Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.0% → 82.8%

Time: 23.0s

Alternatives: 30

Speedup: 0.5×

• 58.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

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) - (i * a)))) + (j * ((c * t) - (i * y)))
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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 74.0% accurate, 1.0× speedup

Math

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

FPCore

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

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

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) - (i * a)))) + (j * ((c * t) - (i * y)))
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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 82.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (t * j) * (c - (a * (x / j)))
	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(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(t * j) * Float64(c - Float64(a * Float64(x / j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (t * j) * (c - (a * (x / j)));
	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[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(t * j), $MachinePrecision] * N[(c - N[(a * N[(x / j), $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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 94.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in j around -inf 16.3%

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

   5. Simplified 16.3%

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

   6. Taylor expanded in t around inf 53.6%

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

      1. associate-*r* 53.5%

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

      2. mul-1-neg 53.5%

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

      3. unsub-neg 53.5%

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

      4. associate-/l* 55.6%

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

   8. Simplified 55.6%

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

4. Final simplification 87.0%

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

Alternative 2: 30.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_2 := a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{if}\;c \leq -1.66 \cdot 10^{+271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -4 \cdot 10^{+203}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.32 \cdot 10^{-272}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-202}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* b (- c)))) (t_2 (* a (* t (- x)))))
   (if (<= c -1.66e+271)
     t_1
     (if (<= c -4e+203)
       (* j (* t c))
       (if (<= c -8e+78)
         t_1
         (if (<= c -1.32e-272)
           t_2
           (if (<= c 1.25e-202)
             (* b (* a i))
             (if (<= c 1.1e-81)
               t_2
               (if (<= c 2.8e-56)
                 (* a (* b i))
                 (if (<= c 1.05e+90)
                   (* y (* i (- j)))
                   (* b (* z (- c)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (b * -c);
	double t_2 = a * (t * -x);
	double tmp;
	if (c <= -1.66e+271) {
		tmp = t_1;
	} else if (c <= -4e+203) {
		tmp = j * (t * c);
	} else if (c <= -8e+78) {
		tmp = t_1;
	} else if (c <= -1.32e-272) {
		tmp = t_2;
	} else if (c <= 1.25e-202) {
		tmp = b * (a * i);
	} else if (c <= 1.1e-81) {
		tmp = t_2;
	} else if (c <= 2.8e-56) {
		tmp = a * (b * i);
	} else if (c <= 1.05e+90) {
		tmp = y * (i * -j);
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (b * -c)
    t_2 = a * (t * -x)
    if (c <= (-1.66d+271)) then
        tmp = t_1
    else if (c <= (-4d+203)) then
        tmp = j * (t * c)
    else if (c <= (-8d+78)) then
        tmp = t_1
    else if (c <= (-1.32d-272)) then
        tmp = t_2
    else if (c <= 1.25d-202) then
        tmp = b * (a * i)
    else if (c <= 1.1d-81) then
        tmp = t_2
    else if (c <= 2.8d-56) then
        tmp = a * (b * i)
    else if (c <= 1.05d+90) then
        tmp = y * (i * -j)
    else
        tmp = b * (z * -c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (b * -c);
	double t_2 = a * (t * -x);
	double tmp;
	if (c <= -1.66e+271) {
		tmp = t_1;
	} else if (c <= -4e+203) {
		tmp = j * (t * c);
	} else if (c <= -8e+78) {
		tmp = t_1;
	} else if (c <= -1.32e-272) {
		tmp = t_2;
	} else if (c <= 1.25e-202) {
		tmp = b * (a * i);
	} else if (c <= 1.1e-81) {
		tmp = t_2;
	} else if (c <= 2.8e-56) {
		tmp = a * (b * i);
	} else if (c <= 1.05e+90) {
		tmp = y * (i * -j);
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (b * -c)
	t_2 = a * (t * -x)
	tmp = 0
	if c <= -1.66e+271:
		tmp = t_1
	elif c <= -4e+203:
		tmp = j * (t * c)
	elif c <= -8e+78:
		tmp = t_1
	elif c <= -1.32e-272:
		tmp = t_2
	elif c <= 1.25e-202:
		tmp = b * (a * i)
	elif c <= 1.1e-81:
		tmp = t_2
	elif c <= 2.8e-56:
		tmp = a * (b * i)
	elif c <= 1.05e+90:
		tmp = y * (i * -j)
	else:
		tmp = b * (z * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(b * Float64(-c)))
	t_2 = Float64(a * Float64(t * Float64(-x)))
	tmp = 0.0
	if (c <= -1.66e+271)
		tmp = t_1;
	elseif (c <= -4e+203)
		tmp = Float64(j * Float64(t * c));
	elseif (c <= -8e+78)
		tmp = t_1;
	elseif (c <= -1.32e-272)
		tmp = t_2;
	elseif (c <= 1.25e-202)
		tmp = Float64(b * Float64(a * i));
	elseif (c <= 1.1e-81)
		tmp = t_2;
	elseif (c <= 2.8e-56)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= 1.05e+90)
		tmp = Float64(y * Float64(i * Float64(-j)));
	else
		tmp = Float64(b * Float64(z * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (b * -c);
	t_2 = a * (t * -x);
	tmp = 0.0;
	if (c <= -1.66e+271)
		tmp = t_1;
	elseif (c <= -4e+203)
		tmp = j * (t * c);
	elseif (c <= -8e+78)
		tmp = t_1;
	elseif (c <= -1.32e-272)
		tmp = t_2;
	elseif (c <= 1.25e-202)
		tmp = b * (a * i);
	elseif (c <= 1.1e-81)
		tmp = t_2;
	elseif (c <= 2.8e-56)
		tmp = a * (b * i);
	elseif (c <= 1.05e+90)
		tmp = y * (i * -j);
	else
		tmp = b * (z * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.66e+271], t$95$1, If[LessEqual[c, -4e+203], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8e+78], t$95$1, If[LessEqual[c, -1.32e-272], t$95$2, If[LessEqual[c, 1.25e-202], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.1e-81], t$95$2, If[LessEqual[c, 2.8e-56], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.05e+90], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -1.66e271 or -4e203 < c < -8.00000000000000007e78

