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

Percentage Accurate: 73.4% → 82.2%

Time: 19.8s

Alternatives: 21

Speedup: 0.5×

• 59.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 49.5%

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

      1. distribute-lft-out-- 49.5%

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

      2. *-commutative 49.5%

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

   5. Simplified 49.5%

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

4. Final simplification 83.9%

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

Alternative 2: 53.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-279}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+117}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 7.3 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -1.5e+65)
     t_2
     (if (<= a -1.55e-279)
       (+ (* j (- (* a c) (* y i))) (* b (* t i)))
       (if (<= a 6.2e-77)
         (* b (- (* t i) (* z c)))
         (if (<= a 4.5e+108)
           t_1
           (if (<= a 2.9e+117)
             (* i (- (* t b) (* y j)))
             (if (<= a 7.3e+130) 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 = x * ((y * z) - (t * a));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.5e+65) {
		tmp = t_2;
	} else if (a <= -1.55e-279) {
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	} else if (a <= 6.2e-77) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 4.5e+108) {
		tmp = t_1;
	} else if (a <= 2.9e+117) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 7.3e+130) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-1.5d+65)) then
        tmp = t_2
    else if (a <= (-1.55d-279)) then
        tmp = (j * ((a * c) - (y * i))) + (b * (t * i))
    else if (a <= 6.2d-77) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 4.5d+108) then
        tmp = t_1
    else if (a <= 2.9d+117) then
        tmp = i * ((t * b) - (y * j))
    else if (a <= 7.3d+130) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.5e+65) {
		tmp = t_2;
	} else if (a <= -1.55e-279) {
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	} else if (a <= 6.2e-77) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 4.5e+108) {
		tmp = t_1;
	} else if (a <= 2.9e+117) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 7.3e+130) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.5e+65:
		tmp = t_2
	elif a <= -1.55e-279:
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i))
	elif a <= 6.2e-77:
		tmp = b * ((t * i) - (z * c))
	elif a <= 4.5e+108:
		tmp = t_1
	elif a <= 2.9e+117:
		tmp = i * ((t * b) - (y * j))
	elif a <= 7.3e+130:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.5e+65)
		tmp = t_2;
	elseif (a <= -1.55e-279)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(b * Float64(t * i)));
	elseif (a <= 6.2e-77)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 4.5e+108)
		tmp = t_1;
	elseif (a <= 2.9e+117)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (a <= 7.3e+130)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.5e+65)
		tmp = t_2;
	elseif (a <= -1.55e-279)
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	elseif (a <= 6.2e-77)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 4.5e+108)
		tmp = t_1;
	elseif (a <= 2.9e+117)
		tmp = i * ((t * b) - (y * j));
	elseif (a <= 7.3e+130)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e+65], t$95$2, If[LessEqual[a, -1.55e-279], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-77], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+108], t$95$1, If[LessEqual[a, 2.9e+117], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.3e+130], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.5000000000000001e65 or 7.3e130 < 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 74.7%

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

      1. +-commutative 74.7%

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

      2. mul-1-neg 74.7%

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

      3. unsub-neg 74.7%

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

      4. *-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -1.5000000000000001e65 < a < -1.55e-279

   1. Initial program 80.3%

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

   3. Taylor expanded in i around inf 61.4%

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

   if -1.55e-279 < a < 6.20000000000000016e-77

   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 b around inf 63.8%

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

   if 6.20000000000000016e-77 < a < 4.5e108 or 2.90000000000000027e117 < a < 7.3e130

   1. Initial program 71.8%

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

   3. Taylor expanded in x around inf 67.1%

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

   if 4.5e108 < a < 2.90000000000000027e117

   1. Initial program 50.9%

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

   3. Taylor expanded in i around -inf 85.2%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-279}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+117}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 7.3 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.46 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-97}:\\ \;\;\;\;y \cdot \left(j \cdot \left(c \cdot \frac{a}{y} - i\right)\right)\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+117}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -1.46e+65)
     t_2
     (if (<= a -3e-97)
       (* y (* j (- (* c (/ a y)) i)))
       (if (<= a 6.6e-77)
         (* b (- (* t i) (* z c)))
         (if (<= a 1e+110)
           t_1
           (if (<= a 3.6e+117)
             (* i (- (* t b) (* y j)))
             (if (<= a 9.2e+131) 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 = x * ((y * z) - (t * a));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.46e+65) {
		tmp = t_2;
	} else if (a <= -3e-97) {
		tmp = y * (j * ((c * (a / y)) - i));
	} else if (a <= 6.6e-77) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1e+110) {
		tmp = t_1;
	} else if (a <= 3.6e+117) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 9.2e+131) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-1.46d+65)) then
        tmp = t_2
    else if (a <= (-3d-97)) then
        tmp = y * (j * ((c * (a / y)) - i))
    else if (a <= 6.6d-77) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 1d+110) then
        tmp = t_1
    else if (a <= 3.6d+117) then
        tmp = i * ((t * b) - (y * j))
    else if (a <= 9.2d+131) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.46e+65) {
		tmp = t_2;
	} else if (a <= -3e-97) {
		tmp = y * (j * ((c * (a / y)) - i));
	} else if (a <= 6.6e-77) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1e+110) {
		tmp = t_1;
	} else if (a <= 3.6e+117) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 9.2e+131) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.46e+65:
		tmp = t_2
	elif a <= -3e-97:
		tmp = y * (j * ((c * (a / y)) - i))
	elif a <= 6.6e-77:
		tmp = b * ((t * i) - (z * c))
	elif a <= 1e+110:
		tmp = t_1
	elif a <= 3.6e+117:
		tmp = i * ((t * b) - (y * j))
	elif a <= 9.2e+131:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.46e+65)
		tmp = t_2;
	elseif (a <= -3e-97)
		tmp = Float64(y * Float64(j * Float64(Float64(c * Float64(a / y)) - i)));
	elseif (a <= 6.6e-77)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 1e+110)
		tmp = t_1;
	elseif (a <= 3.6e+117)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (a <= 9.2e+131)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.46e+65)
		tmp = t_2;
	elseif (a <= -3e-97)
		tmp = y * (j * ((c * (a / y)) - i));
	elseif (a <= 6.6e-77)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 1e+110)
		tmp = t_1;
	elseif (a <= 3.6e+117)
		tmp = i * ((t * b) - (y * j));
	elseif (a <= 9.2e+131)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.46e+65], t$95$2, If[LessEqual[a, -3e-97], N[(y * N[(j * N[(N[(c * N[(a / y), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.6e-77], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+110], t$95$1, If[LessEqual[a, 3.6e+117], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e+131], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.45999999999999999e65 or 9.19999999999999966e131 < 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 74.7%

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

      1. +-commutative 74.7%

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

      2. mul-1-neg 74.7%

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

      3. unsub-neg 74.7%

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

      4. *-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -1.45999999999999999e65 < a < -3.00000000000000024e-97

   1. Initial program 78.7%

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

   3. Taylor expanded in j around inf 61.5%

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

   4. Taylor expanded in y around inf 61.5%

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

      1. associate-/l* 61.6%

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

   6. Simplified 61.6%

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

   7. Taylor expanded in j around 0 61.5%

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

      1. *-commutative 61.5%

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

      2. associate-*r/ 61.6%

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

      3. fma-neg 61.6%

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

      4. associate-*l* 61.7%

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

      5. fma-neg 61.7%

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

      6. associate-*r/ 61.6%

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

      7. *-commutative 61.6%

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

      8. associate-/l* 61.7%

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

   9. Simplified 61.7%

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

   if -3.00000000000000024e-97 < a < 6.59999999999999982e-77

   1. Initial program 82.9%

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

   3. Taylor expanded in b around inf 58.1%

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

   if 6.59999999999999982e-77 < a < 1e110 or 3.60000000000000013e117 < a < 9.19999999999999966e131

