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

Percentage Accurate: 72.9% → 82.4%

Time: 25.2s

Alternatives: 28

Speedup: 0.5×

• 59.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 72.9% 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: 82.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.9%

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

   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 a around inf 47.1%

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

      1. +-commutative 47.1%

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

      2. mul-1-neg 47.1%

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

      3. unsub-neg 47.1%

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

   5. Simplified 47.1%

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

   6. Taylor expanded in c around inf 54.2%

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

      1. mul-1-neg 54.2%

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

      2. unsub-neg 54.2%

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

      3. associate-/l* 58.0%

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

   8. Simplified 58.0%

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

4. Final simplification 85.8%

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

Alternative 2: 51.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -4.5 \cdot 10^{+19}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -6.1 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-35}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -4.4 \cdot 10^{-170}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -3.7 \cdot 10^{-272}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 8 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-208}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.36 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* i (- (* t b) (* y j)))))
   (if (<= i -4.5e+19)
     t_3
     (if (<= i -6.1e-12)
       t_2
       (if (<= i -3.8e-35)
         t_3
         (if (<= i -4.4e-170)
           (* c (- (* a j) (* z b)))
           (if (<= i -3.7e-272)
             t_2
             (if (<= i 8e-270)
               t_1
               (if (<= i 3.8e-208)
                 (* j (- (* a c) (* y i)))
                 (if (<= i 1.75e-80)
                   t_1
                   (if (<= i 1.36e+35) (* x (- (* y z) (* t a))) t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4.5e+19) {
		tmp = t_3;
	} else if (i <= -6.1e-12) {
		tmp = t_2;
	} else if (i <= -3.8e-35) {
		tmp = t_3;
	} else if (i <= -4.4e-170) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= -3.7e-272) {
		tmp = t_2;
	} else if (i <= 8e-270) {
		tmp = t_1;
	} else if (i <= 3.8e-208) {
		tmp = j * ((a * c) - (y * i));
	} else if (i <= 1.75e-80) {
		tmp = t_1;
	} else if (i <= 1.36e+35) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = a * ((c * j) - (x * t))
    t_3 = i * ((t * b) - (y * j))
    if (i <= (-4.5d+19)) then
        tmp = t_3
    else if (i <= (-6.1d-12)) then
        tmp = t_2
    else if (i <= (-3.8d-35)) then
        tmp = t_3
    else if (i <= (-4.4d-170)) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= (-3.7d-272)) then
        tmp = t_2
    else if (i <= 8d-270) then
        tmp = t_1
    else if (i <= 3.8d-208) then
        tmp = j * ((a * c) - (y * i))
    else if (i <= 1.75d-80) then
        tmp = t_1
    else if (i <= 1.36d+35) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4.5e+19) {
		tmp = t_3;
	} else if (i <= -6.1e-12) {
		tmp = t_2;
	} else if (i <= -3.8e-35) {
		tmp = t_3;
	} else if (i <= -4.4e-170) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= -3.7e-272) {
		tmp = t_2;
	} else if (i <= 8e-270) {
		tmp = t_1;
	} else if (i <= 3.8e-208) {
		tmp = j * ((a * c) - (y * i));
	} else if (i <= 1.75e-80) {
		tmp = t_1;
	} else if (i <= 1.36e+35) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = a * ((c * j) - (x * t))
	t_3 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -4.5e+19:
		tmp = t_3
	elif i <= -6.1e-12:
		tmp = t_2
	elif i <= -3.8e-35:
		tmp = t_3
	elif i <= -4.4e-170:
		tmp = c * ((a * j) - (z * b))
	elif i <= -3.7e-272:
		tmp = t_2
	elif i <= 8e-270:
		tmp = t_1
	elif i <= 3.8e-208:
		tmp = j * ((a * c) - (y * i))
	elif i <= 1.75e-80:
		tmp = t_1
	elif i <= 1.36e+35:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -4.5e+19)
		tmp = t_3;
	elseif (i <= -6.1e-12)
		tmp = t_2;
	elseif (i <= -3.8e-35)
		tmp = t_3;
	elseif (i <= -4.4e-170)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= -3.7e-272)
		tmp = t_2;
	elseif (i <= 8e-270)
		tmp = t_1;
	elseif (i <= 3.8e-208)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (i <= 1.75e-80)
		tmp = t_1;
	elseif (i <= 1.36e+35)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = a * ((c * j) - (x * t));
	t_3 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -4.5e+19)
		tmp = t_3;
	elseif (i <= -6.1e-12)
		tmp = t_2;
	elseif (i <= -3.8e-35)
		tmp = t_3;
	elseif (i <= -4.4e-170)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= -3.7e-272)
		tmp = t_2;
	elseif (i <= 8e-270)
		tmp = t_1;
	elseif (i <= 3.8e-208)
		tmp = j * ((a * c) - (y * i));
	elseif (i <= 1.75e-80)
		tmp = t_1;
	elseif (i <= 1.36e+35)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.5e+19], t$95$3, If[LessEqual[i, -6.1e-12], t$95$2, If[LessEqual[i, -3.8e-35], t$95$3, If[LessEqual[i, -4.4e-170], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.7e-272], t$95$2, If[LessEqual[i, 8e-270], t$95$1, If[LessEqual[i, 3.8e-208], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.75e-80], t$95$1, If[LessEqual[i, 1.36e+35], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -4.5e19 or -6.1000000000000003e-12 < i < -3.8000000000000001e-35 or 1.36e35 < i

   1. Initial program 66.3%

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

   3. Taylor expanded in i around inf 65.5%

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

      1. distribute-lft-out-- 65.5%

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

   5. Simplified 65.5%

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

   if -4.5e19 < i < -6.1000000000000003e-12 or -4.40000000000000029e-170 < i < -3.6999999999999997e-272

   1. Initial program 88.0%

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

   3. Taylor expanded in a around inf 77.5%

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

      1. +-commutative 77.5%

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

      2. mul-1-neg 77.5%

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

      3. unsub-neg 77.5%

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

   5. Simplified 77.5%

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

   if -3.8000000000000001e-35 < i < -4.40000000000000029e-170

   1. Initial program 64.3%

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

   3. Taylor expanded in c around inf 69.1%

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

      1. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   if -3.6999999999999997e-272 < i < 8.0000000000000003e-270 or 3.80000000000000011e-208 < i < 1.75000000000000007e-80

   1. Initial program 79.1%

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

   3. Taylor expanded in z around inf 70.4%

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

      1. *-commutative 70.4%

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

   5. Simplified 70.4%

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

   if 8.0000000000000003e-270 < i < 3.80000000000000011e-208

   1. Initial program 74.6%

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

   3. Taylor expanded in j around inf 63.7%

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

      1. *-commutative 63.7%

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

   5. Simplified 63.7%

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

   if 1.75000000000000007e-80 < i < 1.36e35

   1. Initial program 89.1%

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

   3. Taylor expanded in x around inf 66.9%

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

      1. cancel-sign-sub-inv 66.9%

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

      2. *-commutative 66.9%

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

      3. *-commutative 66.9%

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

      4. distribute-rgt-neg-out 66.9%

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

      5. sub-neg 66.9%

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

   5. Simplified 66.9%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.5 \cdot 10^{+19}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -6.1 \cdot 10^{-12}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-35}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -4.4 \cdot 10^{-170}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -3.7 \cdot 10^{-272}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{-270}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-208}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.36 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+204}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+142}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-108}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-264}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-242}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+24}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= z -2.2e+204)
     t_2
     (if (<= z -1.2e+142)
       (* y (- (* x z) (* i j)))
       (if (<= z -9.5e+85)
         t_2
         (if (<= z -2.8e+33)
           (* a (- (* c j) (* x t)))
           (if (<= z -2.9e-108)
             t_3
             (if (<= z 2.7e-264)
               t_1
               (if (<= z 8.2e-242)
                 t_3
                 (if (<= z 6.1e-204)
                   t_1
                   (if (<= z 3.8e+24) t_3 (* x (- (* y z) (* t a))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (z <= -2.2e+204) {
		tmp = t_2;
	} else if (z <= -1.2e+142) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -9.5e+85) {
		tmp = t_2;
	} else if (z <= -2.8e+33) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= -2.9e-108) {
		tmp = t_3;
	} else if (z <= 2.7e-264) {
		tmp = t_1;
	} else if (z <= 8.2e-242) {
		tmp = t_3;
	} else if (z <= 6.1e-204) {
		tmp = t_1;
	} else if (z <= 3.8e+24) {
		tmp = t_3;
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    t_2 = z * ((x * y) - (b * c))
    t_3 = j * ((a * c) - (y * i))
    if (z <= (-2.2d+204)) then
        tmp = t_2
    else if (z <= (-1.2d+142)) then
        tmp = y * ((x * z) - (i * j))
    else if (z <= (-9.5d+85)) then
        tmp = t_2
    else if (z <= (-2.8d+33)) then
        tmp = a * ((c * j) - (x * t))
    else if (z <= (-2.9d-108)) then
        tmp = t_3
    else if (z <= 2.7d-264) then
        tmp = t_1
    else if (z <= 8.2d-242) then
        tmp = t_3
    else if (z <= 6.1d-204) then
        tmp = t_1
    else if (z <= 3.8d+24) then
        tmp = t_3
    else
        tmp = x * ((y * z) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (z <= -2.2e+204) {
		tmp = t_2;
	} else if (z <= -1.2e+142) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= -9.5e+85) {
		tmp = t_2;
	} else if (z <= -2.8e+33) {
		tmp = a * ((c * j) - (x * t));
	} else if (z <= -2.9e-108) {
		tmp = t_3;
	} else if (z <= 2.7e-264) {
		tmp = t_1;
	} else if (z <= 8.2e-242) {
		tmp = t_3;
	} else if (z <= 6.1e-204) {
		tmp = t_1;
	} else if (z <= 3.8e+24) {
		tmp = t_3;
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = z * ((x * y) - (b * c))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if z <= -2.2e+204:
		tmp = t_2
	elif z <= -1.2e+142:
		tmp = y * ((x * z) - (i * j))
	elif z <= -9.5e+85:
		tmp = t_2
	elif z <= -2.8e+33:
		tmp = a * ((c * j) - (x * t))
	elif z <= -2.9e-108:
		tmp = t_3
	elif z <= 2.7e-264:
		tmp = t_1
	elif z <= 8.2e-242:
		tmp = t_3
	elif z <= 6.1e-204:
		tmp = t_1
	elif z <= 3.8e+24:
		tmp = t_3
	else:
		tmp = x * ((y * z) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (z <= -2.2e+204)
		tmp = t_2;
	elseif (z <= -1.2e+142)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (z <= -9.5e+85)
		tmp = t_2;
	elseif (z <= -2.8e+33)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (z <= -2.9e-108)
		tmp = t_3;
	elseif (z <= 2.7e-264)
		tmp = t_1;
	elseif (z <= 8.2e-242)
		tmp = t_3;
	elseif (z <= 6.1e-204)
		tmp = t_1;
	elseif (z <= 3.8e+24)
		tmp = t_3;
	else
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	t_2 = z * ((x * y) - (b * c));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (z <= -2.2e+204)
		tmp = t_2;
	elseif (z <= -1.2e+142)
		tmp = y * ((x * z) - (i * j));
	elseif (z <= -9.5e+85)
		tmp = t_2;
	elseif (z <= -2.8e+33)
		tmp = a * ((c * j) - (x * t));
	elseif (z <= -2.9e-108)
		tmp = t_3;
	elseif (z <= 2.7e-264)
		tmp = t_1;
	elseif (z <= 8.2e-242)
		tmp = t_3;
	elseif (z <= 6.1e-204)
		tmp = t_1;
	elseif (z <= 3.8e+24)
		tmp = t_3;
	else
		tmp = x * ((y * z) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+204], t$95$2, If[LessEqual[z, -1.2e+142], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e+85], t$95$2, If[LessEqual[z, -2.8e+33], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e-108], t$95$3, If[LessEqual[z, 2.7e-264], t$95$1, If[LessEqual[z, 8.2e-242], t$95$3, If[LessEqual[z, 6.1e-204], t$95$1, If[LessEqual[z, 3.8e+24], t$95$3, N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.20000000000000011e204 or -1.2e142 < z < -9.49999999999999945e85

   1. Initial program 67.7%

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

   3. Taylor expanded in z around inf 73.0%

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

      1. *-commutative 73.0%

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

   5. Simplified 73.0%

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

   if -2.20000000000000011e204 < z < -1.2e142

   1. Initial program 58.3%

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

   3. Taylor expanded in y around inf 63.7%

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

      1. +-commutative 63.7%

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

      2. mul-1-neg 63.7%

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

      3. unsub-neg 63.7%

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

      4. *-commutative 63.7%

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

   5. Simplified 63.7%

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

   if -9.49999999999999945e85 < z < -2.8000000000000001e33

   1. Initial program 73.1%

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

   3. Taylor expanded in a around inf 74.0%

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

      1. +-commutative 74.0%

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

      2. mul-1-neg 74.0%

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

      3. unsub-neg 74.0%

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

   5. Simplified 74.0%

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

   if -2.8000000000000001e33 < z < -2.9000000000000001e-108 or 2.69999999999999994e-264 < z < 8.19999999999999942e-242 or 6.09999999999999974e-204 < z < 3.80000000000000015e24

   1. Initial program 84.0%

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

   3. Taylor expanded in j around inf 67.6%

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

      1. *-commutative 67.6%

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

   5. Simplified 67.6%

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

   if -2.9000000000000001e-108 < z < 2.69999999999999994e-264 or 8.19999999999999942e-242 < z < 6.09999999999999974e-204