   1. Initial program 75.9%

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

   3. Taylor expanded in b around inf 57.6%

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

      1. *-commutative 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in c around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

      4. associate-/l* 60.0%

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

   8. Simplified 60.0%

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

   9. Taylor expanded in c around inf 44.9%

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

       1. mul-1-neg 44.9%

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

       2. associate-*r* 60.1%

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

       3. distribute-rgt-neg-in 60.1%

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

   11. Simplified 60.1%

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

   if -1.66e271 < c < -4e203

   1. Initial program 52.9%

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

   3. Taylor expanded in x around 0 52.9%

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

      1. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in j around inf 63.6%

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

   7. Taylor expanded in c around inf 58.6%

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

   if -8.00000000000000007e78 < c < -1.31999999999999996e-272 or 1.24999999999999993e-202 < c < 1.1e-81

   1. Initial program 84.8%

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

   3. Taylor expanded in z around 0 62.6%

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

   4. Taylor expanded in x around inf 38.8%

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

      1. *-commutative 38.8%

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

      2. neg-mul-1 38.8%

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

      3. distribute-rgt-neg-in 38.8%

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

      4. *-commutative 38.8%

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

      5. mul-1-neg 38.8%

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

      6. associate-*r* 38.8%

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

      7. mul-1-neg 38.8%

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

   6. Simplified 38.8%

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

   if -1.31999999999999996e-272 < c < 1.24999999999999993e-202

   1. Initial program 85.9%

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

   3. Taylor expanded in b around inf 58.9%

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

      1. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in i around inf 58.9%

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

   if 1.1e-81 < c < 2.79999999999999993e-56

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 75.7%

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

      1. *-commutative 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in i around inf 75.7%