   1. Initial program 71.8%

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

   3. Taylor expanded in x around inf 67.1%

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

   if 1e110 < a < 3.60000000000000013e117

   1. Initial program 50.9%

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

   3. Taylor expanded in i around -inf 85.2%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-97}:\\ \;\;\;\;y \cdot \left(j \cdot \left(c \cdot \frac{a}{y} - i\right)\right)\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 10^{+110}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+117}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-94}:\\ \;\;\;\;j \cdot \left(y \cdot \left(a \cdot \frac{c}{y} - i\right)\right)\\ \mathbf{elif}\;a \leq 6.7 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+118}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 3.85 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -1.5e+65)
     t_2
     (if (<= a -3.6e-94)
       (* j (* y (- (* a (/ c y)) i)))
       (if (<= a 6.7e-77)
         (* b (- (* t i) (* z c)))
         (if (<= a 1.2e+108)
           t_1
           (if (<= a 1.3e+118)
             (* i (- (* t b) (* y j)))
             (if (<= a 3.85e+130) 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 = x * ((y * z) - (t * a));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.5e+65) {
		tmp = t_2;
	} else if (a <= -3.6e-94) {
		tmp = j * (y * ((a * (c / y)) - i));
	} else if (a <= 6.7e-77) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.2e+108) {
		tmp = t_1;
	} else if (a <= 1.3e+118) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 3.85e+130) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-1.5d+65)) then
        tmp = t_2
    else if (a <= (-3.6d-94)) then
        tmp = j * (y * ((a * (c / y)) - i))
    else if (a <= 6.7d-77) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 1.2d+108) then
        tmp = t_1
    else if (a <= 1.3d+118) then
        tmp = i * ((t * b) - (y * j))
    else if (a <= 3.85d+130) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.5e+65) {
		tmp = t_2;
	} else if (a <= -3.6e-94) {
		tmp = j * (y * ((a * (c / y)) - i));
	} else if (a <= 6.7e-77) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.2e+108) {
		tmp = t_1;
	} else if (a <= 1.3e+118) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 3.85e+130) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.5e+65:
		tmp = t_2
	elif a <= -3.6e-94:
		tmp = j * (y * ((a * (c / y)) - i))
	elif a <= 6.7e-77:
		tmp = b * ((t * i) - (z * c))
	elif a <= 1.2e+108:
		tmp = t_1
	elif a <= 1.3e+118:
		tmp = i * ((t * b) - (y * j))
	elif a <= 3.85e+130:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.5e+65)
		tmp = t_2;
	elseif (a <= -3.6e-94)
		tmp = Float64(j * Float64(y * Float64(Float64(a * Float64(c / y)) - i)));
	elseif (a <= 6.7e-77)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 1.2e+108)
		tmp = t_1;
	elseif (a <= 1.3e+118)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (a <= 3.85e+130)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.5e+65)
		tmp = t_2;
	elseif (a <= -3.6e-94)
		tmp = j * (y * ((a * (c / y)) - i));
	elseif (a <= 6.7e-77)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 1.2e+108)
		tmp = t_1;
	elseif (a <= 1.3e+118)
		tmp = i * ((t * b) - (y * j));
	elseif (a <= 3.85e+130)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e+65], t$95$2, If[LessEqual[a, -3.6e-94], N[(j * N[(y * N[(N[(a * N[(c / y), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.7e-77], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+108], t$95$1, If[LessEqual[a, 1.3e+118], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.85e+130], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.5000000000000001e65 or 3.8500000000000002e130 < 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 74.7%

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

      1. +-commutative 74.7%

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

      2. mul-1-neg 74.7%

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

      3. unsub-neg 74.7%

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

      4. *-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -1.5000000000000001e65 < a < -3.6e-94

   1. Initial program 78.7%

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

   3. Taylor expanded in j around inf 61.5%

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

   4. Taylor expanded in y around inf 61.5%

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

      1. associate-/l* 61.6%

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

   6. Simplified 61.6%

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

   if -3.6e-94 < a < 6.6999999999999997e-77

   1. Initial program 82.9%

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

   3. Taylor expanded in b around inf 58.1%

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

   if 6.6999999999999997e-77 < a < 1.20000000000000009e108 or 1.30000000000000008e118 < a < 3.8500000000000002e130

   1. Initial program 71.8%

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

   3. Taylor expanded in x around inf 67.1%

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

   if 1.20000000000000009e108 < a < 1.30000000000000008e118

   1. Initial program 50.9%

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

   3. Taylor expanded in i around -inf 85.2%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-94}:\\ \;\;\;\;j \cdot \left(y \cdot \left(a \cdot \frac{c}{y} - i\right)\right)\\ \mathbf{elif}\;a \leq 6.7 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+118}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 3.85 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.46 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-95}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+117}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.68 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -1.46e+65)
     t_2
     (if (<= a -1.4e-95)
       (* j (- (* a c) (* y i)))
       (if (<= a 4.9e-77)
         (* b (- (* t i) (* z c)))
         (if (<= a 2.3e+110)
           t_1
           (if (<= a 2.9e+117)
             (* i (- (* t b) (* y j)))
             (if (<= a 1.68e+131) 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 = x * ((y * z) - (t * a));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.46e+65) {
		tmp = t_2;
	} else if (a <= -1.4e-95) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 4.9e-77) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 2.3e+110) {
		tmp = t_1;
	} else if (a <= 2.9e+117) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 1.68e+131) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-1.46d+65)) then
        tmp = t_2
    else if (a <= (-1.4d-95)) then
        tmp = j * ((a * c) - (y * i))
    else if (a <= 4.9d-77) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 2.3d+110) then
        tmp = t_1
    else if (a <= 2.9d+117) then
        tmp = i * ((t * b) - (y * j))
    else if (a <= 1.68d+131) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.46e+65) {
		tmp = t_2;
	} else if (a <= -1.4e-95) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 4.9e-77) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 2.3e+110) {
		tmp = t_1;
	} else if (a <= 2.9e+117) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 1.68e+131) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.46e+65:
		tmp = t_2
	elif a <= -1.4e-95:
		tmp = j * ((a * c) - (y * i))
	elif a <= 4.9e-77:
		tmp = b * ((t * i) - (z * c))
	elif a <= 2.3e+110:
		tmp = t_1
	elif a <= 2.9e+117:
		tmp = i * ((t * b) - (y * j))
	elif a <= 1.68e+131:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.46e+65)
		tmp = t_2;
	elseif (a <= -1.4e-95)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (a <= 4.9e-77)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 2.3e+110)
		tmp = t_1;
	elseif (a <= 2.9e+117)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (a <= 1.68e+131)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.46e+65)
		tmp = t_2;
	elseif (a <= -1.4e-95)
		tmp = j * ((a * c) - (y * i));
	elseif (a <= 4.9e-77)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 2.3e+110)
		tmp = t_1;
	elseif (a <= 2.9e+117)
		tmp = i * ((t * b) - (y * j));
	elseif (a <= 1.68e+131)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.46e+65], t$95$2, If[LessEqual[a, -1.4e-95], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.9e-77], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+110], t$95$1, If[LessEqual[a, 2.9e+117], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.68e+131], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.45999999999999999e65 or 1.67999999999999992e131 < 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 74.7%

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

      1. +-commutative 74.7%

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

      2. mul-1-neg 74.7%

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

      3. unsub-neg 74.7%

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

      4. *-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -1.45999999999999999e65 < a < -1.4e-95

   1. Initial program 78.7%

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

   3. Taylor expanded in j around inf 61.5%

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

   if -1.4e-95 < a < 4.8999999999999997e-77

   1. Initial program 82.9%

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

   3. Taylor expanded in b around inf 58.1%

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

   if 4.8999999999999997e-77 < a < 2.3e110 or 2.90000000000000027e117 < a < 1.67999999999999992e131