   1. Initial program 85.7%

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

   3. Taylor expanded in y around 0 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in t around inf 68.0%

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

      1. +-commutative 68.0%

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

      2. mul-1-neg 68.0%

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

      3. unsub-neg 68.0%

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

   8. Simplified 68.0%

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

   if 3.80000000000000015e24 < z

   1. Initial program 60.5%

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

   3. Taylor expanded in x around inf 61.8%

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

      1. cancel-sign-sub-inv 61.8%

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

      2. *-commutative 61.8%

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

      3. *-commutative 61.8%

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

      4. distribute-rgt-neg-out 61.8%

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

      5. sub-neg 61.8%

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

   5. Simplified 61.8%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+204}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+142}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+85}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-108}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-264}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-242}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-204}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+24}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := t\_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_4 := t\_3 - b \cdot \left(z \cdot c\right)\\ t_5 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+100}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+40}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{t\_1}{a} - x \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-263}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 0.0003:\\ \;\;\;\;t\_3 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z)))
        (t_2 (+ t_1 (* j (- (* a c) (* y i)))))
        (t_3 (* a (- (* c j) (* x t))))
        (t_4 (- t_3 (* b (* z c))))
        (t_5 (* y (- (* x z) (* i j)))))
   (if (<= y -2e+100)
     t_5
     (if (<= y -5.6e+40)
       t_4
       (if (<= y -5e-68)
         t_2
         (if (<= y -1.1e-141)
           (* a (+ (* c j) (- (/ t_1 a) (* x t))))
           (if (<= y -3e-160)
             t_2
             (if (<= y -5e-263)
               t_4
               (if (<= y 0.0003) (+ t_3 (* b (- (* t i) (* z c)))) t_5)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = t_1 + (j * ((a * c) - (y * i)));
	double t_3 = a * ((c * j) - (x * t));
	double t_4 = t_3 - (b * (z * c));
	double t_5 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2e+100) {
		tmp = t_5;
	} else if (y <= -5.6e+40) {
		tmp = t_4;
	} else if (y <= -5e-68) {
		tmp = t_2;
	} else if (y <= -1.1e-141) {
		tmp = a * ((c * j) + ((t_1 / a) - (x * t)));
	} else if (y <= -3e-160) {
		tmp = t_2;
	} else if (y <= -5e-263) {
		tmp = t_4;
	} else if (y <= 0.0003) {
		tmp = t_3 + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = t_1 + (j * ((a * c) - (y * i)))
    t_3 = a * ((c * j) - (x * t))
    t_4 = t_3 - (b * (z * c))
    t_5 = y * ((x * z) - (i * j))
    if (y <= (-2d+100)) then
        tmp = t_5
    else if (y <= (-5.6d+40)) then
        tmp = t_4
    else if (y <= (-5d-68)) then
        tmp = t_2
    else if (y <= (-1.1d-141)) then
        tmp = a * ((c * j) + ((t_1 / a) - (x * t)))
    else if (y <= (-3d-160)) then
        tmp = t_2
    else if (y <= (-5d-263)) then
        tmp = t_4
    else if (y <= 0.0003d0) then
        tmp = t_3 + (b * ((t * i) - (z * c)))
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = t_1 + (j * ((a * c) - (y * i)));
	double t_3 = a * ((c * j) - (x * t));
	double t_4 = t_3 - (b * (z * c));
	double t_5 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2e+100) {
		tmp = t_5;
	} else if (y <= -5.6e+40) {
		tmp = t_4;
	} else if (y <= -5e-68) {
		tmp = t_2;
	} else if (y <= -1.1e-141) {
		tmp = a * ((c * j) + ((t_1 / a) - (x * t)));
	} else if (y <= -3e-160) {
		tmp = t_2;
	} else if (y <= -5e-263) {
		tmp = t_4;
	} else if (y <= 0.0003) {
		tmp = t_3 + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = t_1 + (j * ((a * c) - (y * i)))
	t_3 = a * ((c * j) - (x * t))
	t_4 = t_3 - (b * (z * c))
	t_5 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -2e+100:
		tmp = t_5
	elif y <= -5.6e+40:
		tmp = t_4
	elif y <= -5e-68:
		tmp = t_2
	elif y <= -1.1e-141:
		tmp = a * ((c * j) + ((t_1 / a) - (x * t)))
	elif y <= -3e-160:
		tmp = t_2
	elif y <= -5e-263:
		tmp = t_4
	elif y <= 0.0003:
		tmp = t_3 + (b * ((t * i) - (z * c)))
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(t_1 + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_4 = Float64(t_3 - Float64(b * Float64(z * c)))
	t_5 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -2e+100)
		tmp = t_5;
	elseif (y <= -5.6e+40)
		tmp = t_4;
	elseif (y <= -5e-68)
		tmp = t_2;
	elseif (y <= -1.1e-141)
		tmp = Float64(a * Float64(Float64(c * j) + Float64(Float64(t_1 / a) - Float64(x * t))));
	elseif (y <= -3e-160)
		tmp = t_2;
	elseif (y <= -5e-263)
		tmp = t_4;
	elseif (y <= 0.0003)
		tmp = Float64(t_3 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = t_1 + (j * ((a * c) - (y * i)));
	t_3 = a * ((c * j) - (x * t));
	t_4 = t_3 - (b * (z * c));
	t_5 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -2e+100)
		tmp = t_5;
	elseif (y <= -5.6e+40)
		tmp = t_4;
	elseif (y <= -5e-68)
		tmp = t_2;
	elseif (y <= -1.1e-141)
		tmp = a * ((c * j) + ((t_1 / a) - (x * t)));
	elseif (y <= -3e-160)
		tmp = t_2;
	elseif (y <= -5e-263)
		tmp = t_4;
	elseif (y <= 0.0003)
		tmp = t_3 + (b * ((t * i) - (z * c)));
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+100], t$95$5, If[LessEqual[y, -5.6e+40], t$95$4, If[LessEqual[y, -5e-68], t$95$2, If[LessEqual[y, -1.1e-141], N[(a * N[(N[(c * j), $MachinePrecision] + N[(N[(t$95$1 / a), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e-160], t$95$2, If[LessEqual[y, -5e-263], t$95$4, If[LessEqual[y, 0.0003], N[(t$95$3 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.00000000000000003e100 or 2.99999999999999974e-4 < y

   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 y around inf 76.1%

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

      1. +-commutative 76.1%

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

      2. mul-1-neg 76.1%

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

      3. unsub-neg 76.1%

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

      4. *-commutative 76.1%

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

   5. Simplified 76.1%

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

   if -2.00000000000000003e100 < y < -5.6000000000000003e40 or -2.99999999999999997e-160 < y < -5.00000000000000006e-263

   1. Initial program 70.6%

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

   3. Taylor expanded in y around 0 60.0%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in i around 0 68.1%

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

      1. +-commutative 68.1%

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

      2. *-commutative 68.1%

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

      3. *-commutative 68.1%

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

      4. mul-1-neg 68.1%

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

      5. unsub-neg 68.1%

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

      6. *-commutative 68.1%

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

      7. *-commutative 68.1%

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

   8. Simplified 68.1%

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

   if -5.6000000000000003e40 < y < -4.99999999999999971e-68 or -1.10000000000000005e-141 < y < -2.99999999999999997e-160

   1. Initial program 74.3%

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

   3. Taylor expanded in b around 0 74.3%

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

   4. Taylor expanded in y around inf 78.1%

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

   if -4.99999999999999971e-68 < y < -1.10000000000000005e-141

   1. Initial program 60.6%

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

   3. Taylor expanded in a around -inf 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in x around inf 70.6%

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

   if -5.00000000000000006e-263 < y < 2.99999999999999974e-4

   1. Initial program 88.0%

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

   3. Taylor expanded in y around 0 76.4%

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

   5. Simplified 76.4%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+100}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{x \cdot \left(y \cdot z\right)}{a} - x \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-263}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 0.0003:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 29.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(c \cdot \left(-b\right)\right)\\ t_2 := x \cdot \left(t \cdot \left(-a\right)\right)\\ t_3 := j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{if}\;i \leq -2.35 \cdot 10^{+48}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -5.4 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{-39}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-273}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{-208}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.34 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+207}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* c (- b))))
        (t_2 (* x (* t (- a))))
        (t_3 (* j (* y (- i)))))
   (if (<= i -2.35e+48)
     t_3
     (if (<= i -5.4e-13)
       t_2
       (if (<= i -4.2e-39)
         (* z (* x y))
         (if (<= i -1.3e-165)
           t_1
           (if (<= i -2.8e-273)
             (* a (* x (- t)))
             (if (<= i 3.7e-208)
               (* j (* a c))
               (if (<= i 1.34e-79)
                 t_1
                 (if (<= i 2.6e+34)
                   t_2
                   (if (<= i 2.2e+207) (* t (* b i)) t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * -b);
	double t_2 = x * (t * -a);
	double t_3 = j * (y * -i);
	double tmp;
	if (i <= -2.35e+48) {
		tmp = t_3;
	} else if (i <= -5.4e-13) {
		tmp = t_2;
	} else if (i <= -4.2e-39) {
		tmp = z * (x * y);
	} else if (i <= -1.3e-165) {
		tmp = t_1;
	} else if (i <= -2.8e-273) {
		tmp = a * (x * -t);
	} else if (i <= 3.7e-208) {
		tmp = j * (a * c);
	} else if (i <= 1.34e-79) {
		tmp = t_1;
	} else if (i <= 2.6e+34) {
		tmp = t_2;
	} else if (i <= 2.2e+207) {
		tmp = t * (b * i);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (c * -b)
    t_2 = x * (t * -a)
    t_3 = j * (y * -i)
    if (i <= (-2.35d+48)) then
        tmp = t_3
    else if (i <= (-5.4d-13)) then
        tmp = t_2
    else if (i <= (-4.2d-39)) then
        tmp = z * (x * y)
    else if (i <= (-1.3d-165)) then
        tmp = t_1
    else if (i <= (-2.8d-273)) then
        tmp = a * (x * -t)
    else if (i <= 3.7d-208) then
        tmp = j * (a * c)
    else if (i <= 1.34d-79) then
        tmp = t_1
    else if (i <= 2.6d+34) then
        tmp = t_2
    else if (i <= 2.2d+207) then
        tmp = t * (b * i)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * -b);
	double t_2 = x * (t * -a);
	double t_3 = j * (y * -i);
	double tmp;
	if (i <= -2.35e+48) {
		tmp = t_3;
	} else if (i <= -5.4e-13) {
		tmp = t_2;
	} else if (i <= -4.2e-39) {
		tmp = z * (x * y);
	} else if (i <= -1.3e-165) {
		tmp = t_1;
	} else if (i <= -2.8e-273) {
		tmp = a * (x * -t);
	} else if (i <= 3.7e-208) {
		tmp = j * (a * c);
	} else if (i <= 1.34e-79) {
		tmp = t_1;
	} else if (i <= 2.6e+34) {
		tmp = t_2;
	} else if (i <= 2.2e+207) {
		tmp = t * (b * i);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (c * -b)
	t_2 = x * (t * -a)
	t_3 = j * (y * -i)
	tmp = 0
	if i <= -2.35e+48:
		tmp = t_3
	elif i <= -5.4e-13:
		tmp = t_2
	elif i <= -4.2e-39:
		tmp = z * (x * y)
	elif i <= -1.3e-165:
		tmp = t_1
	elif i <= -2.8e-273:
		tmp = a * (x * -t)
	elif i <= 3.7e-208:
		tmp = j * (a * c)
	elif i <= 1.34e-79:
		tmp = t_1
	elif i <= 2.6e+34:
		tmp = t_2
	elif i <= 2.2e+207:
		tmp = t * (b * i)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(c * Float64(-b)))
	t_2 = Float64(x * Float64(t * Float64(-a)))
	t_3 = Float64(j * Float64(y * Float64(-i)))
	tmp = 0.0
	if (i <= -2.35e+48)
		tmp = t_3;
	elseif (i <= -5.4e-13)
		tmp = t_2;
	elseif (i <= -4.2e-39)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= -1.3e-165)
		tmp = t_1;
	elseif (i <= -2.8e-273)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (i <= 3.7e-208)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 1.34e-79)
		tmp = t_1;
	elseif (i <= 2.6e+34)
		tmp = t_2;
	elseif (i <= 2.2e+207)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (c * -b);
	t_2 = x * (t * -a);
	t_3 = j * (y * -i);
	tmp = 0.0;
	if (i <= -2.35e+48)
		tmp = t_3;
	elseif (i <= -5.4e-13)
		tmp = t_2;
	elseif (i <= -4.2e-39)
		tmp = z * (x * y);
	elseif (i <= -1.3e-165)
		tmp = t_1;
	elseif (i <= -2.8e-273)
		tmp = a * (x * -t);
	elseif (i <= 3.7e-208)
		tmp = j * (a * c);
	elseif (i <= 1.34e-79)
		tmp = t_1;
	elseif (i <= 2.6e+34)
		tmp = t_2;
	elseif (i <= 2.2e+207)
		tmp = t * (b * i);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.35e+48], t$95$3, If[LessEqual[i, -5.4e-13], t$95$2, If[LessEqual[i, -4.2e-39], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.3e-165], t$95$1, If[LessEqual[i, -2.8e-273], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.7e-208], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.34e-79], t$95$1, If[LessEqual[i, 2.6e+34], t$95$2, If[LessEqual[i, 2.2e+207], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if i < -2.35000000000000006e48 or 2.20000000000000009e207 < i

   1. Initial program 60.5%

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

   3. Taylor expanded in j around inf 62.7%

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

      1. *-commutative 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in c around 0 57.6%

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

      1. mul-1-neg 57.6%

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

   8. Simplified 57.6%

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

   if -2.35000000000000006e48 < i < -5.40000000000000021e-13 or 1.34e-79 < i < 2.59999999999999997e34

   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 a around inf 54.5%

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

      1. +-commutative 54.5%

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

      2. mul-1-neg 54.5%

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

      3. unsub-neg 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in c around 0 37.6%

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

      1. mul-1-neg 37.6%

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

      2. associate-*r* 49.9%

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

      3. distribute-lft-neg-in 49.9%

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

      4. *-commutative 49.9%

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

      5. distribute-rgt-neg-in 49.9%

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

   8. Simplified 49.9%

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

   if -5.40000000000000021e-13 < i < -4.19999999999999987e-39

   1. Initial program 81.1%

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

   3. Taylor expanded in z around inf 41.8%

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

      1. *-commutative 41.8%

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

   5. Simplified 41.8%

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

   6. Taylor expanded in y around inf 42.0%

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

      1. *-commutative 42.0%

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

   8. Simplified 42.0%

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

   if -4.19999999999999987e-39 < i < -1.30000000000000004e-165 or 3.7000000000000002e-208 < i < 1.34e-79

   1. Initial program 72.1%

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

   3. Taylor expanded in z around inf 65.0%

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

      1. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in y around 0 43.6%

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

      1. neg-mul-1 43.6%

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

      2. distribute-rgt-neg-in 43.6%

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

   8. Simplified 43.6%

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

   if -1.30000000000000004e-165 < i < -2.79999999999999985e-273

   1. Initial program 91.1%

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

   3. Taylor expanded in a around inf 79.8%

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

      1. +-commutative 79.8%

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

      2. mul-1-neg 79.8%

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

      3. unsub-neg 79.8%

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

   5. Simplified 79.8%

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

   6. Taylor expanded in c around 0 58.9%

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

      1. associate-*r* 58.9%

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

      2. neg-mul-1 58.9%

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

   8. Simplified 58.9%

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

   if -2.79999999999999985e-273 < i < 3.7000000000000002e-208

   1. Initial program 76.4%

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

   3. Taylor expanded in j around inf 45.6%

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

      1. *-commutative 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in c around inf 37.1%