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

   if 2.79999999999999993e-56 < c < 1.0499999999999999e90

   1. Initial program 72.6%

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

   3. Taylor expanded in y around inf 55.7%

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

      1. +-commutative 55.7%

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

      2. mul-1-neg 55.7%

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

      3. unsub-neg 55.7%

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

      4. *-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in z around 0 44.6%

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

      1. neg-mul-1 44.6%

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

      2. distribute-rgt-neg-in 44.6%

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

   8. Simplified 44.6%

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

   if 1.0499999999999999e90 < c

   1. Initial program 61.4%

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

   3. Taylor expanded in b around inf 46.3%

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

      1. *-commutative 46.3%

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

   5. Simplified 46.3%

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

   6. Taylor expanded in i around 0 48.8%

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

      1. associate-*r* 48.8%

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

      2. neg-mul-1 48.8%

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

   8. Simplified 48.8%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.66 \cdot 10^{+271}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{+203}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{+78}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -1.32 \cdot 10^{-272}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-202}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-81}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 29.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ t_2 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+241}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+201}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{+151}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-7}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-200}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-293}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))) (t_2 (* b (* z (- c)))))
   (if (<= a -5.2e+241)
     (* a (* b i))
     (if (<= a -9.2e+201)
       (* a (* t (- x)))
       (if (<= a -1.15e+151)
         (* b (* a i))
         (if (<= a -2.6e+57)
           t_1
           (if (<= a -3e-7)
             t_2
             (if (<= a -4.4e-200)
               (* c (* t j))
               (if (<= a -2.45e-293)
                 (* y (* x z))
                 (if (<= a 2.15e-36) t_2 t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double t_2 = b * (z * -c);
	double tmp;
	if (a <= -5.2e+241) {
		tmp = a * (b * i);
	} else if (a <= -9.2e+201) {
		tmp = a * (t * -x);
	} else if (a <= -1.15e+151) {
		tmp = b * (a * i);
	} else if (a <= -2.6e+57) {
		tmp = t_1;
	} else if (a <= -3e-7) {
		tmp = t_2;
	} else if (a <= -4.4e-200) {
		tmp = c * (t * j);
	} else if (a <= -2.45e-293) {
		tmp = y * (x * z);
	} else if (a <= 2.15e-36) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t * -a)
    t_2 = b * (z * -c)
    if (a <= (-5.2d+241)) then
        tmp = a * (b * i)
    else if (a <= (-9.2d+201)) then
        tmp = a * (t * -x)
    else if (a <= (-1.15d+151)) then
        tmp = b * (a * i)
    else if (a <= (-2.6d+57)) then
        tmp = t_1
    else if (a <= (-3d-7)) then
        tmp = t_2
    else if (a <= (-4.4d-200)) then
        tmp = c * (t * j)
    else if (a <= (-2.45d-293)) then
        tmp = y * (x * z)
    else if (a <= 2.15d-36) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double t_2 = b * (z * -c);
	double tmp;
	if (a <= -5.2e+241) {
		tmp = a * (b * i);
	} else if (a <= -9.2e+201) {
		tmp = a * (t * -x);
	} else if (a <= -1.15e+151) {
		tmp = b * (a * i);
	} else if (a <= -2.6e+57) {
		tmp = t_1;
	} else if (a <= -3e-7) {
		tmp = t_2;
	} else if (a <= -4.4e-200) {
		tmp = c * (t * j);
	} else if (a <= -2.45e-293) {
		tmp = y * (x * z);
	} else if (a <= 2.15e-36) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	t_2 = b * (z * -c)
	tmp = 0
	if a <= -5.2e+241:
		tmp = a * (b * i)
	elif a <= -9.2e+201:
		tmp = a * (t * -x)
	elif a <= -1.15e+151:
		tmp = b * (a * i)
	elif a <= -2.6e+57:
		tmp = t_1
	elif a <= -3e-7:
		tmp = t_2
	elif a <= -4.4e-200:
		tmp = c * (t * j)
	elif a <= -2.45e-293:
		tmp = y * (x * z)
	elif a <= 2.15e-36:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(t * Float64(-a)))
	t_2 = Float64(b * Float64(z * Float64(-c)))
	tmp = 0.0
	if (a <= -5.2e+241)
		tmp = Float64(a * Float64(b * i));
	elseif (a <= -9.2e+201)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (a <= -1.15e+151)
		tmp = Float64(b * Float64(a * i));
	elseif (a <= -2.6e+57)
		tmp = t_1;
	elseif (a <= -3e-7)
		tmp = t_2;
	elseif (a <= -4.4e-200)
		tmp = Float64(c * Float64(t * j));
	elseif (a <= -2.45e-293)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 2.15e-36)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (t * -a);
	t_2 = b * (z * -c);
	tmp = 0.0;
	if (a <= -5.2e+241)
		tmp = a * (b * i);
	elseif (a <= -9.2e+201)
		tmp = a * (t * -x);
	elseif (a <= -1.15e+151)
		tmp = b * (a * i);
	elseif (a <= -2.6e+57)
		tmp = t_1;
	elseif (a <= -3e-7)
		tmp = t_2;
	elseif (a <= -4.4e-200)
		tmp = c * (t * j);
	elseif (a <= -2.45e-293)
		tmp = y * (x * z);
	elseif (a <= 2.15e-36)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e+241], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.2e+201], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.15e+151], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.6e+57], t$95$1, If[LessEqual[a, -3e-7], t$95$2, If[LessEqual[a, -4.4e-200], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.45e-293], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.15e-36], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -5.20000000000000015e241

   1. Initial program 76.4%

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

   3. Taylor expanded in b around inf 59.4%

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

      1. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in i around inf 58.0%

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

   if -5.20000000000000015e241 < a < -9.2000000000000004e201

   1. Initial program 36.4%

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

   3. Taylor expanded in z around 0 72.7%

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

   4. Taylor expanded in x around inf 90.9%

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

      1. *-commutative 90.9%

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

      2. neg-mul-1 90.9%

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

      3. distribute-rgt-neg-in 90.9%

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

      4. *-commutative 90.9%

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

      5. mul-1-neg 90.9%

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

      6. associate-*r* 90.9%

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

      7. mul-1-neg 90.9%

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

   6. Simplified 90.9%

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

   if -9.2000000000000004e201 < a < -1.15e151

   1. Initial program 70.3%

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

   3. Taylor expanded in b around inf 63.4%

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

      1. *-commutative 63.4%

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

   5. Simplified 63.4%

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

   6. Taylor expanded in i around inf 52.0%

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

   if -1.15e151 < a < -2.6e57 or 2.1500000000000001e-36 < a

   1. Initial program 67.9%

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

   3. Taylor expanded in j around -inf 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in x around -inf 54.7%

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

      1. *-commutative 54.7%

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

   8. Simplified 54.7%

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

   9. Taylor expanded in z around 0 43.7%

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

       1. associate-*r* 43.7%

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

       2. neg-mul-1 43.7%

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

   11. Simplified 43.7%

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

   if -2.6e57 < a < -2.9999999999999999e-7 or -2.45e-293 < a < 2.1500000000000001e-36

   1. Initial program 89.8%

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

   3. Taylor expanded in b around inf 53.1%

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

      1. *-commutative 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in i around 0 43.7%

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

      1. associate-*r* 43.7%

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

      2. neg-mul-1 43.7%

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

   8. Simplified 43.7%

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

   if -2.9999999999999999e-7 < a < -4.40000000000000027e-200

   1. Initial program 91.4%

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

   3. Taylor expanded in x around 0 77.1%

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

      1. *-commutative 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in t around inf 39.9%

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

   if -4.40000000000000027e-200 < a < -2.45e-293

   1. Initial program 71.2%

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

   3. Taylor expanded in y around inf 90.2%

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

      1. +-commutative 90.2%

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

      2. mul-1-neg 90.2%

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

      3. unsub-neg 90.2%

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

      4. *-commutative 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in z around inf 71.8%