   1. Initial program 71.8%

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

   3. Taylor expanded in x around inf 67.1%

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

   if 2.3e110 < a < 2.90000000000000027e117

   1. Initial program 50.9%

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

   3. Taylor expanded in i around -inf 85.2%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-95}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+117}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.68 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-95}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -1.5e+65)
     t_2
     (if (<= a -5.2e-95)
       (* j (- (* a c) (* y i)))
       (if (<= a 3.2e-40)
         t_1
         (if (<= a 8.6e+111)
           t_2
           (if (<= a 9.5e+119)
             t_1
             (if (<= a 6e+158) (* t (* x (- a))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.5e+65) {
		tmp = t_2;
	} else if (a <= -5.2e-95) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 3.2e-40) {
		tmp = t_1;
	} else if (a <= 8.6e+111) {
		tmp = t_2;
	} else if (a <= 9.5e+119) {
		tmp = t_1;
	} else if (a <= 6e+158) {
		tmp = t * (x * -a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-1.5d+65)) then
        tmp = t_2
    else if (a <= (-5.2d-95)) then
        tmp = j * ((a * c) - (y * i))
    else if (a <= 3.2d-40) then
        tmp = t_1
    else if (a <= 8.6d+111) then
        tmp = t_2
    else if (a <= 9.5d+119) then
        tmp = t_1
    else if (a <= 6d+158) then
        tmp = t * (x * -a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.5e+65) {
		tmp = t_2;
	} else if (a <= -5.2e-95) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 3.2e-40) {
		tmp = t_1;
	} else if (a <= 8.6e+111) {
		tmp = t_2;
	} else if (a <= 9.5e+119) {
		tmp = t_1;
	} else if (a <= 6e+158) {
		tmp = t * (x * -a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.5e+65:
		tmp = t_2
	elif a <= -5.2e-95:
		tmp = j * ((a * c) - (y * i))
	elif a <= 3.2e-40:
		tmp = t_1
	elif a <= 8.6e+111:
		tmp = t_2
	elif a <= 9.5e+119:
		tmp = t_1
	elif a <= 6e+158:
		tmp = t * (x * -a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.5e+65)
		tmp = t_2;
	elseif (a <= -5.2e-95)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (a <= 3.2e-40)
		tmp = t_1;
	elseif (a <= 8.6e+111)
		tmp = t_2;
	elseif (a <= 9.5e+119)
		tmp = t_1;
	elseif (a <= 6e+158)
		tmp = Float64(t * Float64(x * Float64(-a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.5e+65)
		tmp = t_2;
	elseif (a <= -5.2e-95)
		tmp = j * ((a * c) - (y * i));
	elseif (a <= 3.2e-40)
		tmp = t_1;
	elseif (a <= 8.6e+111)
		tmp = t_2;
	elseif (a <= 9.5e+119)
		tmp = t_1;
	elseif (a <= 6e+158)
		tmp = t * (x * -a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e+65], t$95$2, If[LessEqual[a, -5.2e-95], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e-40], t$95$1, If[LessEqual[a, 8.6e+111], t$95$2, If[LessEqual[a, 9.5e+119], t$95$1, If[LessEqual[a, 6e+158], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.5000000000000001e65 or 3.20000000000000002e-40 < a < 8.59999999999999987e111 or 6e158 < a

   1. Initial program 66.8%

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

   3. Taylor expanded in a around inf 69.4%

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

      1. +-commutative 69.4%

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

      2. mul-1-neg 69.4%

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

      3. unsub-neg 69.4%

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

      4. *-commutative 69.4%

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

   5. Simplified 69.4%

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

   if -1.5000000000000001e65 < a < -5.20000000000000001e-95

   1. Initial program 78.7%

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

   3. Taylor expanded in j around inf 61.5%

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

   if -5.20000000000000001e-95 < a < 3.20000000000000002e-40 or 8.59999999999999987e111 < a < 9.4999999999999994e119

   1. Initial program 81.4%

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

   3. Taylor expanded in b around inf 59.0%

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

   if 9.4999999999999994e119 < a < 6e158

   1. Initial program 55.6%

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

   3. Taylor expanded in t around inf 66.7%

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

      1. distribute-lft-out-- 66.7%

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

      2. *-commutative 66.7%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in a around inf 56.4%

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

      1. *-commutative 56.4%

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

   8. Simplified 56.4%

      \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(x \cdot a\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-95}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-40}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+111}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+157}:\\ \;\;\;\;z \cdot \left(x \cdot y - \frac{x \cdot \left(t \cdot a\right)}{z}\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1.55e+65)
     t_1
     (if (<= a -1.95e-103)
       (+ (* j (- (* a c) (* y i))) (* b (* t i)))
       (if (<= a 3.1e+157)
         (+ (* z (- (* x y) (/ (* x (* t a)) z))) (* b (- (* t i) (* z c))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.55e+65) {
		tmp = t_1;
	} else if (a <= -1.95e-103) {
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	} else if (a <= 3.1e+157) {
		tmp = (z * ((x * y) - ((x * (t * a)) / z))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-1.55d+65)) then
        tmp = t_1
    else if (a <= (-1.95d-103)) then
        tmp = (j * ((a * c) - (y * i))) + (b * (t * i))
    else if (a <= 3.1d+157) then
        tmp = (z * ((x * y) - ((x * (t * a)) / z))) + (b * ((t * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.55e+65) {
		tmp = t_1;
	} else if (a <= -1.95e-103) {
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	} else if (a <= 3.1e+157) {
		tmp = (z * ((x * y) - ((x * (t * a)) / z))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.55e+65:
		tmp = t_1
	elif a <= -1.95e-103:
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i))
	elif a <= 3.1e+157:
		tmp = (z * ((x * y) - ((x * (t * a)) / z))) + (b * ((t * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.55e+65)
		tmp = t_1;
	elseif (a <= -1.95e-103)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(b * Float64(t * i)));
	elseif (a <= 3.1e+157)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(Float64(x * Float64(t * a)) / z))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.55e+65)
		tmp = t_1;
	elseif (a <= -1.95e-103)
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	elseif (a <= 3.1e+157)
		tmp = (z * ((x * y) - ((x * (t * a)) / z))) + (b * ((t * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e+65], t$95$1, If[LessEqual[a, -1.95e-103], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e+157], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.54999999999999995e65 or 3.0999999999999997e157 < a