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

      1. *-commutative 37.1%

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

   8. Simplified 37.1%

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

   if 2.59999999999999997e34 < i < 2.20000000000000009e207

   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 y around 0 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in i around inf 54.4%

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

   7. Taylor expanded in a around 0 39.5%

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

      1. *-commutative 39.5%

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

      2. *-commutative 39.5%

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

      3. associate-*r* 43.5%

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

   9. Simplified 43.5%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.35 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -5.4 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{-39}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-165}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-273}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{-208}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.34 \cdot 10^{-79}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+207}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_4 := t\_3 - b \cdot \left(z \cdot c\right)\\ t_5 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{+99}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+41}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-138}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{t\_1}{a} - x \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-253}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 0.0004:\\ \;\;\;\;t\_3 + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i)))
        (t_2 (+ (* x (* y z)) (* j (- (* a c) (* y i)))))
        (t_3 (* a (- (* c j) (* x t))))
        (t_4 (- t_3 (* b (* z c))))
        (t_5 (* y (- (* x z) (* i j)))))
   (if (<= y -4e+99)
     t_5
     (if (<= y -1.05e+41)
       t_4
       (if (<= y -8.2e-28)
         t_2
         (if (<= y -1.05e-138)
           (* a (+ (* c j) (- (/ t_1 a) (* x t))))
           (if (<= y -3.5e-160)
             t_2
             (if (<= y 2.25e-253)
               t_4
               (if (<= y 0.0004) (+ t_3 t_1) t_5)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = (x * (y * z)) + (j * ((a * c) - (y * i)));
	double t_3 = a * ((c * j) - (x * t));
	double t_4 = t_3 - (b * (z * c));
	double t_5 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4e+99) {
		tmp = t_5;
	} else if (y <= -1.05e+41) {
		tmp = t_4;
	} else if (y <= -8.2e-28) {
		tmp = t_2;
	} else if (y <= -1.05e-138) {
		tmp = a * ((c * j) + ((t_1 / a) - (x * t)));
	} else if (y <= -3.5e-160) {
		tmp = t_2;
	} else if (y <= 2.25e-253) {
		tmp = t_4;
	} else if (y <= 0.0004) {
		tmp = t_3 + t_1;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = (x * (y * z)) + (j * ((a * c) - (y * i)))
    t_3 = a * ((c * j) - (x * t))
    t_4 = t_3 - (b * (z * c))
    t_5 = y * ((x * z) - (i * j))
    if (y <= (-4d+99)) then
        tmp = t_5
    else if (y <= (-1.05d+41)) then
        tmp = t_4
    else if (y <= (-8.2d-28)) then
        tmp = t_2
    else if (y <= (-1.05d-138)) then
        tmp = a * ((c * j) + ((t_1 / a) - (x * t)))
    else if (y <= (-3.5d-160)) then
        tmp = t_2
    else if (y <= 2.25d-253) then
        tmp = t_4
    else if (y <= 0.0004d0) then
        tmp = t_3 + t_1
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = (x * (y * z)) + (j * ((a * c) - (y * i)));
	double t_3 = a * ((c * j) - (x * t));
	double t_4 = t_3 - (b * (z * c));
	double t_5 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4e+99) {
		tmp = t_5;
	} else if (y <= -1.05e+41) {
		tmp = t_4;
	} else if (y <= -8.2e-28) {
		tmp = t_2;
	} else if (y <= -1.05e-138) {
		tmp = a * ((c * j) + ((t_1 / a) - (x * t)));
	} else if (y <= -3.5e-160) {
		tmp = t_2;
	} else if (y <= 2.25e-253) {
		tmp = t_4;
	} else if (y <= 0.0004) {
		tmp = t_3 + t_1;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = (x * (y * z)) + (j * ((a * c) - (y * i)))
	t_3 = a * ((c * j) - (x * t))
	t_4 = t_3 - (b * (z * c))
	t_5 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -4e+99:
		tmp = t_5
	elif y <= -1.05e+41:
		tmp = t_4
	elif y <= -8.2e-28:
		tmp = t_2
	elif y <= -1.05e-138:
		tmp = a * ((c * j) + ((t_1 / a) - (x * t)))
	elif y <= -3.5e-160:
		tmp = t_2
	elif y <= 2.25e-253:
		tmp = t_4
	elif y <= 0.0004:
		tmp = t_3 + t_1
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(Float64(x * Float64(y * z)) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_4 = Float64(t_3 - Float64(b * Float64(z * c)))
	t_5 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -4e+99)
		tmp = t_5;
	elseif (y <= -1.05e+41)
		tmp = t_4;
	elseif (y <= -8.2e-28)
		tmp = t_2;
	elseif (y <= -1.05e-138)
		tmp = Float64(a * Float64(Float64(c * j) + Float64(Float64(t_1 / a) - Float64(x * t))));
	elseif (y <= -3.5e-160)
		tmp = t_2;
	elseif (y <= 2.25e-253)
		tmp = t_4;
	elseif (y <= 0.0004)
		tmp = Float64(t_3 + t_1);
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = (x * (y * z)) + (j * ((a * c) - (y * i)));
	t_3 = a * ((c * j) - (x * t));
	t_4 = t_3 - (b * (z * c));
	t_5 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -4e+99)
		tmp = t_5;
	elseif (y <= -1.05e+41)
		tmp = t_4;
	elseif (y <= -8.2e-28)
		tmp = t_2;
	elseif (y <= -1.05e-138)
		tmp = a * ((c * j) + ((t_1 / a) - (x * t)));
	elseif (y <= -3.5e-160)
		tmp = t_2;
	elseif (y <= 2.25e-253)
		tmp = t_4;
	elseif (y <= 0.0004)
		tmp = t_3 + t_1;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e+99], t$95$5, If[LessEqual[y, -1.05e+41], t$95$4, If[LessEqual[y, -8.2e-28], t$95$2, If[LessEqual[y, -1.05e-138], N[(a * N[(N[(c * j), $MachinePrecision] + N[(N[(t$95$1 / a), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-160], t$95$2, If[LessEqual[y, 2.25e-253], t$95$4, If[LessEqual[y, 0.0004], N[(t$95$3 + t$95$1), $MachinePrecision], t$95$5]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.9999999999999999e99 or 4.00000000000000019e-4 < y

   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 y around inf 76.1%

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

      1. +-commutative 76.1%

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

      2. mul-1-neg 76.1%

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

      3. unsub-neg 76.1%

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

      4. *-commutative 76.1%

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

   5. Simplified 76.1%

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

   if -3.9999999999999999e99 < y < -1.05e41 or -3.5000000000000003e-160 < y < 2.25000000000000014e-253

   1. Initial program 74.3%

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

   3. Taylor expanded in y around 0 66.5%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in i around 0 64.6%

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

      1. +-commutative 64.6%

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

      2. *-commutative 64.6%

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

      3. *-commutative 64.6%

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

      4. mul-1-neg 64.6%

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

      5. unsub-neg 64.6%

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

      6. *-commutative 64.6%

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

      7. *-commutative 64.6%

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

   8. Simplified 64.6%

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

   if -1.05e41 < y < -8.2000000000000005e-28 or -1.04999999999999993e-138 < y < -3.5000000000000003e-160

   1. Initial program 72.8%

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

   3. Taylor expanded in b around 0 78.1%

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

   4. Taylor expanded in y around inf 89.2%

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

   if -8.2000000000000005e-28 < y < -1.04999999999999993e-138

   1. Initial program 65.8%

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

   3. Taylor expanded in a around -inf 72.9%

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

   5. Simplified 72.9%

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

   6. Taylor expanded in t around inf 63.2%

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

   if 2.25000000000000014e-253 < y < 4.00000000000000019e-4

   1. Initial program 92.0%

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

   3. Taylor expanded in y around 0 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in i around inf 68.8%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-138}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{b \cdot \left(t \cdot i\right)}{a} - x \cdot t\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 0.0004:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.8 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq -1.55 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{b \cdot \left(t \cdot i\right)}{a} - x \cdot t\right)\right)\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-163}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-230}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{x \cdot \left(y \cdot z\right)}{a} - x \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+104}:\\ \;\;\;\;i \cdot \left(t \cdot b + \frac{a \cdot \left(c \cdot j - x \cdot t\right)}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -5.8e+49)
   (* y (- (* x z) (* i j)))
   (if (<= i -1.55e-35)
     (* a (+ (* c j) (- (/ (* b (* t i)) a) (* x t))))
     (if (<= i -1.35e-163)
       (* c (- (* a j) (* z b)))
       (if (<= i 1.3e-230)
         (* a (+ (* c j) (- (/ (* x (* y z)) a) (* x t))))
         (if (<= i 2.7e-81)
           (* z (- (* x y) (* b c)))
           (if (<= i 5.5e+104)
             (* i (+ (* t b) (/ (* a (- (* c j) (* x t))) i)))
             (* i (- (* t b) (* y j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -5.8e+49) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= -1.55e-35) {
		tmp = a * ((c * j) + (((b * (t * i)) / a) - (x * t)));
	} else if (i <= -1.35e-163) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 1.3e-230) {
		tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)));
	} else if (i <= 2.7e-81) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 5.5e+104) {
		tmp = i * ((t * b) + ((a * ((c * j) - (x * t))) / i));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-5.8d+49)) then
        tmp = y * ((x * z) - (i * j))
    else if (i <= (-1.55d-35)) then
        tmp = a * ((c * j) + (((b * (t * i)) / a) - (x * t)))
    else if (i <= (-1.35d-163)) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 1.3d-230) then
        tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)))
    else if (i <= 2.7d-81) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 5.5d+104) then
        tmp = i * ((t * b) + ((a * ((c * j) - (x * t))) / i))
    else
        tmp = i * ((t * b) - (y * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -5.8e+49) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= -1.55e-35) {
		tmp = a * ((c * j) + (((b * (t * i)) / a) - (x * t)));
	} else if (i <= -1.35e-163) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 1.3e-230) {
		tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)));
	} else if (i <= 2.7e-81) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 5.5e+104) {
		tmp = i * ((t * b) + ((a * ((c * j) - (x * t))) / i));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -5.8e+49:
		tmp = y * ((x * z) - (i * j))
	elif i <= -1.55e-35:
		tmp = a * ((c * j) + (((b * (t * i)) / a) - (x * t)))
	elif i <= -1.35e-163:
		tmp = c * ((a * j) - (z * b))
	elif i <= 1.3e-230:
		tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)))
	elif i <= 2.7e-81:
		tmp = z * ((x * y) - (b * c))
	elif i <= 5.5e+104:
		tmp = i * ((t * b) + ((a * ((c * j) - (x * t))) / i))
	else:
		tmp = i * ((t * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -5.8e+49)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (i <= -1.55e-35)
		tmp = Float64(a * Float64(Float64(c * j) + Float64(Float64(Float64(b * Float64(t * i)) / a) - Float64(x * t))));
	elseif (i <= -1.35e-163)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 1.3e-230)
		tmp = Float64(a * Float64(Float64(c * j) + Float64(Float64(Float64(x * Float64(y * z)) / a) - Float64(x * t))));
	elseif (i <= 2.7e-81)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 5.5e+104)
		tmp = Float64(i * Float64(Float64(t * b) + Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) / i)));
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -5.8e+49)
		tmp = y * ((x * z) - (i * j));
	elseif (i <= -1.55e-35)
		tmp = a * ((c * j) + (((b * (t * i)) / a) - (x * t)));
	elseif (i <= -1.35e-163)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 1.3e-230)
		tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)));
	elseif (i <= 2.7e-81)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 5.5e+104)
		tmp = i * ((t * b) + ((a * ((c * j) - (x * t))) / i));
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -5.8e+49], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.55e-35], N[(a * N[(N[(c * j), $MachinePrecision] + N[(N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.35e-163], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e-230], N[(a * N[(N[(c * j), $MachinePrecision] + N[(N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.7e-81], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.5e+104], N[(i * N[(N[(t * b), $MachinePrecision] + N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if i < -5.8e49

   1. Initial program 62.5%

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

   3. Taylor expanded in y around inf 67.3%

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

      1. +-commutative 67.3%

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

      2. mul-1-neg 67.3%

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

      3. unsub-neg 67.3%

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

      4. *-commutative 67.3%

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

   5. Simplified 67.3%

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

   if -5.8e49 < i < -1.55000000000000006e-35

   1. Initial program 75.3%

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

   3. Taylor expanded in a around -inf 69.7%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in t around inf 68.5%

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

   if -1.55000000000000006e-35 < i < -1.35000000000000007e-163

   1. Initial program 64.3%

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

   3. Taylor expanded in c around inf 69.1%

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

      1. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   if -1.35000000000000007e-163 < i < 1.3000000000000001e-230