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

      1. *-commutative 71.8%

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

   8. Simplified 71.8%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+241}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+201}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{+151}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-200}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-293}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-36}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot j\right) \cdot \left(c - a \cdot \frac{x}{j}\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7.6 \cdot 10^{+134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -100:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-40}:\\ \;\;\;\;c \cdot \left(b \cdot \left(\frac{a \cdot i}{c} - z\right)\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-140}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \left(j \cdot \left(\frac{x \cdot z}{j} - i\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* t j) (- c (* a (/ x j))))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -7.6e+134)
     t_2
     (if (<= b -100.0)
       t_1
       (if (<= b -2.9e-40)
         (* c (* b (- (/ (* a i) c) z)))
         (if (<= b 5.6e-291)
           (* x (- (* y z) (* t a)))
           (if (<= b 8e-140)
             (* j (- (* t c) (* y i)))
             (if (<= b 3.4e-36)
               (* y (* j (- (/ (* x z) j) i)))
               (if (<= b 5.5e-7) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * j) * (c - (a * (x / j)));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7.6e+134) {
		tmp = t_2;
	} else if (b <= -100.0) {
		tmp = t_1;
	} else if (b <= -2.9e-40) {
		tmp = c * (b * (((a * i) / c) - z));
	} else if (b <= 5.6e-291) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 8e-140) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 3.4e-36) {
		tmp = y * (j * (((x * z) / j) - i));
	} else if (b <= 5.5e-7) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t * j) * (c - (a * (x / j)))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-7.6d+134)) then
        tmp = t_2
    else if (b <= (-100.0d0)) then
        tmp = t_1
    else if (b <= (-2.9d-40)) then
        tmp = c * (b * (((a * i) / c) - z))
    else if (b <= 5.6d-291) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 8d-140) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 3.4d-36) then
        tmp = y * (j * (((x * z) / j) - i))
    else if (b <= 5.5d-7) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * j) * (c - (a * (x / j)));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7.6e+134) {
		tmp = t_2;
	} else if (b <= -100.0) {
		tmp = t_1;
	} else if (b <= -2.9e-40) {
		tmp = c * (b * (((a * i) / c) - z));
	} else if (b <= 5.6e-291) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 8e-140) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 3.4e-36) {
		tmp = y * (j * (((x * z) / j) - i));
	} else if (b <= 5.5e-7) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * j) * (c - (a * (x / j)))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -7.6e+134:
		tmp = t_2
	elif b <= -100.0:
		tmp = t_1
	elif b <= -2.9e-40:
		tmp = c * (b * (((a * i) / c) - z))
	elif b <= 5.6e-291:
		tmp = x * ((y * z) - (t * a))
	elif b <= 8e-140:
		tmp = j * ((t * c) - (y * i))
	elif b <= 3.4e-36:
		tmp = y * (j * (((x * z) / j) - i))
	elif b <= 5.5e-7:
		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(t * j) * Float64(c - Float64(a * Float64(x / j))))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -7.6e+134)
		tmp = t_2;
	elseif (b <= -100.0)
		tmp = t_1;
	elseif (b <= -2.9e-40)
		tmp = Float64(c * Float64(b * Float64(Float64(Float64(a * i) / c) - z)));
	elseif (b <= 5.6e-291)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 8e-140)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 3.4e-36)
		tmp = Float64(y * Float64(j * Float64(Float64(Float64(x * z) / j) - i)));
	elseif (b <= 5.5e-7)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * j) * (c - (a * (x / j)));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -7.6e+134)
		tmp = t_2;
	elseif (b <= -100.0)
		tmp = t_1;
	elseif (b <= -2.9e-40)
		tmp = c * (b * (((a * i) / c) - z));
	elseif (b <= 5.6e-291)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 8e-140)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 3.4e-36)
		tmp = y * (j * (((x * z) / j) - i));
	elseif (b <= 5.5e-7)
		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[(t * j), $MachinePrecision] * N[(c - N[(a * N[(x / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.6e+134], t$95$2, If[LessEqual[b, -100.0], t$95$1, If[LessEqual[b, -2.9e-40], N[(c * N[(b * N[(N[(N[(a * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e-291], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e-140], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e-36], N[(y * N[(j * N[(N[(N[(x * z), $MachinePrecision] / j), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e-7], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -7.59999999999999997e134 or 5.5000000000000003e-7 < b

   1. Initial program 79.0%

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

   3. Taylor expanded in b around inf 72.7%

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

      1. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   if -7.59999999999999997e134 < b < -100 or 3.4000000000000003e-36 < b < 5.5000000000000003e-7

   1. Initial program 81.0%

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

   3. Taylor expanded in j around -inf 72.6%

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

   5. Simplified 72.6%

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

   6. Taylor expanded in t around inf 58.0%

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

      1. associate-*r* 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

      4. associate-/l* 64.2%

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

   8. Simplified 64.2%

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

   if -100 < b < -2.8999999999999999e-40

   1. Initial program 64.8%

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

   3. Taylor expanded in b around inf 59.3%

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

      1. *-commutative 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in c around inf 72.5%

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

      1. +-commutative 72.5%

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

      2. mul-1-neg 72.5%

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

      3. unsub-neg 72.5%

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

      4. associate-/l* 58.6%

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

   8. Simplified 58.6%

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

   9. Taylor expanded in b around 0 72.4%

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

   if -2.8999999999999999e-40 < b < 5.5999999999999999e-291

   1. Initial program 74.0%

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

   3. Taylor expanded in x around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   if 5.5999999999999999e-291 < b < 7.9999999999999999e-140