   1. Initial program 65.7%

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

   3. Taylor expanded in a around inf 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

      4. *-commutative 75.6%

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

   5. Simplified 75.6%

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

   if -1.54999999999999995e65 < a < -1.9500000000000001e-103

   1. Initial program 76.8%

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

   3. Taylor expanded in i around inf 63.9%

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

   if -1.9500000000000001e-103 < a < 3.0999999999999997e157

   1. Initial program 77.8%

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

   3. Taylor expanded in z around inf 67.5%

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

      1. +-commutative 67.5%

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

      2. mul-1-neg 67.5%

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

      3. unsub-neg 67.5%

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

      4. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in j around 0 59.3%

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

      1. *-commutative 59.3%

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

      2. *-commutative 59.3%

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

      3. *-commutative 59.3%

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

      4. *-commutative 59.3%

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

      5. associate-*l* 65.7%

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

      6. *-commutative 65.7%

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

      7. *-commutative 65.7%

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

      8. *-commutative 65.7%

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

   8. Simplified 65.7%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+157}:\\ \;\;\;\;z \cdot \left(x \cdot y - \frac{x \cdot \left(t \cdot a\right)}{z}\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-85}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-110}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -6.2e+56)
     t_2
     (if (<= a -4.1e-16)
       t_1
       (if (<= a -1.55e-85)
         (* c (- (* a j) (* z b)))
         (if (<= a -4.4e-110)
           (* (* y i) (- j))
           (if (<= a 1.25e-40) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -6.2e+56) {
		tmp = t_2;
	} else if (a <= -4.1e-16) {
		tmp = t_1;
	} else if (a <= -1.55e-85) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= -4.4e-110) {
		tmp = (y * i) * -j;
	} else if (a <= 1.25e-40) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-6.2d+56)) then
        tmp = t_2
    else if (a <= (-4.1d-16)) then
        tmp = t_1
    else if (a <= (-1.55d-85)) then
        tmp = c * ((a * j) - (z * b))
    else if (a <= (-4.4d-110)) then
        tmp = (y * i) * -j
    else if (a <= 1.25d-40) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -6.2e+56) {
		tmp = t_2;
	} else if (a <= -4.1e-16) {
		tmp = t_1;
	} else if (a <= -1.55e-85) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= -4.4e-110) {
		tmp = (y * i) * -j;
	} else if (a <= 1.25e-40) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -6.2e+56:
		tmp = t_2
	elif a <= -4.1e-16:
		tmp = t_1
	elif a <= -1.55e-85:
		tmp = c * ((a * j) - (z * b))
	elif a <= -4.4e-110:
		tmp = (y * i) * -j
	elif a <= 1.25e-40:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -6.2e+56)
		tmp = t_2;
	elseif (a <= -4.1e-16)
		tmp = t_1;
	elseif (a <= -1.55e-85)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (a <= -4.4e-110)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (a <= 1.25e-40)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -6.2e+56)
		tmp = t_2;
	elseif (a <= -4.1e-16)
		tmp = t_1;
	elseif (a <= -1.55e-85)
		tmp = c * ((a * j) - (z * b));
	elseif (a <= -4.4e-110)
		tmp = (y * i) * -j;
	elseif (a <= 1.25e-40)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.2e+56], t$95$2, If[LessEqual[a, -4.1e-16], t$95$1, If[LessEqual[a, -1.55e-85], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.4e-110], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[a, 1.25e-40], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.20000000000000009e56 or 1.24999999999999991e-40 < a

   1. Initial program 65.4%

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

   3. Taylor expanded in a around inf 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   if -6.20000000000000009e56 < a < -4.10000000000000006e-16 or -4.3999999999999999e-110 < a < 1.24999999999999991e-40

   1. Initial program 83.1%

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

   3. Taylor expanded in b around inf 58.2%

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

   if -4.10000000000000006e-16 < a < -1.5500000000000001e-85

   1. Initial program 89.4%

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

   3. Taylor expanded in c around inf 60.9%

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

      1. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   if -1.5500000000000001e-85 < a < -4.3999999999999999e-110

   1. Initial program 66.7%

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

   3. Taylor expanded in j around inf 66.7%

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

   4. Taylor expanded in a around 0 66.7%

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

      1. mul-1-neg 66.7%

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

      2. distribute-rgt-neg-in 66.7%

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

   6. Simplified 66.7%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+56}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-16}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-85}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-110}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-40}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-83}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-122}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -3.1e+56)
     t_2
     (if (<= a -1.9e-15)
       t_1
       (if (<= a -6.5e-83)
         t_2
         (if (<= a -1.6e-122) (* (* y i) (- j)) (if (<= a 3e-41) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.1e+56) {
		tmp = t_2;
	} else if (a <= -1.9e-15) {
		tmp = t_1;
	} else if (a <= -6.5e-83) {
		tmp = t_2;
	} else if (a <= -1.6e-122) {
		tmp = (y * i) * -j;
	} else if (a <= 3e-41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-3.1d+56)) then
        tmp = t_2
    else if (a <= (-1.9d-15)) then
        tmp = t_1
    else if (a <= (-6.5d-83)) then
        tmp = t_2
    else if (a <= (-1.6d-122)) then
        tmp = (y * i) * -j
    else if (a <= 3d-41) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.1e+56) {
		tmp = t_2;
	} else if (a <= -1.9e-15) {
		tmp = t_1;
	} else if (a <= -6.5e-83) {
		tmp = t_2;
	} else if (a <= -1.6e-122) {
		tmp = (y * i) * -j;
	} else if (a <= 3e-41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -3.1e+56:
		tmp = t_2
	elif a <= -1.9e-15:
		tmp = t_1
	elif a <= -6.5e-83:
		tmp = t_2
	elif a <= -1.6e-122:
		tmp = (y * i) * -j
	elif a <= 3e-41:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.1e+56)
		tmp = t_2;
	elseif (a <= -1.9e-15)
		tmp = t_1;
	elseif (a <= -6.5e-83)
		tmp = t_2;
	elseif (a <= -1.6e-122)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (a <= 3e-41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -3.1e+56)
		tmp = t_2;
	elseif (a <= -1.9e-15)
		tmp = t_1;
	elseif (a <= -6.5e-83)
		tmp = t_2;
	elseif (a <= -1.6e-122)
		tmp = (y * i) * -j;
	elseif (a <= 3e-41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.1e+56], t$95$2, If[LessEqual[a, -1.9e-15], t$95$1, If[LessEqual[a, -6.5e-83], t$95$2, If[LessEqual[a, -1.6e-122], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[a, 3e-41], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.10000000000000005e56 or -1.9000000000000001e-15 < a < -6.5e-83 or 2.99999999999999989e-41 < a

   1. Initial program 67.0%

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

   3. Taylor expanded in a around inf 65.4%

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

      1. +-commutative 65.4%

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

      2. mul-1-neg 65.4%

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

      3. unsub-neg 65.4%

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

      4. *-commutative 65.4%

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

   5. Simplified 65.4%

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

   if -3.10000000000000005e56 < a < -1.9000000000000001e-15 or -1.6000000000000001e-122 < a < 2.99999999999999989e-41

   1. Initial program 83.1%

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

   3. Taylor expanded in b around inf 58.2%

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

   if -6.5e-83 < a < -1.6000000000000001e-122

   1. Initial program 66.7%

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

   3. Taylor expanded in j around inf 66.7%

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

   4. Taylor expanded in a around 0 66.7%

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

      1. mul-1-neg 66.7%

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

      2. distribute-rgt-neg-in 66.7%

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

   6. Simplified 66.7%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+56}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-122}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{if}\;a \leq -1.46 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-40}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* t a) (- x))))
   (if (<= a -1.46e+65)
     t_1
     (if (<= a -2.3e-100)
       (* y (* i (- j)))
       (if (<= a 1.05e-139)
         (* t (* b i))
         (if (<= a 2.3e-40)
           (* b (* z (- c)))
           (if (<= a 4.2e+200) t_1 (* c (* a j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * a) * -x;
	double tmp;
	if (a <= -1.46e+65) {
		tmp = t_1;
	} else if (a <= -2.3e-100) {
		tmp = y * (i * -j);
	} else if (a <= 1.05e-139) {
		tmp = t * (b * i);
	} else if (a <= 2.3e-40) {
		tmp = b * (z * -c);
	} else if (a <= 4.2e+200) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (t * a) * -x
    if (a <= (-1.46d+65)) then
        tmp = t_1
    else if (a <= (-2.3d-100)) then
        tmp = y * (i * -j)
    else if (a <= 1.05d-139) then
        tmp = t * (b * i)
    else if (a <= 2.3d-40) then
        tmp = b * (z * -c)
    else if (a <= 4.2d+200) then
        tmp = t_1
    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 t_1 = (t * a) * -x;
	double tmp;
	if (a <= -1.46e+65) {
		tmp = t_1;
	} else if (a <= -2.3e-100) {
		tmp = y * (i * -j);
	} else if (a <= 1.05e-139) {
		tmp = t * (b * i);
	} else if (a <= 2.3e-40) {
		tmp = b * (z * -c);
	} else if (a <= 4.2e+200) {
		tmp = t_1;
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * a) * -x
	tmp = 0
	if a <= -1.46e+65:
		tmp = t_1
	elif a <= -2.3e-100:
		tmp = y * (i * -j)
	elif a <= 1.05e-139:
		tmp = t * (b * i)
	elif a <= 2.3e-40:
		tmp = b * (z * -c)
	elif a <= 4.2e+200:
		tmp = t_1
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * a) * Float64(-x))
	tmp = 0.0
	if (a <= -1.46e+65)
		tmp = t_1;
	elseif (a <= -2.3e-100)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (a <= 1.05e-139)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 2.3e-40)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 4.2e+200)
		tmp = t_1;
	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)
	t_1 = (t * a) * -x;
	tmp = 0.0;
	if (a <= -1.46e+65)
		tmp = t_1;
	elseif (a <= -2.3e-100)
		tmp = y * (i * -j);
	elseif (a <= 1.05e-139)
		tmp = t * (b * i);
	elseif (a <= 2.3e-40)
		tmp = b * (z * -c);
	elseif (a <= 4.2e+200)
		tmp = t_1;
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[a, -1.46e+65], t$95$1, If[LessEqual[a, -2.3e-100], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e-139], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e-40], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e+200], t$95$1, N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.45999999999999999e65 or 2.3e-40 < a < 4.19999999999999994e200