   1. Initial program 87.8%

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

   3. Taylor expanded in a around -inf 77.9%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in x around inf 82.9%

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

   if 1.3000000000000001e-230 < i < 2.6999999999999999e-81

   1. Initial program 74.3%

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

   3. Taylor expanded in z around inf 60.6%

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

      1. *-commutative 60.6%

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

   5. Simplified 60.6%

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

   if 2.6999999999999999e-81 < i < 5.50000000000000017e104

   1. Initial program 78.2%

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

   3. Taylor expanded in y around 0 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in i around inf 64.1%

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

   7. Taylor expanded in i around inf 66.9%

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

   if 5.50000000000000017e104 < i

   1. Initial program 68.7%

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

   3. Taylor expanded in i around inf 70.7%

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

      1. distribute-lft-out-- 70.7%

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

   5. Simplified 70.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.8 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq -1.55 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{b \cdot \left(t \cdot i\right)}{a} - x \cdot t\right)\right)\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-163}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-230}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{x \cdot \left(y \cdot z\right)}{a} - x \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+104}:\\ \;\;\;\;i \cdot \left(t \cdot b + \frac{a \cdot \left(c \cdot j - x \cdot t\right)}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(c \cdot \left(j - t \cdot \frac{x}{c}\right)\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-162}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-220}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 0.035:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -3.8e+99)
     t_1
     (if (<= y -1.05e+40)
       (* a (* c (- j (* t (/ x c)))))
       (if (<= y -4.5e-162)
         (+ (* x (* y z)) (* j (- (* a c) (* y i))))
         (if (<= y -2.9e-220)
           (* t (- (* b i) (* x a)))
           (if (<= y -2.1e-304)
             (* c (- (* a j) (* z b)))
             (if (<= y 0.035)
               (+ (* a (- (* c j) (* x t))) (* b (* t i)))
               t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -3.8e+99) {
		tmp = t_1;
	} else if (y <= -1.05e+40) {
		tmp = a * (c * (j - (t * (x / c))));
	} else if (y <= -4.5e-162) {
		tmp = (x * (y * z)) + (j * ((a * c) - (y * i)));
	} else if (y <= -2.9e-220) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= -2.1e-304) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 0.035) {
		tmp = (a * ((c * j) - (x * t))) + (b * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (y <= (-3.8d+99)) then
        tmp = t_1
    else if (y <= (-1.05d+40)) then
        tmp = a * (c * (j - (t * (x / c))))
    else if (y <= (-4.5d-162)) then
        tmp = (x * (y * z)) + (j * ((a * c) - (y * i)))
    else if (y <= (-2.9d-220)) then
        tmp = t * ((b * i) - (x * a))
    else if (y <= (-2.1d-304)) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= 0.035d0) then
        tmp = (a * ((c * j) - (x * t))) + (b * (t * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -3.8e+99) {
		tmp = t_1;
	} else if (y <= -1.05e+40) {
		tmp = a * (c * (j - (t * (x / c))));
	} else if (y <= -4.5e-162) {
		tmp = (x * (y * z)) + (j * ((a * c) - (y * i)));
	} else if (y <= -2.9e-220) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= -2.1e-304) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 0.035) {
		tmp = (a * ((c * j) - (x * t))) + (b * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -3.8e+99:
		tmp = t_1
	elif y <= -1.05e+40:
		tmp = a * (c * (j - (t * (x / c))))
	elif y <= -4.5e-162:
		tmp = (x * (y * z)) + (j * ((a * c) - (y * i)))
	elif y <= -2.9e-220:
		tmp = t * ((b * i) - (x * a))
	elif y <= -2.1e-304:
		tmp = c * ((a * j) - (z * b))
	elif y <= 0.035:
		tmp = (a * ((c * j) - (x * t))) + (b * (t * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -3.8e+99)
		tmp = t_1;
	elseif (y <= -1.05e+40)
		tmp = Float64(a * Float64(c * Float64(j - Float64(t * Float64(x / c)))));
	elseif (y <= -4.5e-162)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	elseif (y <= -2.9e-220)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (y <= -2.1e-304)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= 0.035)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(t * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -3.8e+99)
		tmp = t_1;
	elseif (y <= -1.05e+40)
		tmp = a * (c * (j - (t * (x / c))));
	elseif (y <= -4.5e-162)
		tmp = (x * (y * z)) + (j * ((a * c) - (y * i)));
	elseif (y <= -2.9e-220)
		tmp = t * ((b * i) - (x * a));
	elseif (y <= -2.1e-304)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= 0.035)
		tmp = (a * ((c * j) - (x * t))) + (b * (t * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+99], t$95$1, If[LessEqual[y, -1.05e+40], N[(a * N[(c * N[(j - N[(t * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.5e-162], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.9e-220], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-304], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.035], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -3.8e99 or 0.035000000000000003 < y

   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 y around inf 76.1%

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

      1. +-commutative 76.1%

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

      2. mul-1-neg 76.1%

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

      3. unsub-neg 76.1%

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

      4. *-commutative 76.1%

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

   5. Simplified 76.1%

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

   if -3.8e99 < y < -1.05000000000000005e40

   1. Initial program 74.7%

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

   3. Taylor expanded in a around inf 57.1%

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

      1. +-commutative 57.1%

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

      2. mul-1-neg 57.1%

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

      3. unsub-neg 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in c around inf 57.4%

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

      1. mul-1-neg 57.4%

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

      2. unsub-neg 57.4%

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

      3. associate-/l* 63.7%

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

   8. Simplified 63.7%

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

   if -1.05000000000000005e40 < y < -4.50000000000000023e-162

   1. Initial program 68.5%

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

   3. Taylor expanded in b around 0 64.4%

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

   4. Taylor expanded in y around inf 64.6%

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

   if -4.50000000000000023e-162 < y < -2.8999999999999998e-220

   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 y around 0 62.1%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in t around inf 59.8%

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

      1. +-commutative 59.8%

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

      2. mul-1-neg 59.8%

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

      3. unsub-neg 59.8%

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

   8. Simplified 59.8%

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

   if -2.8999999999999998e-220 < y < -2.10000000000000008e-304

   1. Initial program 64.2%

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

   3. Taylor expanded in c around inf 74.7%

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

      1. *-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -2.10000000000000008e-304 < y < 0.035000000000000003

   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 y around 0 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in i around inf 66.4%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(c \cdot \left(j - t \cdot \frac{x}{c}\right)\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-162}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-220}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 0.035:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 45.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-265}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-242}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-200}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* t (- (* b i) (* x a)))))
   (if (<= z -3.1e+95)
     (* b (- (* t i) (* z c)))
     (if (<= z -1.9e+34)
       t_2
       (if (<= z -2.9e-105)
         t_1
         (if (<= z 4.8e-265)
           t_3
           (if (<= z 1.85e-242)
             t_1
             (if (<= z 4.5e-200) t_3 (if (<= z 4e+21) 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 * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (z <= -3.1e+95) {
		tmp = b * ((t * i) - (z * c));
	} else if (z <= -1.9e+34) {
		tmp = t_2;
	} else if (z <= -2.9e-105) {
		tmp = t_1;
	} else if (z <= 4.8e-265) {
		tmp = t_3;
	} else if (z <= 1.85e-242) {
		tmp = t_1;
	} else if (z <= 4.5e-200) {
		tmp = t_3;
	} else if (z <= 4e+21) {
		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) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    t_3 = t * ((b * i) - (x * a))
    if (z <= (-3.1d+95)) then
        tmp = b * ((t * i) - (z * c))
    else if (z <= (-1.9d+34)) then
        tmp = t_2
    else if (z <= (-2.9d-105)) then
        tmp = t_1
    else if (z <= 4.8d-265) then
        tmp = t_3
    else if (z <= 1.85d-242) then
        tmp = t_1
    else if (z <= 4.5d-200) then
        tmp = t_3
    else if (z <= 4d+21) 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 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (z <= -3.1e+95) {
		tmp = b * ((t * i) - (z * c));
	} else if (z <= -1.9e+34) {
		tmp = t_2;
	} else if (z <= -2.9e-105) {
		tmp = t_1;
	} else if (z <= 4.8e-265) {
		tmp = t_3;
	} else if (z <= 1.85e-242) {
		tmp = t_1;
	} else if (z <= 4.5e-200) {
		tmp = t_3;
	} else if (z <= 4e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	t_3 = t * ((b * i) - (x * a))
	tmp = 0
	if z <= -3.1e+95:
		tmp = b * ((t * i) - (z * c))
	elif z <= -1.9e+34:
		tmp = t_2
	elif z <= -2.9e-105:
		tmp = t_1
	elif z <= 4.8e-265:
		tmp = t_3
	elif z <= 1.85e-242:
		tmp = t_1
	elif z <= 4.5e-200:
		tmp = t_3
	elif z <= 4e+21:
		tmp = 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(a * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (z <= -3.1e+95)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (z <= -1.9e+34)
		tmp = t_2;
	elseif (z <= -2.9e-105)
		tmp = t_1;
	elseif (z <= 4.8e-265)
		tmp = t_3;
	elseif (z <= 1.85e-242)
		tmp = t_1;
	elseif (z <= 4.5e-200)
		tmp = t_3;
	elseif (z <= 4e+21)
		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 = j * ((a * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	t_3 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (z <= -3.1e+95)
		tmp = b * ((t * i) - (z * c));
	elseif (z <= -1.9e+34)
		tmp = t_2;
	elseif (z <= -2.9e-105)
		tmp = t_1;
	elseif (z <= 4.8e-265)
		tmp = t_3;
	elseif (z <= 1.85e-242)
		tmp = t_1;
	elseif (z <= 4.5e-200)
		tmp = t_3;
	elseif (z <= 4e+21)
		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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+95], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.9e+34], t$95$2, If[LessEqual[z, -2.9e-105], t$95$1, If[LessEqual[z, 4.8e-265], t$95$3, If[LessEqual[z, 1.85e-242], t$95$1, If[LessEqual[z, 4.5e-200], t$95$3, If[LessEqual[z, 4e+21], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1000000000000003e95

   1. Initial program 62.4%

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

   3. Taylor expanded in b around inf 47.8%

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

   if -3.1000000000000003e95 < z < -1.9000000000000001e34 or 4e21 < z

   1. Initial program 65.2%

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

   3. Taylor expanded in x around inf 63.2%

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

      1. cancel-sign-sub-inv 63.2%

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

      2. *-commutative 63.2%

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

      3. *-commutative 63.2%

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

      4. distribute-rgt-neg-out 63.2%

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

      5. sub-neg 63.2%

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

   5. Simplified 63.2%

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

   if -1.9000000000000001e34 < z < -2.90000000000000003e-105 or 4.7999999999999999e-265 < z < 1.84999999999999998e-242 or 4.5000000000000002e-200 < z < 4e21

   1. Initial program 84.0%

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

   3. Taylor expanded in j around inf 67.6%

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

      1. *-commutative 67.6%

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

   5. Simplified 67.6%

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

   if -2.90000000000000003e-105 < z < 4.7999999999999999e-265 or 1.84999999999999998e-242 < z < 4.5000000000000002e-200

   1. Initial program 85.7%

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

   3. Taylor expanded in y around 0 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in t around inf 68.0%

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

      1. +-commutative 68.0%

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

      2. mul-1-neg 68.0%

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

      3. unsub-neg 68.0%

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

   8. Simplified 68.0%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-105}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-265}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-242}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-200}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right) + t\_2\\ \mathbf{if}\;y \leq -8.7 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8.1 \cdot 10^{+62}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) + t\_2\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-217}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 0.00086:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+123}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (+ (* j (- (* a c) (* y i))) t_2)))
   (if (<= y -8.7e+99)
     t_1
     (if (<= y -8.1e+62)
       (- (+ (* a (* c j)) t_2) (* b (* z c)))
       (if (<= y -2.6e-217)
         t_3
         (if (<= y 0.00086)
           (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))
           (if (<= y 2.3e+123) t_3 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 = y * ((x * z) - (i * j));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = (j * ((a * c) - (y * i))) + t_2;
	double tmp;
	if (y <= -8.7e+99) {
		tmp = t_1;
	} else if (y <= -8.1e+62) {
		tmp = ((a * (c * j)) + t_2) - (b * (z * c));
	} else if (y <= -2.6e-217) {
		tmp = t_3;
	} else if (y <= 0.00086) {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	} else if (y <= 2.3e+123) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = x * ((y * z) - (t * a))
    t_3 = (j * ((a * c) - (y * i))) + t_2
    if (y <= (-8.7d+99)) then
        tmp = t_1
    else if (y <= (-8.1d+62)) then
        tmp = ((a * (c * j)) + t_2) - (b * (z * c))
    else if (y <= (-2.6d-217)) then
        tmp = t_3
    else if (y <= 0.00086d0) then
        tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    else if (y <= 2.3d+123) then
        tmp = t_3
    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 = y * ((x * z) - (i * j));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = (j * ((a * c) - (y * i))) + t_2;
	double tmp;
	if (y <= -8.7e+99) {
		tmp = t_1;
	} else if (y <= -8.1e+62) {
		tmp = ((a * (c * j)) + t_2) - (b * (z * c));
	} else if (y <= -2.6e-217) {
		tmp = t_3;
	} else if (y <= 0.00086) {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	} else if (y <= 2.3e+123) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = x * ((y * z) - (t * a))
	t_3 = (j * ((a * c) - (y * i))) + t_2
	tmp = 0
	if y <= -8.7e+99:
		tmp = t_1
	elif y <= -8.1e+62:
		tmp = ((a * (c * j)) + t_2) - (b * (z * c))
	elif y <= -2.6e-217:
		tmp = t_3
	elif y <= 0.00086:
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	elif y <= 2.3e+123:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_2)
	tmp = 0.0
	if (y <= -8.7e+99)
		tmp = t_1;
	elseif (y <= -8.1e+62)
		tmp = Float64(Float64(Float64(a * Float64(c * j)) + t_2) - Float64(b * Float64(z * c)));
	elseif (y <= -2.6e-217)
		tmp = t_3;
	elseif (y <= 0.00086)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (y <= 2.3e+123)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = x * ((y * z) - (t * a));
	t_3 = (j * ((a * c) - (y * i))) + t_2;
	tmp = 0.0;
	if (y <= -8.7e+99)
		tmp = t_1;
	elseif (y <= -8.1e+62)
		tmp = ((a * (c * j)) + t_2) - (b * (z * c));
	elseif (y <= -2.6e-217)
		tmp = t_3;
	elseif (y <= 0.00086)
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	elseif (y <= 2.3e+123)
		tmp = t_3;
	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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[y, -8.7e+99], t$95$1, If[LessEqual[y, -8.1e+62], N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.6e-217], t$95$3, If[LessEqual[y, 0.00086], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+123], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.6999999999999997e99 or 2.2999999999999999e123 < y

   1. Initial program 62.0%

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

   3. Taylor expanded in y around inf 81.0%

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

      1. +-commutative 81.0%

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

      2. mul-1-neg 81.0%

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

      3. unsub-neg 81.0%

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

      4. *-commutative 81.0%

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

   5. Simplified 81.0%

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

   if -8.6999999999999997e99 < y < -8.09999999999999998e62

   1. Initial program 77.3%

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

   3. Taylor expanded in i around 0 67.0%

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

   if -8.09999999999999998e62 < y < -2.59999999999999993e-217 or 8.59999999999999979e-4 < y < 2.2999999999999999e123