   1. Initial program 87.4%

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

   3. Taylor expanded in x around 0 56.9%

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

      1. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in j around inf 63.3%

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

   if 7.9999999999999999e-140 < b < 3.4000000000000003e-36

   1. Initial program 47.6%

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

   3. Taylor expanded in y around inf 59.9%

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

      1. +-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

      4. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in j around inf 65.9%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+134}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -100:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(c - a \cdot \frac{x}{j}\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-40}:\\ \;\;\;\;c \cdot \left(b \cdot \left(\frac{a \cdot i}{c} - z\right)\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-140}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \left(j \cdot \left(\frac{x \cdot z}{j} - i\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-7}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(c - a \cdot \frac{x}{j}\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.5 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.55 \cdot 10^{-214}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(a \cdot \frac{b}{j} - y\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-176}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+87}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -3.5e+61)
     t_2
     (if (<= c 1.55e-262)
       t_1
       (if (<= c 3.55e-214)
         (* (* i j) (- (* a (/ b j)) y))
         (if (<= c 6.8e-176)
           (* t (- (* c j) (* x a)))
           (if (<= c 4.6e-144)
             (* y (- (* x z) (* i j)))
             (if (<= c 5.5e-60)
               t_1
               (if (<= c 6.2e+87) (* j (- (* t c) (* y i))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.5e+61) {
		tmp = t_2;
	} else if (c <= 1.55e-262) {
		tmp = t_1;
	} else if (c <= 3.55e-214) {
		tmp = (i * j) * ((a * (b / j)) - y);
	} else if (c <= 6.8e-176) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 4.6e-144) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 5.5e-60) {
		tmp = t_1;
	} else if (c <= 6.2e+87) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-3.5d+61)) then
        tmp = t_2
    else if (c <= 1.55d-262) then
        tmp = t_1
    else if (c <= 3.55d-214) then
        tmp = (i * j) * ((a * (b / j)) - y)
    else if (c <= 6.8d-176) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= 4.6d-144) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 5.5d-60) then
        tmp = t_1
    else if (c <= 6.2d+87) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.5e+61) {
		tmp = t_2;
	} else if (c <= 1.55e-262) {
		tmp = t_1;
	} else if (c <= 3.55e-214) {
		tmp = (i * j) * ((a * (b / j)) - y);
	} else if (c <= 6.8e-176) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 4.6e-144) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 5.5e-60) {
		tmp = t_1;
	} else if (c <= 6.2e+87) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3.5e+61:
		tmp = t_2
	elif c <= 1.55e-262:
		tmp = t_1
	elif c <= 3.55e-214:
		tmp = (i * j) * ((a * (b / j)) - y)
	elif c <= 6.8e-176:
		tmp = t * ((c * j) - (x * a))
	elif c <= 4.6e-144:
		tmp = y * ((x * z) - (i * j))
	elif c <= 5.5e-60:
		tmp = t_1
	elif c <= 6.2e+87:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.5e+61)
		tmp = t_2;
	elseif (c <= 1.55e-262)
		tmp = t_1;
	elseif (c <= 3.55e-214)
		tmp = Float64(Float64(i * j) * Float64(Float64(a * Float64(b / j)) - y));
	elseif (c <= 6.8e-176)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= 4.6e-144)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 5.5e-60)
		tmp = t_1;
	elseif (c <= 6.2e+87)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.5e+61)
		tmp = t_2;
	elseif (c <= 1.55e-262)
		tmp = t_1;
	elseif (c <= 3.55e-214)
		tmp = (i * j) * ((a * (b / j)) - y);
	elseif (c <= 6.8e-176)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= 4.6e-144)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 5.5e-60)
		tmp = t_1;
	elseif (c <= 6.2e+87)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.5e+61], t$95$2, If[LessEqual[c, 1.55e-262], t$95$1, If[LessEqual[c, 3.55e-214], N[(N[(i * j), $MachinePrecision] * N[(N[(a * N[(b / j), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.8e-176], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.6e-144], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.5e-60], t$95$1, If[LessEqual[c, 6.2e+87], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -3.50000000000000018e61 or 6.1999999999999999e87 < c

   1. Initial program 66.2%

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

   3. Taylor expanded in c around inf 70.3%

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

   if -3.50000000000000018e61 < c < 1.5499999999999999e-262 or 4.6e-144 < c < 5.4999999999999997e-60

   1. Initial program 83.8%

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

   3. Taylor expanded in a around inf 62.6%

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

      1. distribute-lft-out-- 62.6%

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

      2. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   if 1.5499999999999999e-262 < c < 3.55000000000000005e-214