   1. Initial program 66.2%

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

   3. Taylor expanded in a around inf 64.0%

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

      1. +-commutative 64.0%

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

      2. mul-1-neg 64.0%

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

      3. unsub-neg 64.0%

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

      4. *-commutative 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in j around 0 44.9%

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

      1. mul-1-neg 44.9%

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

      2. associate-*r* 46.5%

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

      3. distribute-rgt-neg-in 46.5%

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

   8. Simplified 46.5%

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

   if -1.45999999999999999e65 < a < -2.29999999999999994e-100

   1. Initial program 78.7%

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

   3. Taylor expanded in j around inf 61.5%

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

   4. Taylor expanded in y around inf 61.5%

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

      1. associate-/l* 61.6%

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

   6. Simplified 61.6%

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

   7. Taylor expanded in y around inf 30.4%

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

      1. associate-*r* 33.9%

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

      2. associate-*r* 33.9%

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

      3. *-commutative 33.9%

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

      4. mul-1-neg 33.9%

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

      5. distribute-rgt-neg-in 33.9%

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

   9. Simplified 33.9%

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

   if -2.29999999999999994e-100 < a < 1.05000000000000004e-139

   1. Initial program 82.8%

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

   3. Taylor expanded in t around inf 39.9%

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

      1. distribute-lft-out-- 39.9%

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

      2. *-commutative 39.9%

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

   5. Simplified 39.9%

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

   6. Taylor expanded in a around 0 37.0%

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

      1. associate-*r* 38.3%

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

   8. Simplified 38.3%

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

   if 1.05000000000000004e-139 < a < 2.3e-40

   1. Initial program 86.6%

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

   3. Taylor expanded in z around inf 60.7%

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

      1. *-commutative 60.7%

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

      2. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in y around 0 54.2%

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

      1. associate-*r* 54.2%

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

      2. neg-mul-1 54.2%

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

   8. Simplified 54.2%

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

   if 4.19999999999999994e200 < a

   1. Initial program 61.7%

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

   3. Taylor expanded in c around inf 62.0%

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

      1. *-commutative 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in j around inf 62.2%

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

      1. *-commutative 62.2%

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

   8. Simplified 62.2%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+65}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-40}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+200}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -1.46 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-137}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+201}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))))
   (if (<= a -1.46e+65)
     t_1
     (if (<= a -3.5e-94)
       (* y (* i (- j)))
       (if (<= a 5.5e-137)
         (* t (* b i))
         (if (<= a 9.2e-41)
           (* b (* z (- c)))
           (if (<= a 1.5e+201) t_1 (* c (* a j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double tmp;
	if (a <= -1.46e+65) {
		tmp = t_1;
	} else if (a <= -3.5e-94) {
		tmp = y * (i * -j);
	} else if (a <= 5.5e-137) {
		tmp = t * (b * i);
	} else if (a <= 9.2e-41) {
		tmp = b * (z * -c);
	} else if (a <= 1.5e+201) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = a * (x * -t)
    if (a <= (-1.46d+65)) then
        tmp = t_1
    else if (a <= (-3.5d-94)) then
        tmp = y * (i * -j)
    else if (a <= 5.5d-137) then
        tmp = t * (b * i)
    else if (a <= 9.2d-41) then
        tmp = b * (z * -c)
    else if (a <= 1.5d+201) then
        tmp = t_1
    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 t_1 = a * (x * -t);
	double tmp;
	if (a <= -1.46e+65) {
		tmp = t_1;
	} else if (a <= -3.5e-94) {
		tmp = y * (i * -j);
	} else if (a <= 5.5e-137) {
		tmp = t * (b * i);
	} else if (a <= 9.2e-41) {
		tmp = b * (z * -c);
	} else if (a <= 1.5e+201) {
		tmp = t_1;
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * -t)
	tmp = 0
	if a <= -1.46e+65:
		tmp = t_1
	elif a <= -3.5e-94:
		tmp = y * (i * -j)
	elif a <= 5.5e-137:
		tmp = t * (b * i)
	elif a <= 9.2e-41:
		tmp = b * (z * -c)
	elif a <= 1.5e+201:
		tmp = t_1
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (a <= -1.46e+65)
		tmp = t_1;
	elseif (a <= -3.5e-94)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (a <= 5.5e-137)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 9.2e-41)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 1.5e+201)
		tmp = t_1;
	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)
	t_1 = a * (x * -t);
	tmp = 0.0;
	if (a <= -1.46e+65)
		tmp = t_1;
	elseif (a <= -3.5e-94)
		tmp = y * (i * -j);
	elseif (a <= 5.5e-137)
		tmp = t * (b * i);
	elseif (a <= 9.2e-41)
		tmp = b * (z * -c);
	elseif (a <= 1.5e+201)
		tmp = t_1;
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.46e+65], t$95$1, If[LessEqual[a, -3.5e-94], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.5e-137], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e-41], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+201], t$95$1, N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.45999999999999999e65 or 9.20000000000000041e-41 < a < 1.50000000000000012e201

   1. Initial program 66.2%

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

   3. Taylor expanded in a around inf 64.0%

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

      1. +-commutative 64.0%

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

      2. mul-1-neg 64.0%

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

      3. unsub-neg 64.0%

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

      4. *-commutative 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in j around 0 44.9%

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

      1. associate-*r* 44.9%

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

      2. mul-1-neg 44.9%

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

   8. Simplified 44.9%

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

   if -1.45999999999999999e65 < a < -3.49999999999999998e-94

   1. Initial program 78.7%

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

   3. Taylor expanded in j around inf 61.5%

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

   4. Taylor expanded in y around inf 61.5%

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

      1. associate-/l* 61.6%

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

   6. Simplified 61.6%

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

   7. Taylor expanded in y around inf 30.4%

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

      1. associate-*r* 33.9%

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

      2. associate-*r* 33.9%

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

      3. *-commutative 33.9%

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

      4. mul-1-neg 33.9%

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

      5. distribute-rgt-neg-in 33.9%

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

   9. Simplified 33.9%

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

   if -3.49999999999999998e-94 < a < 5.5000000000000003e-137

   1. Initial program 82.8%

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

   3. Taylor expanded in t around inf 39.9%

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

      1. distribute-lft-out-- 39.9%

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

      2. *-commutative 39.9%

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

   5. Simplified 39.9%

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

   6. Taylor expanded in a around 0 37.0%

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

      1. associate-*r* 38.3%

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

   8. Simplified 38.3%

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

   if 5.5000000000000003e-137 < a < 9.20000000000000041e-41

   1. Initial program 86.6%

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

   3. Taylor expanded in z around inf 60.7%

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

      1. *-commutative 60.7%

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

      2. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in y around 0 54.2%

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

      1. associate-*r* 54.2%

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

      2. neg-mul-1 54.2%

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

   8. Simplified 54.2%

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

   if 1.50000000000000012e201 < a

   1. Initial program 61.7%

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

   3. Taylor expanded in c around inf 62.0%

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

      1. *-commutative 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in j around inf 62.2%