   1. Initial program 74.0%

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

   3. Taylor expanded in b around 0 71.5%

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

   if -2.59999999999999993e-217 < y < 8.59999999999999979e-4

   1. Initial program 85.5%

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

   3. Taylor expanded in y around 0 75.1%

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

   5. Simplified 75.0%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.7 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -8.1 \cdot 10^{+62}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-217}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 0.00086:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+123}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(c \cdot \left(-b\right)\right)\\ t_2 := j \cdot \left(y \cdot \left(-i\right)\right)\\ t_3 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;i \leq -3.7 \cdot 10^{-37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.7 \cdot 10^{-273}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq 5.4 \cdot 10^{-208}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{-29}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+216}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* c (- b))))
        (t_2 (* j (* y (- i))))
        (t_3 (* a (* x (- t)))))
   (if (<= i -3.7e-37)
     t_2
     (if (<= i -4.5e-166)
       t_1
       (if (<= i -2.7e-273)
         t_3
         (if (<= i 5.4e-208)
           (* j (* a c))
           (if (<= i 1.1e-80)
             t_1
             (if (<= i 2.6e-29)
               t_3
               (if (<= i 3.7e+216) (* t (* b i)) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * -b);
	double t_2 = j * (y * -i);
	double t_3 = a * (x * -t);
	double tmp;
	if (i <= -3.7e-37) {
		tmp = t_2;
	} else if (i <= -4.5e-166) {
		tmp = t_1;
	} else if (i <= -2.7e-273) {
		tmp = t_3;
	} else if (i <= 5.4e-208) {
		tmp = j * (a * c);
	} else if (i <= 1.1e-80) {
		tmp = t_1;
	} else if (i <= 2.6e-29) {
		tmp = t_3;
	} else if (i <= 3.7e+216) {
		tmp = t * (b * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (c * -b)
    t_2 = j * (y * -i)
    t_3 = a * (x * -t)
    if (i <= (-3.7d-37)) then
        tmp = t_2
    else if (i <= (-4.5d-166)) then
        tmp = t_1
    else if (i <= (-2.7d-273)) then
        tmp = t_3
    else if (i <= 5.4d-208) then
        tmp = j * (a * c)
    else if (i <= 1.1d-80) then
        tmp = t_1
    else if (i <= 2.6d-29) then
        tmp = t_3
    else if (i <= 3.7d+216) then
        tmp = t * (b * i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * -b);
	double t_2 = j * (y * -i);
	double t_3 = a * (x * -t);
	double tmp;
	if (i <= -3.7e-37) {
		tmp = t_2;
	} else if (i <= -4.5e-166) {
		tmp = t_1;
	} else if (i <= -2.7e-273) {
		tmp = t_3;
	} else if (i <= 5.4e-208) {
		tmp = j * (a * c);
	} else if (i <= 1.1e-80) {
		tmp = t_1;
	} else if (i <= 2.6e-29) {
		tmp = t_3;
	} else if (i <= 3.7e+216) {
		tmp = t * (b * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (c * -b)
	t_2 = j * (y * -i)
	t_3 = a * (x * -t)
	tmp = 0
	if i <= -3.7e-37:
		tmp = t_2
	elif i <= -4.5e-166:
		tmp = t_1
	elif i <= -2.7e-273:
		tmp = t_3
	elif i <= 5.4e-208:
		tmp = j * (a * c)
	elif i <= 1.1e-80:
		tmp = t_1
	elif i <= 2.6e-29:
		tmp = t_3
	elif i <= 3.7e+216:
		tmp = t * (b * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(c * Float64(-b)))
	t_2 = Float64(j * Float64(y * Float64(-i)))
	t_3 = Float64(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (i <= -3.7e-37)
		tmp = t_2;
	elseif (i <= -4.5e-166)
		tmp = t_1;
	elseif (i <= -2.7e-273)
		tmp = t_3;
	elseif (i <= 5.4e-208)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 1.1e-80)
		tmp = t_1;
	elseif (i <= 2.6e-29)
		tmp = t_3;
	elseif (i <= 3.7e+216)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (c * -b);
	t_2 = j * (y * -i);
	t_3 = a * (x * -t);
	tmp = 0.0;
	if (i <= -3.7e-37)
		tmp = t_2;
	elseif (i <= -4.5e-166)
		tmp = t_1;
	elseif (i <= -2.7e-273)
		tmp = t_3;
	elseif (i <= 5.4e-208)
		tmp = j * (a * c);
	elseif (i <= 1.1e-80)
		tmp = t_1;
	elseif (i <= 2.6e-29)
		tmp = t_3;
	elseif (i <= 3.7e+216)
		tmp = t * (b * i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.7e-37], t$95$2, If[LessEqual[i, -4.5e-166], t$95$1, If[LessEqual[i, -2.7e-273], t$95$3, If[LessEqual[i, 5.4e-208], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.1e-80], t$95$1, If[LessEqual[i, 2.6e-29], t$95$3, If[LessEqual[i, 3.7e+216], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -3.7e-37 or 3.6999999999999999e216 < i

   1. Initial program 64.1%

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

   3. Taylor expanded in j around inf 56.7%

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

      1. *-commutative 56.7%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in c around 0 49.8%

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

      1. mul-1-neg 49.8%

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

   8. Simplified 49.8%

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

   if -3.7e-37 < i < -4.4999999999999998e-166 or 5.4e-208 < i < 1.10000000000000005e-80

   1. Initial program 72.1%

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

   3. Taylor expanded in z around inf 65.0%

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

      1. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in y around 0 43.6%

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

      1. neg-mul-1 43.6%

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

      2. distribute-rgt-neg-in 43.6%

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

   8. Simplified 43.6%

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

   if -4.4999999999999998e-166 < i < -2.69999999999999984e-273 or 1.10000000000000005e-80 < i < 2.6000000000000002e-29

   1. Initial program 91.0%

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

   3. Taylor expanded in a around inf 74.0%

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

      1. +-commutative 74.0%

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

      2. mul-1-neg 74.0%

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

      3. unsub-neg 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in c around 0 56.1%

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

      1. associate-*r* 56.1%

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

      2. neg-mul-1 56.1%

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

   8. Simplified 56.1%

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

   if -2.69999999999999984e-273 < i < 5.4e-208

   1. Initial program 76.4%

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

   3. Taylor expanded in j around inf 45.6%

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

      1. *-commutative 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in c around inf 37.1%

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

      1. *-commutative 37.1%

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

   8. Simplified 37.1%

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

   if 2.6000000000000002e-29 < i < 3.6999999999999999e216

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in i around inf 56.5%

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

   7. Taylor expanded in a around 0 38.2%

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

      1. *-commutative 38.2%

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

      2. *-commutative 38.2%

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

      3. associate-*r* 41.6%

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

   9. Simplified 41.6%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.7 \cdot 10^{-37}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-166}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq -2.7 \cdot 10^{-273}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 5.4 \cdot 10^{-208}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{-29}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+216}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -5.1 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-269}:\\ \;\;\;\;a \cdot \left(c \cdot \left(j - t \cdot \frac{x}{c}\right)\right)\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-298}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-276}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq 10^{-236}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.0042:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -5.1e+99)
     t_1
     (if (<= y -2.75e-269)
       (* a (* c (- j (* t (/ x c)))))
       (if (<= y 3.05e-298)
         (* c (- (* a j) (* z b)))
         (if (<= y 5.9e-276)
           (* z (- (* x y) (* b c)))
           (if (<= y 1e-236)
             (* t (- (* b i) (* x a)))
             (if (<= y 0.0042) (+ (* a (* c j)) (* b (* t i))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -5.1e+99) {
		tmp = t_1;
	} else if (y <= -2.75e-269) {
		tmp = a * (c * (j - (t * (x / c))));
	} else if (y <= 3.05e-298) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 5.9e-276) {
		tmp = z * ((x * y) - (b * c));
	} else if (y <= 1e-236) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 0.0042) {
		tmp = (a * (c * j)) + (b * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (y <= (-5.1d+99)) then
        tmp = t_1
    else if (y <= (-2.75d-269)) then
        tmp = a * (c * (j - (t * (x / c))))
    else if (y <= 3.05d-298) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= 5.9d-276) then
        tmp = z * ((x * y) - (b * c))
    else if (y <= 1d-236) then
        tmp = t * ((b * i) - (x * a))
    else if (y <= 0.0042d0) then
        tmp = (a * (c * j)) + (b * (t * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -5.1e+99) {
		tmp = t_1;
	} else if (y <= -2.75e-269) {
		tmp = a * (c * (j - (t * (x / c))));
	} else if (y <= 3.05e-298) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 5.9e-276) {
		tmp = z * ((x * y) - (b * c));
	} else if (y <= 1e-236) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 0.0042) {
		tmp = (a * (c * j)) + (b * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -5.1e+99:
		tmp = t_1
	elif y <= -2.75e-269:
		tmp = a * (c * (j - (t * (x / c))))
	elif y <= 3.05e-298:
		tmp = c * ((a * j) - (z * b))
	elif y <= 5.9e-276:
		tmp = z * ((x * y) - (b * c))
	elif y <= 1e-236:
		tmp = t * ((b * i) - (x * a))
	elif y <= 0.0042:
		tmp = (a * (c * j)) + (b * (t * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -5.1e+99)
		tmp = t_1;
	elseif (y <= -2.75e-269)
		tmp = Float64(a * Float64(c * Float64(j - Float64(t * Float64(x / c)))));
	elseif (y <= 3.05e-298)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= 5.9e-276)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (y <= 1e-236)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (y <= 0.0042)
		tmp = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(t * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -5.1e+99)
		tmp = t_1;
	elseif (y <= -2.75e-269)
		tmp = a * (c * (j - (t * (x / c))));
	elseif (y <= 3.05e-298)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= 5.9e-276)
		tmp = z * ((x * y) - (b * c));
	elseif (y <= 1e-236)
		tmp = t * ((b * i) - (x * a));
	elseif (y <= 0.0042)
		tmp = (a * (c * j)) + (b * (t * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.1e+99], t$95$1, If[LessEqual[y, -2.75e-269], N[(a * N[(c * N[(j - N[(t * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.05e-298], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.9e-276], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-236], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0042], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -5.09999999999999952e99 or 0.00419999999999999974 < y

   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 y around inf 76.1%

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

      1. +-commutative 76.1%

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

      2. mul-1-neg 76.1%

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

      3. unsub-neg 76.1%

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

      4. *-commutative 76.1%

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

   5. Simplified 76.1%

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

   if -5.09999999999999952e99 < y < -2.75000000000000005e-269

   1. Initial program 70.1%

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

   3. Taylor expanded in a around inf 51.3%

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

      1. +-commutative 51.3%

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

      2. mul-1-neg 51.3%

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

      3. unsub-neg 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in c around inf 50.2%

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

      1. mul-1-neg 50.2%

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

      2. unsub-neg 50.2%

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

      3. associate-/l* 52.6%

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

   8. Simplified 52.6%

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

   if -2.75000000000000005e-269 < y < 3.05000000000000006e-298

   1. Initial program 73.1%

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

   3. Taylor expanded in c around inf 68.2%

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

      1. *-commutative 68.2%

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

   5. Simplified 68.2%

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

   if 3.05000000000000006e-298 < y < 5.89999999999999976e-276

   1. Initial program 83.6%

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

   3. Taylor expanded in z around inf 67.6%

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

      1. *-commutative 67.6%

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

   5. Simplified 67.6%

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

   if 5.89999999999999976e-276 < y < 1e-236

   1. Initial program 89.3%

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

   3. Taylor expanded in y around 0 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in t around inf 74.2%

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

      1. +-commutative 74.2%

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

      2. mul-1-neg 74.2%

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

      3. unsub-neg 74.2%

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

   8. Simplified 74.2%

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

   if 1e-236 < y < 0.00419999999999999974

   1. Initial program 91.3%

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

   3. Taylor expanded in y around 0 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in i around inf 66.1%

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

   7. Taylor expanded in x around 0 60.5%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-269}:\\ \;\;\;\;a \cdot \left(c \cdot \left(j - t \cdot \frac{x}{c}\right)\right)\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-298}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-276}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq 10^{-236}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.0042:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := t\_1 - b \cdot \left(z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+99}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 8.3 \cdot 10^{-255}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 0.00086:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (- t_1 (* b (* z c))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -3.9e+99)
     t_3
     (if (<= y -1.2e+41)
       t_2
       (if (<= y -1.32e-160)
         (+ (* x (* y z)) (* j (- (* a c) (* y i))))
         (if (<= y 8.3e-255)
           t_2
           (if (<= y 0.00086) (+ t_1 (* b (* t i))) t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = t_1 - (b * (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -3.9e+99) {
		tmp = t_3;
	} else if (y <= -1.2e+41) {
		tmp = t_2;
	} else if (y <= -1.32e-160) {
		tmp = (x * (y * z)) + (j * ((a * c) - (y * i)));
	} else if (y <= 8.3e-255) {
		tmp = t_2;
	} else if (y <= 0.00086) {
		tmp = t_1 + (b * (t * i));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = t_1 - (b * (z * c))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-3.9d+99)) then
        tmp = t_3
    else if (y <= (-1.2d+41)) then
        tmp = t_2
    else if (y <= (-1.32d-160)) then
        tmp = (x * (y * z)) + (j * ((a * c) - (y * i)))
    else if (y <= 8.3d-255) then
        tmp = t_2
    else if (y <= 0.00086d0) then
        tmp = t_1 + (b * (t * i))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = t_1 - (b * (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -3.9e+99) {
		tmp = t_3;
	} else if (y <= -1.2e+41) {
		tmp = t_2;
	} else if (y <= -1.32e-160) {
		tmp = (x * (y * z)) + (j * ((a * c) - (y * i)));
	} else if (y <= 8.3e-255) {
		tmp = t_2;
	} else if (y <= 0.00086) {
		tmp = t_1 + (b * (t * i));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = t_1 - (b * (z * c))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -3.9e+99:
		tmp = t_3
	elif y <= -1.2e+41:
		tmp = t_2
	elif y <= -1.32e-160:
		tmp = (x * (y * z)) + (j * ((a * c) - (y * i)))
	elif y <= 8.3e-255:
		tmp = t_2
	elif y <= 0.00086:
		tmp = t_1 + (b * (t * i))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(t_1 - Float64(b * Float64(z * c)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -3.9e+99)
		tmp = t_3;
	elseif (y <= -1.2e+41)
		tmp = t_2;
	elseif (y <= -1.32e-160)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	elseif (y <= 8.3e-255)
		tmp = t_2;
	elseif (y <= 0.00086)
		tmp = Float64(t_1 + Float64(b * Float64(t * i)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = t_1 - (b * (z * c));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -3.9e+99)
		tmp = t_3;
	elseif (y <= -1.2e+41)
		tmp = t_2;
	elseif (y <= -1.32e-160)
		tmp = (x * (y * z)) + (j * ((a * c) - (y * i)));
	elseif (y <= 8.3e-255)
		tmp = t_2;
	elseif (y <= 0.00086)
		tmp = t_1 + (b * (t * i));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e+99], t$95$3, If[LessEqual[y, -1.2e+41], t$95$2, If[LessEqual[y, -1.32e-160], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.3e-255], t$95$2, If[LessEqual[y, 0.00086], N[(t$95$1 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.89999999999999995e99 or 8.59999999999999979e-4 < y

   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 y around inf 76.1%

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

      1. +-commutative 76.1%

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

      2. mul-1-neg 76.1%

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

      3. unsub-neg 76.1%

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

      4. *-commutative 76.1%

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

   5. Simplified 76.1%

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

   if -3.89999999999999995e99 < y < -1.2000000000000001e41 or -1.3199999999999999e-160 < y < 8.29999999999999992e-255