   1. Initial program 99.8%

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

   3. Taylor expanded in j around -inf 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in i around -inf 64.0%

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

      1. associate-*r* 73.6%

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

      2. +-commutative 73.6%

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

      3. mul-1-neg 73.6%

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

      4. unsub-neg 73.6%

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

      5. associate-/l* 86.2%

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

   8. Simplified 86.2%

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

   if 3.55000000000000005e-214 < c < 6.7999999999999994e-176

   1. Initial program 56.0%

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

   3. Taylor expanded in t around inf 78.0%

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

      1. +-commutative 78.0%

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

      2. mul-1-neg 78.0%

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

      3. unsub-neg 78.0%

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

      4. *-commutative 78.0%

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

   5. Simplified 78.0%

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

   if 6.7999999999999994e-176 < c < 4.6e-144

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 74.0%

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

      1. +-commutative 74.0%

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

      2. mul-1-neg 74.0%

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

      3. unsub-neg 74.0%

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

      4. *-commutative 74.0%

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

   5. Simplified 74.0%

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

   if 5.4999999999999997e-60 < c < 6.1999999999999999e87

   1. Initial program 76.4%

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

   3. Taylor expanded in x around 0 63.9%

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

      1. *-commutative 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in j around inf 56.2%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{+61}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-262}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3.55 \cdot 10^{-214}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(a \cdot \frac{b}{j} - y\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-176}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+87}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7.6 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{+91}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(a \cdot \frac{x}{-j}\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -20:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -7.6e+134)
     t_1
     (if (<= b -1.9e+91)
       (* (* t j) (* a (/ x (- j))))
       (if (<= b -3.5e+42)
         t_1
         (if (<= b -20.0)
           (* t (- (* c j) (* x a)))
           (if (<= b -5.4e-47)
             t_1
             (if (<= b 5.5e-291)
               (* x (- (* y z) (* t a)))
               (if (<= b 2.1e-9) (* j (- (* t c) (* y 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7.6e+134) {
		tmp = t_1;
	} else if (b <= -1.9e+91) {
		tmp = (t * j) * (a * (x / -j));
	} else if (b <= -3.5e+42) {
		tmp = t_1;
	} else if (b <= -20.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= -5.4e-47) {
		tmp = t_1;
	} else if (b <= 5.5e-291) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 2.1e-9) {
		tmp = j * ((t * c) - (y * 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 = b * ((a * i) - (z * c))
    if (b <= (-7.6d+134)) then
        tmp = t_1
    else if (b <= (-1.9d+91)) then
        tmp = (t * j) * (a * (x / -j))
    else if (b <= (-3.5d+42)) then
        tmp = t_1
    else if (b <= (-20.0d0)) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= (-5.4d-47)) then
        tmp = t_1
    else if (b <= 5.5d-291) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 2.1d-9) then
        tmp = j * ((t * c) - (y * 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7.6e+134) {
		tmp = t_1;
	} else if (b <= -1.9e+91) {
		tmp = (t * j) * (a * (x / -j));
	} else if (b <= -3.5e+42) {
		tmp = t_1;
	} else if (b <= -20.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= -5.4e-47) {
		tmp = t_1;
	} else if (b <= 5.5e-291) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 2.1e-9) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -7.6e+134:
		tmp = t_1
	elif b <= -1.9e+91:
		tmp = (t * j) * (a * (x / -j))
	elif b <= -3.5e+42:
		tmp = t_1
	elif b <= -20.0:
		tmp = t * ((c * j) - (x * a))
	elif b <= -5.4e-47:
		tmp = t_1
	elif b <= 5.5e-291:
		tmp = x * ((y * z) - (t * a))
	elif b <= 2.1e-9:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -7.6e+134)
		tmp = t_1;
	elseif (b <= -1.9e+91)
		tmp = Float64(Float64(t * j) * Float64(a * Float64(x / Float64(-j))));
	elseif (b <= -3.5e+42)
		tmp = t_1;
	elseif (b <= -20.0)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= -5.4e-47)
		tmp = t_1;
	elseif (b <= 5.5e-291)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 2.1e-9)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * 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 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -7.6e+134)
		tmp = t_1;
	elseif (b <= -1.9e+91)
		tmp = (t * j) * (a * (x / -j));
	elseif (b <= -3.5e+42)
		tmp = t_1;
	elseif (b <= -20.0)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= -5.4e-47)
		tmp = t_1;
	elseif (b <= 5.5e-291)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 2.1e-9)
		tmp = j * ((t * c) - (y * 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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.6e+134], t$95$1, If[LessEqual[b, -1.9e+91], N[(N[(t * j), $MachinePrecision] * N[(a * N[(x / (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.5e+42], t$95$1, If[LessEqual[b, -20.0], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.4e-47], t$95$1, If[LessEqual[b, 5.5e-291], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-9], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -7.59999999999999997e134 or -1.8999999999999999e91 < b < -3.50000000000000023e42 or -20 < b < -5.3999999999999996e-47 or 2.10000000000000019e-9 < b

   1. Initial program 78.1%

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

   3. Taylor expanded in b around inf 71.6%

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

      1. *-commutative 71.6%

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

   5. Simplified 71.6%

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

   if -7.59999999999999997e134 < b < -1.8999999999999999e91

   1. Initial program 74.8%

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

   3. Taylor expanded in j around -inf 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in t around inf 65.6%

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

      1. associate-*r* 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

      4. associate-/l* 65.7%

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

   8. Simplified 65.7%

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

   9. Taylor expanded in c around 0 65.8%

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

       1. mul-1-neg 65.8%

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

       2. distribute-frac-neg2 65.8%

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

       3. associate-*r/ 65.9%

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

   11. Simplified 65.9%

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

   if -3.50000000000000023e42 < b < -20

   1. Initial program 81.7%

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

   3. Taylor expanded in t around inf 81.9%

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

      1. +-commutative 81.9%

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

      2. mul-1-neg 81.9%

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

      3. unsub-neg 81.9%

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

      4. *-commutative 81.9%

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

   5. Simplified 81.9%

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

   if -5.3999999999999996e-47 < b < 5.5000000000000002e-291

   1. Initial program 73.1%

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

   3. Taylor expanded in x around inf 65.3%

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

      1. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   if 5.5000000000000002e-291 < b < 2.10000000000000019e-9