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

      1. *-commutative 62.2%

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

   8. Simplified 62.2%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-137}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+201}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-94}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1.55e+65)
     t_1
     (if (<= a -8.5e-94)
       (* j (- (* a c) (* y i)))
       (if (<= a 5.8e-77)
         (* b (- (* t i) (* z c)))
         (if (<= a 2.55e+130) (* x (- (* y z) (* t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.55e+65) {
		tmp = t_1;
	} else if (a <= -8.5e-94) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 5.8e-77) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 2.55e+130) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-1.55d+65)) then
        tmp = t_1
    else if (a <= (-8.5d-94)) then
        tmp = j * ((a * c) - (y * i))
    else if (a <= 5.8d-77) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 2.55d+130) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.55e+65) {
		tmp = t_1;
	} else if (a <= -8.5e-94) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 5.8e-77) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 2.55e+130) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.55e+65:
		tmp = t_1
	elif a <= -8.5e-94:
		tmp = j * ((a * c) - (y * i))
	elif a <= 5.8e-77:
		tmp = b * ((t * i) - (z * c))
	elif a <= 2.55e+130:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.55e+65)
		tmp = t_1;
	elseif (a <= -8.5e-94)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (a <= 5.8e-77)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 2.55e+130)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.55e+65)
		tmp = t_1;
	elseif (a <= -8.5e-94)
		tmp = j * ((a * c) - (y * i));
	elseif (a <= 5.8e-77)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 2.55e+130)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e+65], t$95$1, If[LessEqual[a, -8.5e-94], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e-77], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.55e+130], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.54999999999999995e65 or 2.5499999999999998e130 < 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 74.7%

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

      1. +-commutative 74.7%

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

      2. mul-1-neg 74.7%

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

      3. unsub-neg 74.7%

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

      4. *-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -1.54999999999999995e65 < a < -8.50000000000000003e-94

   1. Initial program 78.7%

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

   3. Taylor expanded in j around inf 61.5%

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

   if -8.50000000000000003e-94 < a < 5.7999999999999997e-77

   1. Initial program 82.9%

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

   3. Taylor expanded in b around inf 58.1%

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

   if 5.7999999999999997e-77 < a < 2.5499999999999998e130

   1. Initial program 68.8%

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

   3. Taylor expanded in x around inf 57.6%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-94}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+65}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-98}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-138}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 10^{-40}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.55e+65)
   (* (* t a) (- x))
   (if (<= a -3.8e-98)
     (* y (* i (- j)))
     (if (<= a 1.7e-138)
       (* t (* b i))
       (if (<= a 1e-40) (* b (* z (- c))) (* t (* 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 (a <= -1.55e+65) {
		tmp = (t * a) * -x;
	} else if (a <= -3.8e-98) {
		tmp = y * (i * -j);
	} else if (a <= 1.7e-138) {
		tmp = t * (b * i);
	} else if (a <= 1e-40) {
		tmp = b * (z * -c);
	} else {
		tmp = t * (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 (a <= (-1.55d+65)) then
        tmp = (t * a) * -x
    else if (a <= (-3.8d-98)) then
        tmp = y * (i * -j)
    else if (a <= 1.7d-138) then
        tmp = t * (b * i)
    else if (a <= 1d-40) then
        tmp = b * (z * -c)
    else
        tmp = t * (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 (a <= -1.55e+65) {
		tmp = (t * a) * -x;
	} else if (a <= -3.8e-98) {
		tmp = y * (i * -j);
	} else if (a <= 1.7e-138) {
		tmp = t * (b * i);
	} else if (a <= 1e-40) {
		tmp = b * (z * -c);
	} else {
		tmp = t * (x * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.55e+65:
		tmp = (t * a) * -x
	elif a <= -3.8e-98:
		tmp = y * (i * -j)
	elif a <= 1.7e-138:
		tmp = t * (b * i)
	elif a <= 1e-40:
		tmp = b * (z * -c)
	else:
		tmp = t * (x * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.55e+65)
		tmp = Float64(Float64(t * a) * Float64(-x));
	elseif (a <= -3.8e-98)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (a <= 1.7e-138)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 1e-40)
		tmp = Float64(b * Float64(z * Float64(-c)));
	else
		tmp = Float64(t * Float64(x * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.55e+65)
		tmp = (t * a) * -x;
	elseif (a <= -3.8e-98)
		tmp = y * (i * -j);
	elseif (a <= 1.7e-138)
		tmp = t * (b * i);
	elseif (a <= 1e-40)
		tmp = b * (z * -c);
	else
		tmp = t * (x * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.55e+65], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[a, -3.8e-98], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-138], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-40], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.54999999999999995e65

   1. Initial program 68.6%

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

   3. Taylor expanded in a around inf 76.2%

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

      1. +-commutative 76.2%

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

      2. mul-1-neg 76.2%

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

      3. unsub-neg 76.2%

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

      4. *-commutative 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in j around 0 49.6%

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

      1. mul-1-neg 49.6%

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

      2. associate-*r* 52.4%

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

      3. distribute-rgt-neg-in 52.4%

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

   8. Simplified 52.4%

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

   if -1.54999999999999995e65 < a < -3.8000000000000003e-98

   1. Initial program 78.7%

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

   3. Taylor expanded in j around inf 61.5%

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

   4. Taylor expanded in y around inf 61.5%

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

      1. associate-/l* 61.6%

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

   6. Simplified 61.6%

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

   7. Taylor expanded in y around inf 30.4%

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

      1. associate-*r* 33.9%

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

      2. associate-*r* 33.9%

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

      3. *-commutative 33.9%

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

      4. mul-1-neg 33.9%

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

      5. distribute-rgt-neg-in 33.9%

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

   9. Simplified 33.9%

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

   if -3.8000000000000003e-98 < a < 1.7000000000000001e-138

   1. Initial program 82.8%

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

   3. Taylor expanded in t around inf 39.9%

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

      1. distribute-lft-out-- 39.9%

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

      2. *-commutative 39.9%

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

   5. Simplified 39.9%

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

   6. Taylor expanded in a around 0 37.0%

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

      1. associate-*r* 38.3%

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

   8. Simplified 38.3%

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

   if 1.7000000000000001e-138 < a < 9.9999999999999993e-41

   1. Initial program 86.6%

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

   3. Taylor expanded in z around inf 60.7%

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

      1. *-commutative 60.7%

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

      2. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in y around 0 54.2%

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

      1. associate-*r* 54.2%

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

      2. neg-mul-1 54.2%

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

   8. Simplified 54.2%

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

   if 9.9999999999999993e-41 < a

   1. Initial program 62.7%

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

   3. Taylor expanded in t around inf 52.7%

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

      1. distribute-lft-out-- 52.7%

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

      2. *-commutative 52.7%

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

   5. Simplified 52.7%

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

   6. Taylor expanded in a around inf 44.1%

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

      1. *-commutative 44.1%

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

   8. Simplified 44.1%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+65}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-98}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-138}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 10^{-40}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;a \leq -1.46 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 3.85 \cdot 10^{-13}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))))
   (if (<= a -1.46e+65)
     t_1
     (if (<= a -7.2e-95)
       (* y (* i (- j)))
       (if (<= a 3.85e-13)
         (* t (* b i))
         (if (<= a 3e+200) t_1 (* c (* a j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double tmp;
	if (a <= -1.46e+65) {
		tmp = t_1;
	} else if (a <= -7.2e-95) {
		tmp = y * (i * -j);
	} else if (a <= 3.85e-13) {
		tmp = t * (b * i);
	} else if (a <= 3e+200) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = a * (x * -t)
    if (a <= (-1.46d+65)) then
        tmp = t_1
    else if (a <= (-7.2d-95)) then
        tmp = y * (i * -j)
    else if (a <= 3.85d-13) then
        tmp = t * (b * i)
    else if (a <= 3d+200) then
        tmp = t_1
    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 t_1 = a * (x * -t);
	double tmp;
	if (a <= -1.46e+65) {
		tmp = t_1;
	} else if (a <= -7.2e-95) {
		tmp = y * (i * -j);
	} else if (a <= 3.85e-13) {
		tmp = t * (b * i);
	} else if (a <= 3e+200) {
		tmp = t_1;
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * -t)
	tmp = 0
	if a <= -1.46e+65:
		tmp = t_1
	elif a <= -7.2e-95:
		tmp = y * (i * -j)
	elif a <= 3.85e-13:
		tmp = t * (b * i)
	elif a <= 3e+200:
		tmp = t_1
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (a <= -1.46e+65)
		tmp = t_1;
	elseif (a <= -7.2e-95)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (a <= 3.85e-13)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 3e+200)
		tmp = t_1;
	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)
	t_1 = a * (x * -t);
	tmp = 0.0;
	if (a <= -1.46e+65)
		tmp = t_1;
	elseif (a <= -7.2e-95)
		tmp = y * (i * -j);
	elseif (a <= 3.85e-13)
		tmp = t * (b * i);
	elseif (a <= 3e+200)
		tmp = t_1;
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.46e+65], t$95$1, If[LessEqual[a, -7.2e-95], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.85e-13], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3e+200], t$95$1, N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.45999999999999999e65 or 3.8499999999999998e-13 < a < 2.99999999999999991e200