   1. Initial program 74.3%

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

   3. Taylor expanded in y around 0 66.5%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in i around 0 64.6%

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

      1. +-commutative 64.6%

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

      2. *-commutative 64.6%

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

      3. *-commutative 64.6%

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

      4. mul-1-neg 64.6%

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

      5. unsub-neg 64.6%

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

      6. *-commutative 64.6%

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

      7. *-commutative 64.6%

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

   8. Simplified 64.6%

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

   if -1.2000000000000001e41 < y < -1.3199999999999999e-160

   1. Initial program 68.5%

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

   3. Taylor expanded in b around 0 64.4%

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

   4. Taylor expanded in y around inf 64.6%

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

   if 8.29999999999999992e-255 < y < 8.59999999999999979e-4

   1. Initial program 92.0%

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

   3. Taylor expanded in y around 0 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in i around inf 68.8%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 8.3 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 0.00086:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 45.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;i \leq -5.2 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq -1.45 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{-168}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 7.4 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= i -5.2e+48)
     (* y (- (* x z) (* i j)))
     (if (<= i -1.45e-35)
       t_1
       (if (<= i -2.15e-168)
         (* c (- (* a j) (* z b)))
         (if (<= i -7.2e-253)
           (* a (- (* c j) (* x t)))
           (if (<= i 7.4e-26)
             (* x (- (* y z) (* t a)))
             (if (<= i 3.8e+106) t_1 (* j (- (* a c) (* y i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (i <= -5.2e+48) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= -1.45e-35) {
		tmp = t_1;
	} else if (i <= -2.15e-168) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= -7.2e-253) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 7.4e-26) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 3.8e+106) {
		tmp = t_1;
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (i <= (-5.2d+48)) then
        tmp = y * ((x * z) - (i * j))
    else if (i <= (-1.45d-35)) then
        tmp = t_1
    else if (i <= (-2.15d-168)) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= (-7.2d-253)) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 7.4d-26) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= 3.8d+106) then
        tmp = t_1
    else
        tmp = j * ((a * c) - (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (i <= -5.2e+48) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= -1.45e-35) {
		tmp = t_1;
	} else if (i <= -2.15e-168) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= -7.2e-253) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 7.4e-26) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 3.8e+106) {
		tmp = t_1;
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if i <= -5.2e+48:
		tmp = y * ((x * z) - (i * j))
	elif i <= -1.45e-35:
		tmp = t_1
	elif i <= -2.15e-168:
		tmp = c * ((a * j) - (z * b))
	elif i <= -7.2e-253:
		tmp = a * ((c * j) - (x * t))
	elif i <= 7.4e-26:
		tmp = x * ((y * z) - (t * a))
	elif i <= 3.8e+106:
		tmp = t_1
	else:
		tmp = j * ((a * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (i <= -5.2e+48)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (i <= -1.45e-35)
		tmp = t_1;
	elseif (i <= -2.15e-168)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= -7.2e-253)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 7.4e-26)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= 3.8e+106)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (i <= -5.2e+48)
		tmp = y * ((x * z) - (i * j));
	elseif (i <= -1.45e-35)
		tmp = t_1;
	elseif (i <= -2.15e-168)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= -7.2e-253)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 7.4e-26)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= 3.8e+106)
		tmp = t_1;
	else
		tmp = j * ((a * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.2e+48], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.45e-35], t$95$1, If[LessEqual[i, -2.15e-168], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7.2e-253], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.4e-26], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.8e+106], t$95$1, N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -5.1999999999999999e48

   1. Initial program 62.5%

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

   3. Taylor expanded in y around inf 67.3%

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

      1. +-commutative 67.3%

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

      2. mul-1-neg 67.3%

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

      3. unsub-neg 67.3%

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

      4. *-commutative 67.3%

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

   5. Simplified 67.3%

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

   if -5.1999999999999999e48 < i < -1.4500000000000001e-35 or 7.3999999999999997e-26 < i < 3.7999999999999998e106

   1. Initial program 73.7%

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

   3. Taylor expanded in y around 0 74.4%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in t around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

   8. Simplified 59.2%

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

   if -1.4500000000000001e-35 < i < -2.14999999999999998e-168

   1. Initial program 64.3%

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

   3. Taylor expanded in c around inf 69.1%

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

      1. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   if -2.14999999999999998e-168 < i < -7.2e-253

   1. Initial program 92.1%

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

   3. Taylor expanded in a around inf 84.5%

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

      1. +-commutative 84.5%

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

      2. mul-1-neg 84.5%

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

      3. unsub-neg 84.5%

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

   5. Simplified 84.5%

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

   if -7.2e-253 < i < 7.3999999999999997e-26

   1. Initial program 81.0%

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

   3. Taylor expanded in x around inf 49.8%

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

      1. cancel-sign-sub-inv 49.8%

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

      2. *-commutative 49.8%

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

      3. *-commutative 49.8%

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

      4. distribute-rgt-neg-out 49.8%

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

      5. sub-neg 49.8%

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

   5. Simplified 49.8%

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

   if 3.7999999999999998e106 < i

   1. Initial program 67.9%

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

   3. Taylor expanded in j around inf 58.3%

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

      1. *-commutative 58.3%

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

   5. Simplified 58.3%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq -1.45 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{-168}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 7.4 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 44.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;i \leq -2 \cdot 10^{+118}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -4 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-251}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+106}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b))))
        (t_2 (* t (- (* b i) (* x a))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= i -2e+118)
     t_3
     (if (<= i -4e-36)
       t_2
       (if (<= i -1.3e-166)
         t_1
         (if (<= i 9.5e-251)
           (* a (- (* c j) (* x t)))
           (if (<= i 1.1e-78) t_1 (if (<= i 4.2e+106) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (i <= -2e+118) {
		tmp = t_3;
	} else if (i <= -4e-36) {
		tmp = t_2;
	} else if (i <= -1.3e-166) {
		tmp = t_1;
	} else if (i <= 9.5e-251) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.1e-78) {
		tmp = t_1;
	} else if (i <= 4.2e+106) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    t_2 = t * ((b * i) - (x * a))
    t_3 = j * ((a * c) - (y * i))
    if (i <= (-2d+118)) then
        tmp = t_3
    else if (i <= (-4d-36)) then
        tmp = t_2
    else if (i <= (-1.3d-166)) then
        tmp = t_1
    else if (i <= 9.5d-251) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 1.1d-78) then
        tmp = t_1
    else if (i <= 4.2d+106) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (i <= -2e+118) {
		tmp = t_3;
	} else if (i <= -4e-36) {
		tmp = t_2;
	} else if (i <= -1.3e-166) {
		tmp = t_1;
	} else if (i <= 9.5e-251) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.1e-78) {
		tmp = t_1;
	} else if (i <= 4.2e+106) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = t * ((b * i) - (x * a))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if i <= -2e+118:
		tmp = t_3
	elif i <= -4e-36:
		tmp = t_2
	elif i <= -1.3e-166:
		tmp = t_1
	elif i <= 9.5e-251:
		tmp = a * ((c * j) - (x * t))
	elif i <= 1.1e-78:
		tmp = t_1
	elif i <= 4.2e+106:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (i <= -2e+118)
		tmp = t_3;
	elseif (i <= -4e-36)
		tmp = t_2;
	elseif (i <= -1.3e-166)
		tmp = t_1;
	elseif (i <= 9.5e-251)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 1.1e-78)
		tmp = t_1;
	elseif (i <= 4.2e+106)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	t_2 = t * ((b * i) - (x * a));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (i <= -2e+118)
		tmp = t_3;
	elseif (i <= -4e-36)
		tmp = t_2;
	elseif (i <= -1.3e-166)
		tmp = t_1;
	elseif (i <= 9.5e-251)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 1.1e-78)
		tmp = t_1;
	elseif (i <= 4.2e+106)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2e+118], t$95$3, If[LessEqual[i, -4e-36], t$95$2, If[LessEqual[i, -1.3e-166], t$95$1, If[LessEqual[i, 9.5e-251], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.1e-78], t$95$1, If[LessEqual[i, 4.2e+106], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.99999999999999993e118 or 4.2000000000000001e106 < i

   1. Initial program 65.2%

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

   3. Taylor expanded in j around inf 59.5%

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

      1. *-commutative 59.5%

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

   5. Simplified 59.5%

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

   if -1.99999999999999993e118 < i < -3.9999999999999998e-36 or 1.0999999999999999e-78 < i < 4.2000000000000001e106

   1. Initial program 75.7%

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

   3. Taylor expanded in y around 0 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in t around inf 54.9%

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

      1. +-commutative 54.9%

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

      2. mul-1-neg 54.9%

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

      3. unsub-neg 54.9%

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

   8. Simplified 54.9%

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

   if -3.9999999999999998e-36 < i < -1.29999999999999995e-166 or 9.49999999999999927e-251 < i < 1.0999999999999999e-78

   1. Initial program 71.9%

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

   3. Taylor expanded in c around inf 54.3%

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

      1. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   if -1.29999999999999995e-166 < i < 9.49999999999999927e-251

   1. Initial program 87.2%

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

   3. Taylor expanded in a around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

   5. Simplified 67.8%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2 \cdot 10^{+118}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq -4 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-166}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-251}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-78}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 48.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+196}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.15 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -5.5e+196)
     t_2
     (if (<= b -3.15e+125)
       t_1
       (if (<= b -8e-29)
         t_2
         (if (<= b 3e-170)
           t_1
           (if (<= b 4.2e-122)
             (* x (* y z))
             (if (<= b 2.5e+128) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.5e+196) {
		tmp = t_2;
	} else if (b <= -3.15e+125) {
		tmp = t_1;
	} else if (b <= -8e-29) {
		tmp = t_2;
	} else if (b <= 3e-170) {
		tmp = t_1;
	} else if (b <= 4.2e-122) {
		tmp = x * (y * z);
	} else if (b <= 2.5e+128) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-5.5d+196)) then
        tmp = t_2
    else if (b <= (-3.15d+125)) then
        tmp = t_1
    else if (b <= (-8d-29)) then
        tmp = t_2
    else if (b <= 3d-170) then
        tmp = t_1
    else if (b <= 4.2d-122) then
        tmp = x * (y * z)
    else if (b <= 2.5d+128) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.5e+196) {
		tmp = t_2;
	} else if (b <= -3.15e+125) {
		tmp = t_1;
	} else if (b <= -8e-29) {
		tmp = t_2;
	} else if (b <= 3e-170) {
		tmp = t_1;
	} else if (b <= 4.2e-122) {
		tmp = x * (y * z);
	} else if (b <= 2.5e+128) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -5.5e+196:
		tmp = t_2
	elif b <= -3.15e+125:
		tmp = t_1
	elif b <= -8e-29:
		tmp = t_2
	elif b <= 3e-170:
		tmp = t_1
	elif b <= 4.2e-122:
		tmp = x * (y * z)
	elif b <= 2.5e+128:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.5e+196)
		tmp = t_2;
	elseif (b <= -3.15e+125)
		tmp = t_1;
	elseif (b <= -8e-29)
		tmp = t_2;
	elseif (b <= 3e-170)
		tmp = t_1;
	elseif (b <= 4.2e-122)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 2.5e+128)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.5e+196)
		tmp = t_2;
	elseif (b <= -3.15e+125)
		tmp = t_1;
	elseif (b <= -8e-29)
		tmp = t_2;
	elseif (b <= 3e-170)
		tmp = t_1;
	elseif (b <= 4.2e-122)
		tmp = x * (y * z);
	elseif (b <= 2.5e+128)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e+196], t$95$2, If[LessEqual[b, -3.15e+125], t$95$1, If[LessEqual[b, -8e-29], t$95$2, If[LessEqual[b, 3e-170], t$95$1, If[LessEqual[b, 4.2e-122], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e+128], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.49999999999999973e196 or -3.1500000000000001e125 < b < -7.99999999999999955e-29 or 2.5e128 < b

   1. Initial program 69.0%

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

   3. Taylor expanded in b around inf 62.3%

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

   if -5.49999999999999973e196 < b < -3.1500000000000001e125 or -7.99999999999999955e-29 < b < 3.00000000000000013e-170 or 4.19999999999999985e-122 < b < 2.5e128

   1. Initial program 76.6%

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

   3. Taylor expanded in a around inf 51.5%

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

      1. +-commutative 51.5%

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

      2. mul-1-neg 51.5%

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

      3. unsub-neg 51.5%

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

   5. Simplified 51.5%

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

   if 3.00000000000000013e-170 < b < 4.19999999999999985e-122

   1. Initial program 75.7%

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

   3. Taylor expanded in i around 0 70.0%

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

   4. Taylor expanded in y around inf 67.1%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+196}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.15 \cdot 10^{+125}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-29}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-170}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{if}\;i \leq -9.6 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{-253}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-294}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-207}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+199}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* y (- i)))))
   (if (<= i -9.6e+42)
     t_1
     (if (<= i -7.5e-253)
       (* c (* a j))
       (if (<= i -5.5e-294)
         (* z (* x y))
         (if (<= i 2.7e-207)
           (* j (* a c))
           (if (<= i 6e-23)
             (* z (* c (- b)))
             (if (<= i 3.2e+199) (* t (* b i)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (y * -i);
	double tmp;
	if (i <= -9.6e+42) {
		tmp = t_1;
	} else if (i <= -7.5e-253) {
		tmp = c * (a * j);
	} else if (i <= -5.5e-294) {
		tmp = z * (x * y);
	} else if (i <= 2.7e-207) {
		tmp = j * (a * c);
	} else if (i <= 6e-23) {
		tmp = z * (c * -b);
	} else if (i <= 3.2e+199) {
		tmp = t * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (y * -i)
    if (i <= (-9.6d+42)) then
        tmp = t_1
    else if (i <= (-7.5d-253)) then
        tmp = c * (a * j)
    else if (i <= (-5.5d-294)) then
        tmp = z * (x * y)
    else if (i <= 2.7d-207) then
        tmp = j * (a * c)
    else if (i <= 6d-23) then
        tmp = z * (c * -b)
    else if (i <= 3.2d+199) then
        tmp = t * (b * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (y * -i);
	double tmp;
	if (i <= -9.6e+42) {
		tmp = t_1;
	} else if (i <= -7.5e-253) {
		tmp = c * (a * j);
	} else if (i <= -5.5e-294) {
		tmp = z * (x * y);
	} else if (i <= 2.7e-207) {
		tmp = j * (a * c);
	} else if (i <= 6e-23) {
		tmp = z * (c * -b);
	} else if (i <= 3.2e+199) {
		tmp = t * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (y * -i)
	tmp = 0
	if i <= -9.6e+42:
		tmp = t_1
	elif i <= -7.5e-253:
		tmp = c * (a * j)
	elif i <= -5.5e-294:
		tmp = z * (x * y)
	elif i <= 2.7e-207:
		tmp = j * (a * c)
	elif i <= 6e-23:
		tmp = z * (c * -b)
	elif i <= 3.2e+199:
		tmp = t * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(y * Float64(-i)))
	tmp = 0.0
	if (i <= -9.6e+42)
		tmp = t_1;
	elseif (i <= -7.5e-253)
		tmp = Float64(c * Float64(a * j));
	elseif (i <= -5.5e-294)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 2.7e-207)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 6e-23)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (i <= 3.2e+199)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (y * -i);
	tmp = 0.0;
	if (i <= -9.6e+42)
		tmp = t_1;
	elseif (i <= -7.5e-253)
		tmp = c * (a * j);
	elseif (i <= -5.5e-294)
		tmp = z * (x * y);
	elseif (i <= 2.7e-207)
		tmp = j * (a * c);
	elseif (i <= 6e-23)
		tmp = z * (c * -b);
	elseif (i <= 3.2e+199)
		tmp = t * (b * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9.6e+42], t$95$1, If[LessEqual[i, -7.5e-253], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.5e-294], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.7e-207], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6e-23], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.2e+199], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -9.5999999999999994e42 or 3.20000000000000006e199 < i