   1. Initial program 74.6%

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

   3. Taylor expanded in x around 0 52.4%

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

      1. *-commutative 52.4%

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

   5. Simplified 52.4%

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

   6. Taylor expanded in j around inf 56.1%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+134}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{+91}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(a \cdot \frac{x}{-j}\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -20:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-47}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{+136}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{+44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -370:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-10}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -2.7e+136)
     t_2
     (if (<= b -4e+83)
       t_1
       (if (<= b -6.8e+44)
         t_2
         (if (<= b -370.0)
           t_1
           (if (<= b -2.6e-45)
             t_2
             (if (<= b 4.8e-291)
               (* x (- (* y z) (* t a)))
               (if (<= b 1.25e-10) (* j (- (* t c) (* y i))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.7e+136) {
		tmp = t_2;
	} else if (b <= -4e+83) {
		tmp = t_1;
	} else if (b <= -6.8e+44) {
		tmp = t_2;
	} else if (b <= -370.0) {
		tmp = t_1;
	} else if (b <= -2.6e-45) {
		tmp = t_2;
	} else if (b <= 4.8e-291) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 1.25e-10) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-2.7d+136)) then
        tmp = t_2
    else if (b <= (-4d+83)) then
        tmp = t_1
    else if (b <= (-6.8d+44)) then
        tmp = t_2
    else if (b <= (-370.0d0)) then
        tmp = t_1
    else if (b <= (-2.6d-45)) then
        tmp = t_2
    else if (b <= 4.8d-291) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 1.25d-10) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.7e+136) {
		tmp = t_2;
	} else if (b <= -4e+83) {
		tmp = t_1;
	} else if (b <= -6.8e+44) {
		tmp = t_2;
	} else if (b <= -370.0) {
		tmp = t_1;
	} else if (b <= -2.6e-45) {
		tmp = t_2;
	} else if (b <= 4.8e-291) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 1.25e-10) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -2.7e+136:
		tmp = t_2
	elif b <= -4e+83:
		tmp = t_1
	elif b <= -6.8e+44:
		tmp = t_2
	elif b <= -370.0:
		tmp = t_1
	elif b <= -2.6e-45:
		tmp = t_2
	elif b <= 4.8e-291:
		tmp = x * ((y * z) - (t * a))
	elif b <= 1.25e-10:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.7e+136)
		tmp = t_2;
	elseif (b <= -4e+83)
		tmp = t_1;
	elseif (b <= -6.8e+44)
		tmp = t_2;
	elseif (b <= -370.0)
		tmp = t_1;
	elseif (b <= -2.6e-45)
		tmp = t_2;
	elseif (b <= 4.8e-291)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 1.25e-10)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.7e+136)
		tmp = t_2;
	elseif (b <= -4e+83)
		tmp = t_1;
	elseif (b <= -6.8e+44)
		tmp = t_2;
	elseif (b <= -370.0)
		tmp = t_1;
	elseif (b <= -2.6e-45)
		tmp = t_2;
	elseif (b <= 4.8e-291)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 1.25e-10)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.7e+136], t$95$2, If[LessEqual[b, -4e+83], t$95$1, If[LessEqual[b, -6.8e+44], t$95$2, If[LessEqual[b, -370.0], t$95$1, If[LessEqual[b, -2.6e-45], t$95$2, If[LessEqual[b, 4.8e-291], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e-10], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.7000000000000002e136 or -4.00000000000000012e83 < b < -6.8e44 or -370 < b < -2.59999999999999987e-45 or 1.25000000000000008e-10 < b

   1. Initial program 78.1%

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

   3. Taylor expanded in b around inf 71.6%

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

      1. *-commutative 71.6%

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

   5. Simplified 71.6%

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

   if -2.7000000000000002e136 < b < -4.00000000000000012e83 or -6.8e44 < b < -370

   1. Initial program 78.8%

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

   3. Taylor expanded in t around inf 75.1%

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

      1. +-commutative 75.1%

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

      2. mul-1-neg 75.1%

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

      3. unsub-neg 75.1%

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

      4. *-commutative 75.1%

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

   5. Simplified 75.1%

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

   if -2.59999999999999987e-45 < b < 4.80000000000000025e-291

   1. Initial program 73.1%

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

   3. Taylor expanded in x around inf 65.3%

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

      1. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   if 4.80000000000000025e-291 < b < 1.25000000000000008e-10