   1. Initial program 66.2%

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

   3. Taylor expanded in a around inf 64.8%

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

      1. +-commutative 64.8%

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

      2. mul-1-neg 64.8%

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

      3. unsub-neg 64.8%

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

      4. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in j around 0 46.0%

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

      1. associate-*r* 46.0%

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

      2. mul-1-neg 46.0%

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

   8. Simplified 46.0%

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

   if -1.45999999999999999e65 < a < -7.2e-95

   1. Initial program 78.7%

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

   3. Taylor expanded in j around inf 61.5%

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

   4. Taylor expanded in y around inf 61.5%

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

      1. associate-/l* 61.6%

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

   6. Simplified 61.6%

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

   7. Taylor expanded in y around inf 30.4%

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

      1. associate-*r* 33.9%

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

      2. associate-*r* 33.9%

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

      3. *-commutative 33.9%

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

      4. mul-1-neg 33.9%

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

      5. distribute-rgt-neg-in 33.9%

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

   9. Simplified 33.9%

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

   if -7.2e-95 < a < 3.8499999999999998e-13

   1. Initial program 82.9%

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

   3. Taylor expanded in t around inf 37.7%

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

      1. distribute-lft-out-- 37.7%

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

      2. *-commutative 37.7%

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

   5. Simplified 37.7%

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

   6. Taylor expanded in a around 0 34.2%

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

      1. associate-*r* 35.2%

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

   8. Simplified 35.2%

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

   if 2.99999999999999991e200 < a

   1. Initial program 61.7%

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

   3. Taylor expanded in c around inf 62.0%

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

      1. *-commutative 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in j around inf 62.2%

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

      1. *-commutative 62.2%

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

   8. Simplified 62.2%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 3.85 \cdot 10^{-13}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+200}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-144}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -2.7e-80)
     t_1
     (if (<= a 4e-144)
       (* t (* b i))
       (if (<= a 1.7e-41) (* b (* z (- c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.7e-80) {
		tmp = t_1;
	} else if (a <= 4e-144) {
		tmp = t * (b * i);
	} else if (a <= 1.7e-41) {
		tmp = b * (z * -c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-2.7d-80)) then
        tmp = t_1
    else if (a <= 4d-144) then
        tmp = t * (b * i)
    else if (a <= 1.7d-41) then
        tmp = b * (z * -c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.7e-80) {
		tmp = t_1;
	} else if (a <= 4e-144) {
		tmp = t * (b * i);
	} else if (a <= 1.7e-41) {
		tmp = b * (z * -c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.7e-80:
		tmp = t_1
	elif a <= 4e-144:
		tmp = t * (b * i)
	elif a <= 1.7e-41:
		tmp = b * (z * -c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.7e-80)
		tmp = t_1;
	elseif (a <= 4e-144)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 1.7e-41)
		tmp = Float64(b * Float64(z * Float64(-c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.7e-80)
		tmp = t_1;
	elseif (a <= 4e-144)
		tmp = t * (b * i);
	elseif (a <= 1.7e-41)
		tmp = b * (z * -c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e-80], t$95$1, If[LessEqual[a, 4e-144], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-41], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7000000000000002e-80 or 1.6999999999999999e-41 < a

   1. Initial program 67.0%

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

   3. Taylor expanded in a around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. unsub-neg 62.1%

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

      4. *-commutative 62.1%

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

   5. Simplified 62.1%

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

   if -2.7000000000000002e-80 < a < 3.9999999999999998e-144

   1. Initial program 83.5%

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

   3. Taylor expanded in t around inf 38.4%

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

      1. distribute-lft-out-- 38.4%

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

      2. *-commutative 38.4%

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

   5. Simplified 38.4%

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

   6. Taylor expanded in a around 0 35.6%

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

      1. associate-*r* 36.9%

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

   8. Simplified 36.9%

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

   if 3.9999999999999998e-144 < a < 1.6999999999999999e-41

   1. Initial program 86.6%

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

   3. Taylor expanded in z around inf 60.7%

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

      1. *-commutative 60.7%

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

      2. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in y around 0 54.2%

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

      1. associate-*r* 54.2%

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

      2. neg-mul-1 54.2%

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

   8. Simplified 54.2%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-144}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-99}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{+158}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* a j))))
   (if (<= a -4.4e-80)
     t_1
     (if (<= a 1.2e-99)
       (* t (* b i))
       (if (<= a 6.3e+158) (* 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 = c * (a * j);
	double tmp;
	if (a <= -4.4e-80) {
		tmp = t_1;
	} else if (a <= 1.2e-99) {
		tmp = t * (b * i);
	} else if (a <= 6.3e+158) {
		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 = c * (a * j)
    if (a <= (-4.4d-80)) then
        tmp = t_1
    else if (a <= 1.2d-99) then
        tmp = t * (b * i)
    else if (a <= 6.3d+158) 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 = c * (a * j);
	double tmp;
	if (a <= -4.4e-80) {
		tmp = t_1;
	} else if (a <= 1.2e-99) {
		tmp = t * (b * i);
	} else if (a <= 6.3e+158) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (a * j)
	tmp = 0
	if a <= -4.4e-80:
		tmp = t_1
	elif a <= 1.2e-99:
		tmp = t * (b * i)
	elif a <= 6.3e+158:
		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(c * Float64(a * j))
	tmp = 0.0
	if (a <= -4.4e-80)
		tmp = t_1;
	elseif (a <= 1.2e-99)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 6.3e+158)
		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 = c * (a * j);
	tmp = 0.0;
	if (a <= -4.4e-80)
		tmp = t_1;
	elseif (a <= 1.2e-99)
		tmp = t * (b * i);
	elseif (a <= 6.3e+158)
		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[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.4e-80], t$95$1, If[LessEqual[a, 1.2e-99], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.3e+158], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.4000000000000002e-80 or 6.2999999999999997e158 < a

   1. Initial program 67.5%

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

   3. Taylor expanded in c around inf 50.7%

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

      1. *-commutative 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in j around inf 42.7%

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

      1. *-commutative 42.7%

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

   8. Simplified 42.7%

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

   if -4.4000000000000002e-80 < a < 1.2e-99

   1. Initial program 82.9%

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

   3. Taylor expanded in t around inf 38.0%

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

      1. distribute-lft-out-- 38.0%

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

      2. *-commutative 38.0%

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

   5. Simplified 38.0%

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

   6. Taylor expanded in a around 0 34.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   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 1.2e-99 < a < 6.2999999999999997e158