   1. Initial program 61.1%

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

   3. Taylor expanded in j around inf 61.7%

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

      1. *-commutative 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in c around 0 56.7%

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

      1. mul-1-neg 56.7%

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

   8. Simplified 56.7%

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

   if -9.5999999999999994e42 < i < -7.49999999999999987e-253

   1. Initial program 78.0%

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

   3. Taylor expanded in i around 0 71.6%

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

   4. Taylor expanded in j around inf 30.4%

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

      1. associate-*r* 33.4%

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

      2. *-commutative 33.4%

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

      3. associate-*r* 36.4%

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

   6. Simplified 36.4%

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

   if -7.49999999999999987e-253 < i < -5.5e-294

   1. Initial program 86.8%

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

   3. Taylor expanded in z around inf 61.0%

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

      1. *-commutative 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in y around inf 48.7%

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

      1. *-commutative 48.7%

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

   8. Simplified 48.7%

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

   if -5.5e-294 < i < 2.7e-207

   1. Initial program 73.9%

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

   3. Taylor expanded in j around inf 53.1%

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

      1. *-commutative 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in c around inf 42.4%

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

      1. *-commutative 42.4%

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

   8. Simplified 42.4%

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

   if 2.7e-207 < i < 6.00000000000000006e-23

   1. Initial program 83.7%

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

   3. Taylor expanded in z around inf 55.0%

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

      1. *-commutative 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in y around 0 32.4%

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

      1. neg-mul-1 32.4%

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

      2. distribute-rgt-neg-in 32.4%

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

   8. Simplified 32.4%

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

   if 6.00000000000000006e-23 < i < 3.20000000000000006e199

   1. Initial program 73.2%

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

   3. Taylor expanded in y around 0 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in i around inf 57.6%

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

   7. Taylor expanded in a around 0 38.9%

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

      1. *-commutative 38.9%

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

      2. *-commutative 38.9%

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

      3. associate-*r* 42.4%

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

   9. Simplified 42.4%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.6 \cdot 10^{+42}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{-253}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-294}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-207}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-23}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+199}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{if}\;i \leq -5.8 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -9.5 \cdot 10^{-253}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq -8.4 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.92 \cdot 10^{-208}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+198}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* y (- i)))))
   (if (<= i -5.8e+43)
     t_1
     (if (<= i -9.5e-253)
       (* c (* a j))
       (if (<= i -8.4e-302)
         (* z (* x y))
         (if (<= i 1.92e-208)
           (* j (* a c))
           (if (<= i 3e-26)
             (* x (* y z))
             (if (<= i 2.5e+198) (* t (* b i)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (y * -i);
	double tmp;
	if (i <= -5.8e+43) {
		tmp = t_1;
	} else if (i <= -9.5e-253) {
		tmp = c * (a * j);
	} else if (i <= -8.4e-302) {
		tmp = z * (x * y);
	} else if (i <= 1.92e-208) {
		tmp = j * (a * c);
	} else if (i <= 3e-26) {
		tmp = x * (y * z);
	} else if (i <= 2.5e+198) {
		tmp = t * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (y * -i)
    if (i <= (-5.8d+43)) then
        tmp = t_1
    else if (i <= (-9.5d-253)) then
        tmp = c * (a * j)
    else if (i <= (-8.4d-302)) then
        tmp = z * (x * y)
    else if (i <= 1.92d-208) then
        tmp = j * (a * c)
    else if (i <= 3d-26) then
        tmp = x * (y * z)
    else if (i <= 2.5d+198) then
        tmp = t * (b * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (y * -i);
	double tmp;
	if (i <= -5.8e+43) {
		tmp = t_1;
	} else if (i <= -9.5e-253) {
		tmp = c * (a * j);
	} else if (i <= -8.4e-302) {
		tmp = z * (x * y);
	} else if (i <= 1.92e-208) {
		tmp = j * (a * c);
	} else if (i <= 3e-26) {
		tmp = x * (y * z);
	} else if (i <= 2.5e+198) {
		tmp = t * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (y * -i)
	tmp = 0
	if i <= -5.8e+43:
		tmp = t_1
	elif i <= -9.5e-253:
		tmp = c * (a * j)
	elif i <= -8.4e-302:
		tmp = z * (x * y)
	elif i <= 1.92e-208:
		tmp = j * (a * c)
	elif i <= 3e-26:
		tmp = x * (y * z)
	elif i <= 2.5e+198:
		tmp = t * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(y * Float64(-i)))
	tmp = 0.0
	if (i <= -5.8e+43)
		tmp = t_1;
	elseif (i <= -9.5e-253)
		tmp = Float64(c * Float64(a * j));
	elseif (i <= -8.4e-302)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 1.92e-208)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 3e-26)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 2.5e+198)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (y * -i);
	tmp = 0.0;
	if (i <= -5.8e+43)
		tmp = t_1;
	elseif (i <= -9.5e-253)
		tmp = c * (a * j);
	elseif (i <= -8.4e-302)
		tmp = z * (x * y);
	elseif (i <= 1.92e-208)
		tmp = j * (a * c);
	elseif (i <= 3e-26)
		tmp = x * (y * z);
	elseif (i <= 2.5e+198)
		tmp = t * (b * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.8e+43], t$95$1, If[LessEqual[i, -9.5e-253], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -8.4e-302], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.92e-208], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3e-26], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.5e+198], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -5.8000000000000004e43 or 2.50000000000000024e198 < i

   1. Initial program 61.1%

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

   3. Taylor expanded in j around inf 61.7%

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

      1. *-commutative 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in c around 0 56.7%

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

      1. mul-1-neg 56.7%

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

   8. Simplified 56.7%

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

   if -5.8000000000000004e43 < i < -9.5e-253

   1. Initial program 78.0%

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

   3. Taylor expanded in i around 0 71.6%

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

   4. Taylor expanded in j around inf 30.4%

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

      1. associate-*r* 33.4%

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

      2. *-commutative 33.4%

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

      3. associate-*r* 36.4%

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

   6. Simplified 36.4%

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

   if -9.5e-253 < i < -8.40000000000000052e-302

   1. Initial program 86.8%

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

   3. Taylor expanded in z around inf 61.0%

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

      1. *-commutative 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in y around inf 48.7%

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

      1. *-commutative 48.7%

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

   8. Simplified 48.7%

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

   if -8.40000000000000052e-302 < i < 1.9200000000000001e-208

   1. Initial program 73.9%

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

   3. Taylor expanded in j around inf 53.1%

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

      1. *-commutative 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in c around inf 42.4%

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

      1. *-commutative 42.4%

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

   8. Simplified 42.4%

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

   if 1.9200000000000001e-208 < i < 3.00000000000000012e-26

   1. Initial program 83.7%

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

   3. Taylor expanded in i around 0 70.3%

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

   4. Taylor expanded in y around inf 31.1%

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

   if 3.00000000000000012e-26 < i < 2.50000000000000024e198

   1. Initial program 73.2%

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

   3. Taylor expanded in y around 0 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in i around inf 57.6%

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

   7. Taylor expanded in a around 0 38.9%

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

      1. *-commutative 38.9%

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

      2. *-commutative 38.9%

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

      3. associate-*r* 42.4%

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

   9. Simplified 42.4%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.8 \cdot 10^{+43}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -9.5 \cdot 10^{-253}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq -8.4 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.92 \cdot 10^{-208}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+198}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 58.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+99}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 0.0072:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* a (- (* c j) (* x t))) (* b (* t i))))
        (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -3.8e+99)
     t_2
     (if (<= y -8e-222)
       t_1
       (if (<= y -1.7e-304)
         (* c (- (* a j) (* z b)))
         (if (<= y 0.0072) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (a * ((c * j) - (x * t))) + (b * (t * i));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -3.8e+99) {
		tmp = t_2;
	} else if (y <= -8e-222) {
		tmp = t_1;
	} else if (y <= -1.7e-304) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 0.0072) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * ((c * j) - (x * t))) + (b * (t * i))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-3.8d+99)) then
        tmp = t_2
    else if (y <= (-8d-222)) then
        tmp = t_1
    else if (y <= (-1.7d-304)) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= 0.0072d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (a * ((c * j) - (x * t))) + (b * (t * i));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -3.8e+99) {
		tmp = t_2;
	} else if (y <= -8e-222) {
		tmp = t_1;
	} else if (y <= -1.7e-304) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 0.0072) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (a * ((c * j) - (x * t))) + (b * (t * i))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -3.8e+99:
		tmp = t_2
	elif y <= -8e-222:
		tmp = t_1
	elif y <= -1.7e-304:
		tmp = c * ((a * j) - (z * b))
	elif y <= 0.0072:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(t * i)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -3.8e+99)
		tmp = t_2;
	elseif (y <= -8e-222)
		tmp = t_1;
	elseif (y <= -1.7e-304)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= 0.0072)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (a * ((c * j) - (x * t))) + (b * (t * i));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -3.8e+99)
		tmp = t_2;
	elseif (y <= -8e-222)
		tmp = t_1;
	elseif (y <= -1.7e-304)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= 0.0072)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+99], t$95$2, If[LessEqual[y, -8e-222], t$95$1, If[LessEqual[y, -1.7e-304], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0072], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8e99 or 0.0071999999999999998 < y

   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 y around inf 76.1%

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

      1. +-commutative 76.1%

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

      2. mul-1-neg 76.1%

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

      3. unsub-neg 76.1%

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

      4. *-commutative 76.1%

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

   5. Simplified 76.1%

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

   if -3.8e99 < y < -8.00000000000000038e-222 or -1.6999999999999999e-304 < y < 0.0071999999999999998

   1. Initial program 79.6%

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

   3. Taylor expanded in y around 0 66.2%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in i around inf 58.6%

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

   if -8.00000000000000038e-222 < y < -1.6999999999999999e-304

   1. Initial program 64.2%

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

   3. Taylor expanded in c around inf 74.7%

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

      1. *-commutative 74.7%

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

   5. Simplified 74.7%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-222}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 0.0072:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 63.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+114} \lor \neg \left(b \leq -3.4 \cdot 10^{-119}\right) \land b \leq 4.9 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.2e+114) (and (not (<= b -3.4e-119)) (<= b 4.9e-55)))
   (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
   (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.2e+114) || (!(b <= -3.4e-119) && (b <= 4.9e-55))) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.2d+114)) .or. (.not. (b <= (-3.4d-119))) .and. (b <= 4.9d-55)) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.2e+114) || (!(b <= -3.4e-119) && (b <= 4.9e-55))) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.2e+114) or (not (b <= -3.4e-119) and (b <= 4.9e-55)):
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.2e+114) || (!(b <= -3.4e-119) && (b <= 4.9e-55)))
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.2e+114) || (~((b <= -3.4e-119)) && (b <= 4.9e-55)))
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.2e+114], And[N[Not[LessEqual[b, -3.4e-119]], $MachinePrecision], LessEqual[b, 4.9e-55]]], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.2e114 or -3.40000000000000024e-119 < b < 4.90000000000000035e-55

   1. Initial program 78.2%

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

   3. Taylor expanded in b around 0 77.4%

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

   if -1.2e114 < b < -3.40000000000000024e-119 or 4.90000000000000035e-55 < b

   1. Initial program 69.1%

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

   3. Taylor expanded in y around 0 63.8%

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

   5. Simplified 64.6%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+114} \lor \neg \left(b \leq -3.4 \cdot 10^{-119}\right) \land b \leq 4.9 \cdot 10^{-55}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 44.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;i \leq -3.15 \cdot 10^{-35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 9.2 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= i -3.15e-35)
     t_2
     (if (<= i -8.5e-166)
       t_1
       (if (<= i 9.2e-253)
         (* a (- (* c j) (* x t)))
         (if (<= i 1.15e+88) 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 = c * ((a * j) - (z * b));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (i <= -3.15e-35) {
		tmp = t_2;
	} else if (i <= -8.5e-166) {
		tmp = t_1;
	} else if (i <= 9.2e-253) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.15e+88) {
		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 = c * ((a * j) - (z * b))
    t_2 = j * ((a * c) - (y * i))
    if (i <= (-3.15d-35)) then
        tmp = t_2
    else if (i <= (-8.5d-166)) then
        tmp = t_1
    else if (i <= 9.2d-253) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 1.15d+88) 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 = c * ((a * j) - (z * b));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (i <= -3.15e-35) {
		tmp = t_2;
	} else if (i <= -8.5e-166) {
		tmp = t_1;
	} else if (i <= 9.2e-253) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.15e+88) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if i <= -3.15e-35:
		tmp = t_2
	elif i <= -8.5e-166:
		tmp = t_1
	elif i <= 9.2e-253:
		tmp = a * ((c * j) - (x * t))
	elif i <= 1.15e+88:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (i <= -3.15e-35)
		tmp = t_2;
	elseif (i <= -8.5e-166)
		tmp = t_1;
	elseif (i <= 9.2e-253)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 1.15e+88)
		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 = c * ((a * j) - (z * b));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (i <= -3.15e-35)
		tmp = t_2;
	elseif (i <= -8.5e-166)
		tmp = t_1;
	elseif (i <= 9.2e-253)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 1.15e+88)
		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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.15e-35], t$95$2, If[LessEqual[i, -8.5e-166], t$95$1, If[LessEqual[i, 9.2e-253], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.15e+88], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.15000000000000023e-35 or 1.1500000000000001e88 < i

