^{+92}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.36 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.36e+97)
   (* a (* c j))
   (if (<= j 1.6e+15) (* x (* y z)) (* c (* a j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.36e+97) {
		tmp = a * (c * j);
	} else if (j <= 1.6e+15) {
		tmp = x * (y * z);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-1.36d+97)) then
        tmp = a * (c * j)
    else if (j <= 1.6d+15) then
        tmp = x * (y * z)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.36e+97) {
		tmp = a * (c * j);
	} else if (j <= 1.6e+15) {
		tmp = x * (y * z);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.36e+97:
		tmp = a * (c * j)
	elif j <= 1.6e+15:
		tmp = x * (y * z)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.36e+97)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= 1.6e+15)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.36e+97)
		tmp = a * (c * j);
	elseif (j <= 1.6e+15)
		tmp = x * (y * z);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.36e+97], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.6e+15], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.36e97

   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. Add Preprocessing

   3. Taylor expanded in a around inf 61.8%

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

      1. +-commutative 61.8%

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

      2. mul-1-neg 61.8%

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

      3. unsub-neg 61.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in c around inf 52.5%

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

   if -1.36e97 < j < 1.6e15

   1. Initial program 69.3%

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

   3. Taylor expanded in y around inf 45.5%

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

      1. +-commutative 45.5%

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

      2. mul-1-neg 45.5%

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

      3. unsub-neg 45.5%

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

      4. *-commutative 45.5%

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

   5. Simplified 45.5%

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

   6. Taylor expanded in z around inf 35.1%

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

      1. *-commutative 35.1%

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

   8. Simplified 35.1%

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

   if 1.6e15 < j

   1. Initial program 76.3%

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

   3. Taylor expanded in c around inf 53.0%

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

   4. Taylor expanded in a around inf 34.1%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.36 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.2% 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 69.8%

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

3. Taylor expanded in a around inf 37.2%

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

   1. +-commutative 37.2%

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

   2. mul-1-neg 37.2%

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

   3. unsub-neg 37.2%

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

5. Simplified 37.2%

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

6. Taylor expanded in c around inf 21.3%

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

Developer Target 1: 58.9% 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 2024145 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

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