   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 z around inf 40.1%

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

      1. *-commutative 40.1%

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

      2. *-commutative 40.1%

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

   5. Simplified 40.1%

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

   6. Taylor expanded in y around inf 30.9%

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

      1. *-commutative 30.9%

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

   8. Simplified 30.9%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-80}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-99}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{+158}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+158}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* a j))))
   (if (<= a -4.2e-80)
     t_1
     (if (<= a 1.2e-99)
       (* b (* t i))
       (if (<= a 9.6e+158) (* 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 = c * (a * j);
	double tmp;
	if (a <= -4.2e-80) {
		tmp = t_1;
	} else if (a <= 1.2e-99) {
		tmp = b * (t * i);
	} else if (a <= 9.6e+158) {
		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 = c * (a * j)
    if (a <= (-4.2d-80)) then
        tmp = t_1
    else if (a <= 1.2d-99) then
        tmp = b * (t * i)
    else if (a <= 9.6d+158) 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 = c * (a * j);
	double tmp;
	if (a <= -4.2e-80) {
		tmp = t_1;
	} else if (a <= 1.2e-99) {
		tmp = b * (t * i);
	} else if (a <= 9.6e+158) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (a * j)
	tmp = 0
	if a <= -4.2e-80:
		tmp = t_1
	elif a <= 1.2e-99:
		tmp = b * (t * i)
	elif a <= 9.6e+158:
		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(c * Float64(a * j))
	tmp = 0.0
	if (a <= -4.2e-80)
		tmp = t_1;
	elseif (a <= 1.2e-99)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 9.6e+158)
		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 = c * (a * j);
	tmp = 0.0;
	if (a <= -4.2e-80)
		tmp = t_1;
	elseif (a <= 1.2e-99)
		tmp = b * (t * i);
	elseif (a <= 9.6e+158)
		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[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e-80], t$95$1, If[LessEqual[a, 1.2e-99], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.6e+158], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.20000000000000003e-80 or 9.60000000000000033e158 < a

   1. Initial program 67.5%

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

   3. Taylor expanded in c around inf 50.7%

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

      1. *-commutative 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in j around inf 42.7%

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

      1. *-commutative 42.7%

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

   8. Simplified 42.7%

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

   if -4.20000000000000003e-80 < a < 1.2e-99

   1. Initial program 82.9%

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

   3. Taylor expanded in i around inf 53.5%

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

   4. Taylor expanded in b around inf 34.3%

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

   if 1.2e-99 < a < 9.60000000000000033e158

   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 z around inf 40.1%

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

      1. *-commutative 40.1%

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

      2. *-commutative 40.1%

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

   5. Simplified 40.1%

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

   6. Taylor expanded in y around inf 30.9%

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

      1. *-commutative 30.9%

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

   8. Simplified 30.9%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-80}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+158}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;a \leq -5.1 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-100}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* a j))))
   (if (<= a -5.1e-82)
     t_1
     (if (<= a 5.4e-100)
       (* b (* t i))
       (if (<= a 3.1e+159) (* 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 = c * (a * j);
	double tmp;
	if (a <= -5.1e-82) {
		tmp = t_1;
	} else if (a <= 5.4e-100) {
		tmp = b * (t * i);
	} else if (a <= 3.1e+159) {
		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 = c * (a * j)
    if (a <= (-5.1d-82)) then
        tmp = t_1
    else if (a <= 5.4d-100) then
        tmp = b * (t * i)
    else if (a <= 3.1d+159) 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 = c * (a * j);
	double tmp;
	if (a <= -5.1e-82) {
		tmp = t_1;
	} else if (a <= 5.4e-100) {
		tmp = b * (t * i);
	} else if (a <= 3.1e+159) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (a * j)
	tmp = 0
	if a <= -5.1e-82:
		tmp = t_1
	elif a <= 5.4e-100:
		tmp = b * (t * i)
	elif a <= 3.1e+159:
		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(c * Float64(a * j))
	tmp = 0.0
	if (a <= -5.1e-82)
		tmp = t_1;
	elseif (a <= 5.4e-100)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 3.1e+159)
		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 = c * (a * j);
	tmp = 0.0;
	if (a <= -5.1e-82)
		tmp = t_1;
	elseif (a <= 5.4e-100)
		tmp = b * (t * i);
	elseif (a <= 3.1e+159)
		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[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.1e-82], t$95$1, If[LessEqual[a, 5.4e-100], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e+159], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.09999999999999992e-82 or 3.0999999999999998e159 < a

   1. Initial program 67.5%

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

   3. Taylor expanded in c around inf 50.7%

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

      1. *-commutative 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in j around inf 42.7%

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

      1. *-commutative 42.7%

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

   8. Simplified 42.7%

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

   if -5.09999999999999992e-82 < a < 5.40000000000000031e-100

   1. Initial program 82.9%

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

   3. Taylor expanded in i around inf 53.5%

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

   4. Taylor expanded in b around inf 34.3%

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

   if 5.40000000000000031e-100 < a < 3.0999999999999998e159

   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 z around inf 40.1%

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

      1. *-commutative 40.1%

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

      2. *-commutative 40.1%

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

   5. Simplified 40.1%

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

   6. Taylor expanded in y around inf 29.9%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{-82}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-100}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 28.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{-82} \lor \neg \left(a \leq 6.6 \cdot 10^{+195}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -2.45e-82) (not (<= a 6.6e+195))) (* c (* a j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -2.45e-82) || !(a <= 6.6e+195)) {
		tmp = c * (a * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-2.45d-82)) .or. (.not. (a <= 6.6d+195))) then
        tmp = c * (a * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -2.45e-82) || !(a <= 6.6e+195)) {
		tmp = c * (a * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -2.45e-82) or not (a <= 6.6e+195):
		tmp = c * (a * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -2.45e-82) || !(a <= 6.6e+195))
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -2.45e-82) || ~((a <= 6.6e+195)))
		tmp = c * (a * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -2.45e-82], N[Not[LessEqual[a, 6.6e+195]], $MachinePrecision]], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.4500000000000001e-82 or 6.5999999999999999e195 < a

   1. Initial program 68.1%

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

   3. Taylor expanded in c around inf 51.1%

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

      1. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in j around inf 44.3%

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

      1. *-commutative 44.3%

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

   8. Simplified 44.3%

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

   if -2.4500000000000001e-82 < a < 6.5999999999999999e195

   1. Initial program 76.9%

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

   3. Taylor expanded in i around inf 47.3%

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

   4. Taylor expanded in b around inf 28.8%

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

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{-82} \lor \neg \left(a \leq 6.6 \cdot 10^{+195}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 27.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-84} \lor \neg \left(a \leq 1.5 \cdot 10^{+193}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -6e-84) (not (<= a 1.5e+193))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -6e-84) || !(a <= 1.5e+193)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-6d-84)) .or. (.not. (a <= 1.5d+193))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -6e-84) || !(a <= 1.5e+193)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -6e-84) or not (a <= 1.5e+193):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -6e-84) || !(a <= 1.5e+193))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -6e-84) || ~((a <= 1.5e+193)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -6e-84], N[Not[LessEqual[a, 1.5e+193]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.0000000000000002e-84 or 1.5e193 < a

   1. Initial program 68.1%

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

   3. Taylor expanded in a around inf 68.4%

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

      1. +-commutative 68.4%

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

      2. mul-1-neg 68.4%

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

      3. unsub-neg 68.4%

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

      4. *-commutative 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in j around inf 41.2%

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

      1. *-commutative 41.2%

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

   8. Simplified 41.2%

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

   if -6.0000000000000002e-84 < a < 1.5e193

   1. Initial program 76.9%

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

   3. Taylor expanded in i around inf 47.3%

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

   4. Taylor expanded in b around inf 28.8%

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

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-84} \lor \neg \left(a \leq 1.5 \cdot 10^{+193}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 22.1% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 a around inf 44.9%

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

   1. +-commutative 44.9%

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

   2. mul-1-neg 44.9%

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

   3. unsub-neg 44.9%

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

   4. *-commutative 44.9%

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

5. Simplified 44.9%

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

6. Taylor expanded in j around inf 24.3%

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

   1. *-commutative 24.3%

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

8. Simplified 24.3%

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

9. Final simplification 24.3%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer target: 59.6% 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 2024106 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

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

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