   1. Initial program 66.5%

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

   3. Taylor expanded in j around inf 54.4%

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

      1. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   if -3.15000000000000023e-35 < i < -8.5e-166 or 9.2000000000000001e-253 < i < 1.1500000000000001e88

   1. Initial program 75.0%

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

   3. Taylor expanded in c around inf 49.5%

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

      1. *-commutative 49.5%

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

   5. Simplified 49.5%

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

   if -8.5e-166 < i < 9.2000000000000001e-253

   1. Initial program 87.2%

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

   3. Taylor expanded in a around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

   5. Simplified 67.8%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.15 \cdot 10^{-35}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{-166}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 9.2 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{+88}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 41.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+136}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+197} \lor \neg \left(y \leq 6 \cdot 10^{+242}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* y (- i)))))
   (if (<= y -6.8e+99)
     t_1
     (if (<= y 1.2e+136)
       (* a (- (* c j) (* x t)))
       (if (or (<= y 1.45e+197) (not (<= y 6e+242))) t_1 (* z (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (y * -i);
	double tmp;
	if (y <= -6.8e+99) {
		tmp = t_1;
	} else if (y <= 1.2e+136) {
		tmp = a * ((c * j) - (x * t));
	} else if ((y <= 1.45e+197) || !(y <= 6e+242)) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (y * -i)
    if (y <= (-6.8d+99)) then
        tmp = t_1
    else if (y <= 1.2d+136) then
        tmp = a * ((c * j) - (x * t))
    else if ((y <= 1.45d+197) .or. (.not. (y <= 6d+242))) then
        tmp = t_1
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (y * -i);
	double tmp;
	if (y <= -6.8e+99) {
		tmp = t_1;
	} else if (y <= 1.2e+136) {
		tmp = a * ((c * j) - (x * t));
	} else if ((y <= 1.45e+197) || !(y <= 6e+242)) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (y * -i)
	tmp = 0
	if y <= -6.8e+99:
		tmp = t_1
	elif y <= 1.2e+136:
		tmp = a * ((c * j) - (x * t))
	elif (y <= 1.45e+197) or not (y <= 6e+242):
		tmp = t_1
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(y * Float64(-i)))
	tmp = 0.0
	if (y <= -6.8e+99)
		tmp = t_1;
	elseif (y <= 1.2e+136)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif ((y <= 1.45e+197) || !(y <= 6e+242))
		tmp = t_1;
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (y * -i);
	tmp = 0.0;
	if (y <= -6.8e+99)
		tmp = t_1;
	elseif (y <= 1.2e+136)
		tmp = a * ((c * j) - (x * t));
	elseif ((y <= 1.45e+197) || ~((y <= 6e+242)))
		tmp = t_1;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e+99], t$95$1, If[LessEqual[y, 1.2e+136], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.45e+197], N[Not[LessEqual[y, 6e+242]], $MachinePrecision]], t$95$1, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.79999999999999968e99 or 1.2e136 < y < 1.45000000000000001e197 or 6.0000000000000001e242 < y

   1. Initial program 64.0%

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

   3. Taylor expanded in j around inf 61.7%

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

      1. *-commutative 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in c around 0 57.4%

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

      1. mul-1-neg 57.4%

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

   8. Simplified 57.4%

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

   if -6.79999999999999968e99 < y < 1.2e136

   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 a around inf 46.1%

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

      1. +-commutative 46.1%

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

      2. mul-1-neg 46.1%

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

      3. unsub-neg 46.1%

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

   5. Simplified 46.1%

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

   if 1.45000000000000001e197 < y < 6.0000000000000001e242

   1. Initial program 60.6%

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

   3. Taylor expanded in z around inf 75.4%

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

      1. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in y around inf 75.4%

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

      1. *-commutative 75.4%

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

   8. Simplified 75.4%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+99}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+136}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+197} \lor \neg \left(y \leq 6 \cdot 10^{+242}\right):\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-237}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{+21}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -8.5e-50)
   (* a (* c j))
   (if (<= c 7.6e-293)
     (* x (* y z))
     (if (<= c 4.2e-237)
       (* b (* t i))
       (if (<= c 4.4e+21) (* z (* x y)) (* j (* a c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -8.5e-50) {
		tmp = a * (c * j);
	} else if (c <= 7.6e-293) {
		tmp = x * (y * z);
	} else if (c <= 4.2e-237) {
		tmp = b * (t * i);
	} else if (c <= 4.4e+21) {
		tmp = z * (x * y);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-8.5d-50)) then
        tmp = a * (c * j)
    else if (c <= 7.6d-293) then
        tmp = x * (y * z)
    else if (c <= 4.2d-237) then
        tmp = b * (t * i)
    else if (c <= 4.4d+21) then
        tmp = z * (x * y)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -8.5e-50) {
		tmp = a * (c * j);
	} else if (c <= 7.6e-293) {
		tmp = x * (y * z);
	} else if (c <= 4.2e-237) {
		tmp = b * (t * i);
	} else if (c <= 4.4e+21) {
		tmp = z * (x * y);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -8.5e-50:
		tmp = a * (c * j)
	elif c <= 7.6e-293:
		tmp = x * (y * z)
	elif c <= 4.2e-237:
		tmp = b * (t * i)
	elif c <= 4.4e+21:
		tmp = z * (x * y)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -8.5e-50)
		tmp = Float64(a * Float64(c * j));
	elseif (c <= 7.6e-293)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 4.2e-237)
		tmp = Float64(b * Float64(t * i));
	elseif (c <= 4.4e+21)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -8.5e-50)
		tmp = a * (c * j);
	elseif (c <= 7.6e-293)
		tmp = x * (y * z);
	elseif (c <= 4.2e-237)
		tmp = b * (t * i);
	elseif (c <= 4.4e+21)
		tmp = z * (x * y);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -8.5e-50], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.6e-293], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.2e-237], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.4e+21], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -8.50000000000000012e-50

   1. Initial program 66.5%

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

   3. Taylor expanded in a around inf 40.9%

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

      1. +-commutative 40.9%

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

      2. mul-1-neg 40.9%

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

      3. unsub-neg 40.9%

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

   5. Simplified 40.9%

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

   6. Taylor expanded in c around inf 36.5%

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

   if -8.50000000000000012e-50 < c < 7.6e-293

   1. Initial program 80.5%

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

   3. Taylor expanded in i around 0 65.2%

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

   4. Taylor expanded in y around inf 31.4%

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

   if 7.6e-293 < c < 4.2000000000000002e-237

   1. Initial program 81.7%

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

   3. Taylor expanded in y around 0 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in i around inf 53.6%

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

   7. Taylor expanded in a around 0 53.6%

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

      1. *-commutative 53.6%

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

   9. Simplified 53.6%

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

   if 4.2000000000000002e-237 < c < 4.4e21

   1. Initial program 85.8%

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

   3. Taylor expanded in z around inf 39.1%

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

      1. *-commutative 39.1%

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

   5. Simplified 39.1%

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

   6. Taylor expanded in y around inf 36.0%

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

      1. *-commutative 36.0%

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

   8. Simplified 36.0%

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

   if 4.4e21 < c

   1. Initial program 63.3%

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

   3. Taylor expanded in j around inf 52.5%

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

      1. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in c around inf 44.5%

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

      1. *-commutative 44.5%

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

   8. Simplified 44.5%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-237}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{+21}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-131}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-33}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= z -9.8e+117)
     t_1
     (if (<= z -5.2e-131)
       (* j (* a c))
       (if (<= z 1.5e-33) (* b (* t i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -9.8e+117) {
		tmp = t_1;
	} else if (z <= -5.2e-131) {
		tmp = j * (a * c);
	} else if (z <= 1.5e-33) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (z <= (-9.8d+117)) then
        tmp = t_1
    else if (z <= (-5.2d-131)) then
        tmp = j * (a * c)
    else if (z <= 1.5d-33) then
        tmp = b * (t * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -9.8e+117) {
		tmp = t_1;
	} else if (z <= -5.2e-131) {
		tmp = j * (a * c);
	} else if (z <= 1.5e-33) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if z <= -9.8e+117:
		tmp = t_1
	elif z <= -5.2e-131:
		tmp = j * (a * c)
	elif z <= 1.5e-33:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -9.8e+117)
		tmp = t_1;
	elseif (z <= -5.2e-131)
		tmp = Float64(j * Float64(a * c));
	elseif (z <= 1.5e-33)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (z <= -9.8e+117)
		tmp = t_1;
	elseif (z <= -5.2e-131)
		tmp = j * (a * c);
	elseif (z <= 1.5e-33)
		tmp = b * (t * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.8e+117], t$95$1, If[LessEqual[z, -5.2e-131], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-33], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.8000000000000002e117 or 1.5000000000000001e-33 < z

   1. Initial program 63.8%

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

   3. Taylor expanded in i around 0 60.5%

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

   4. Taylor expanded in y around inf 35.0%

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

   if -9.8000000000000002e117 < z < -5.19999999999999993e-131

   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 j around inf 56.3%

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

      1. *-commutative 56.3%

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

   5. Simplified 56.3%

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

   6. Taylor expanded in c around inf 38.8%

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

      1. *-commutative 38.8%

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

   8. Simplified 38.8%

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

   if -5.19999999999999993e-131 < z < 1.5000000000000001e-33

   1. Initial program 85.0%

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

   3. Taylor expanded in y around 0 63.4%

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

   5. Simplified 63.4%

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

   6. Taylor expanded in i around inf 60.6%

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

   7. Taylor expanded in a around 0 33.2%

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

      1. *-commutative 33.2%

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

   9. Simplified 33.2%

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

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-131}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-33}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3 \cdot 10^{+64} \lor \neg \left(j \leq 6.8 \cdot 10^{+86}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -3e+64) (not (<= j 6.8e+86))) (* 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 ((j <= -3e+64) || !(j <= 6.8e+86)) {
		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 ((j <= (-3d+64)) .or. (.not. (j <= 6.8d+86))) 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 ((j <= -3e+64) || !(j <= 6.8e+86)) {
		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 (j <= -3e+64) or not (j <= 6.8e+86):
		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 ((j <= -3e+64) || !(j <= 6.8e+86))
		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 ((j <= -3e+64) || ~((j <= 6.8e+86)))
		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[j, -3e+64], N[Not[LessEqual[j, 6.8e+86]], $MachinePrecision]], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -3.0000000000000002e64 or 6.7999999999999995e86 < j

   1. Initial program 67.3%

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

   3. Taylor expanded in i around 0 50.1%

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

   4. Taylor expanded in j around inf 41.6%

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

      1. associate-*r* 41.6%

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

      2. *-commutative 41.6%

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

      3. associate-*r* 45.1%

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

   6. Simplified 45.1%

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

   if -3.0000000000000002e64 < j < 6.7999999999999995e86

   1. Initial program 78.8%

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

   3. Taylor expanded in y around 0 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in i around inf 47.2%

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

   7. Taylor expanded in a around 0 26.9%

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

      1. *-commutative 26.9%

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

   9. Simplified 26.9%

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

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3 \cdot 10^{+64} \lor \neg \left(j \leq 6.8 \cdot 10^{+86}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+64} \lor \neg \left(j \leq 1.2 \cdot 10^{+93}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -4e+64) (not (<= j 1.2e+93))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -4e+64) || !(j <= 1.2e+93)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-4d+64)) .or. (.not. (j <= 1.2d+93))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -4e+64) || !(j <= 1.2e+93)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -4e+64) or not (j <= 1.2e+93):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -4e+64) || !(j <= 1.2e+93))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -4e+64) || ~((j <= 1.2e+93)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -4e+64], N[Not[LessEqual[j, 1.2e+93]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -4.00000000000000009e64 or 1.20000000000000005e93 < j

   1. Initial program 67.3%

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

   3. Taylor expanded in a around inf 53.1%

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

      1. +-commutative 53.1%

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

      2. mul-1-neg 53.1%

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

      3. unsub-neg 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in c around inf 41.6%

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

   if -4.00000000000000009e64 < j < 1.20000000000000005e93

   1. Initial program 78.8%

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

   3. Taylor expanded in y around 0 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in i around inf 47.2%

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

   7. Taylor expanded in a around 0 26.9%

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

      1. *-commutative 26.9%

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

   9. Simplified 26.9%

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

4. Final simplification 33.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+64} \lor \neg \left(j \leq 1.2 \cdot 10^{+93}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{-83}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -8.5e-83)
   (* c (* a j))
   (if (<= c 1.6e+14) (* b (* t i)) (* j (* a c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -8.5e-83) {
		tmp = c * (a * j);
	} else if (c <= 1.6e+14) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-8.5d-83)) then
        tmp = c * (a * j)
    else if (c <= 1.6d+14) then
        tmp = b * (t * i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -8.5e-83) {
		tmp = c * (a * j);
	} else if (c <= 1.6e+14) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -8.5e-83:
		tmp = c * (a * j)
	elif c <= 1.6e+14:
		tmp = b * (t * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -8.5e-83)
		tmp = Float64(c * Float64(a * j));
	elseif (c <= 1.6e+14)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -8.5e-83)
		tmp = c * (a * j);
	elseif (c <= 1.6e+14)
		tmp = b * (t * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -8.5e-83], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.6e+14], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -8.49999999999999938e-83

   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 i around 0 55.5%

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

   4. Taylor expanded in j around inf 33.3%

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

      1. associate-*r* 30.8%

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

      2. *-commutative 30.8%

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

      3. associate-*r* 34.5%

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

   6. Simplified 34.5%

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

   if -8.49999999999999938e-83 < c < 1.6e14

   1. Initial program 84.6%

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

   3. Taylor expanded in y around 0 49.5%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in i around inf 44.3%

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

   7. Taylor expanded in a around 0 25.9%

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

      1. *-commutative 25.9%

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

   9. Simplified 25.9%

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

   if 1.6e14 < c

   1. Initial program 62.4%

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

   3. Taylor expanded in j around inf 51.7%

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

      1. *-commutative 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in c around inf 43.9%

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

      1. *-commutative 43.9%

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

   8. Simplified 43.9%

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

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{-83}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 22.0% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.0%

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

3. Taylor expanded in a around inf 39.1%

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

   1. +-commutative 39.1%

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

   2. mul-1-neg 39.1%

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

   3. unsub-neg 39.1%

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

5. Simplified 39.1%

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

6. Taylor expanded in c around inf 22.5%

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

Developer target: 59.1% 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 2024086 
(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)))))