   1. Initial program 74.6%

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

   3. Taylor expanded in x around 0 52.4%

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

      1. *-commutative 52.4%

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

   5. Simplified 52.4%

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

   6. Taylor expanded in j around inf 56.1%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+136}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{+83}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -370:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-10}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := j \cdot \left(\left(t \cdot c - y \cdot i\right) + \frac{a \cdot \left(b \cdot i\right)}{j}\right)\\ \mathbf{if}\;j \leq -1.8 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.1 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-13}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t))))
        (t_2 (* j (+ (- (* t c) (* y i)) (/ (* a (* b i)) j)))))
   (if (<= j -1.8e+20)
     t_2
     (if (<= j 4.7e-132)
       (- (* x (- (* y z) (* t a))) (* b (* z c)))
       (if (<= j 4.1e-57)
         t_1
         (if (<= j 1.65e-13)
           (+ (* j (* t c)) (* b (- (* a i) (* z c))))
           (if (<= j 8e+63) 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 * ((b * i) - (x * t));
	double t_2 = j * (((t * c) - (y * i)) + ((a * (b * i)) / j));
	double tmp;
	if (j <= -1.8e+20) {
		tmp = t_2;
	} else if (j <= 4.7e-132) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else if (j <= 4.1e-57) {
		tmp = t_1;
	} else if (j <= 1.65e-13) {
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)));
	} else if (j <= 8e+63) {
		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 * ((b * i) - (x * t))
    t_2 = j * (((t * c) - (y * i)) + ((a * (b * i)) / j))
    if (j <= (-1.8d+20)) then
        tmp = t_2
    else if (j <= 4.7d-132) then
        tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
    else if (j <= 4.1d-57) then
        tmp = t_1
    else if (j <= 1.65d-13) then
        tmp = (j * (t * c)) + (b * ((a * i) - (z * c)))
    else if (j <= 8d+63) 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 * ((b * i) - (x * t));
	double t_2 = j * (((t * c) - (y * i)) + ((a * (b * i)) / j));
	double tmp;
	if (j <= -1.8e+20) {
		tmp = t_2;
	} else if (j <= 4.7e-132) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else if (j <= 4.1e-57) {
		tmp = t_1;
	} else if (j <= 1.65e-13) {
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)));
	} else if (j <= 8e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = j * (((t * c) - (y * i)) + ((a * (b * i)) / j))
	tmp = 0
	if j <= -1.8e+20:
		tmp = t_2
	elif j <= 4.7e-132:
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
	elif j <= 4.1e-57:
		tmp = t_1
	elif j <= 1.65e-13:
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)))
	elif j <= 8e+63:
		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(b * i) - Float64(x * t)))
	t_2 = Float64(j * Float64(Float64(Float64(t * c) - Float64(y * i)) + Float64(Float64(a * Float64(b * i)) / j)))
	tmp = 0.0
	if (j <= -1.8e+20)
		tmp = t_2;
	elseif (j <= 4.7e-132)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(z * c)));
	elseif (j <= 4.1e-57)
		tmp = t_1;
	elseif (j <= 1.65e-13)
		tmp = Float64(Float64(j * Float64(t * c)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 8e+63)
		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 * ((b * i) - (x * t));
	t_2 = j * (((t * c) - (y * i)) + ((a * (b * i)) / j));
	tmp = 0.0;
	if (j <= -1.8e+20)
		tmp = t_2;
	elseif (j <= 4.7e-132)
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	elseif (j <= 4.1e-57)
		tmp = t_1;
	elseif (j <= 1.65e-13)
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)));
	elseif (j <= 8e+63)
		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[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.8e+20], t$95$2, If[LessEqual[j, 4.7e-132], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.1e-57], t$95$1, If[LessEqual[j, 1.65e-13], N[(N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8e+63], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.8e20 or 8.00000000000000046e63 < j

   1. Initial program 68.7%

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

   3. Taylor expanded in j around -inf 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in i around inf 72.3%

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

   if -1.8e20 < j < 4.7000000000000002e-132

   1. Initial program 82.2%

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

   3. Taylor expanded in j around 0 81.4%

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

      1. *-commutative 81.4%

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

      2. *-commutative 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in c around inf 69.7%

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

   if 4.7000000000000002e-132 < j < 4.1000000000000001e-57 or 1.65e-13 < j < 8.00000000000000046e63

   1. Initial program 80.1%

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

   3. Taylor expanded in a around inf 71.4%

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

      1. distribute-lft-out-- 71.4%

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

      2. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   if 4.1000000000000001e-57 < j < 1.65e-13

   1. Initial program 75.5%

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

   3. Taylor expanded in x around 0 84.3%

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

      1. *-commutative 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in c around inf 88.4%

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

      1. *-commutative 88.4%

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

      2. associate-*l* 88.4%

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

      3. *-commutative 88.4%

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

   8. Simplified 88.4%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.8 \cdot 10^{+20}:\\ \;\;\;\;j \cdot \left(\left(t \cdot c - y \cdot i\right) + \frac{a \cdot \left(b \cdot i\right)}{j}\right)\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.1 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-13}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(\left(t \cdot c - y \cdot i\right) + \frac{a \cdot \left(b \cdot i\right)}{j}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.75 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-291}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 10^{-21}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -2.75e+42)
     t_2
     (if (<= b -1.2e-6)
       t_1
       (if (<= b -4e-61)
         t_2
         (if (<= b 5.5e-291)
           (* a (* t (- x)))
           (if (<= b 9.5e-125)
             t_1
             (if (<= b 1e-21) (* (* y i) (- j)) 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 * (t * j);
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.75e+42) {
		tmp = t_2;
	} else if (b <= -1.2e-6) {
		tmp = t_1;
	} else if (b <= -4e-61) {
		tmp = t_2;
	} else if (b <= 5.5e-291) {
		tmp = a * (t * -x);
	} else if (b <= 9.5e-125) {
		tmp = t_1;
	} else if (b <= 1e-21) {
		tmp = (y * i) * -j;
	} 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 * (t * j)
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-2.75d+42)) then
        tmp = t_2
    else if (b <= (-1.2d-6)) then
        tmp = t_1
    else if (b <= (-4d-61)) then
        tmp = t_2
    else if (b <= 5.5d-291) then
        tmp = a * (t * -x)
    else if (b <= 9.5d-125) then
        tmp = t_1
    else if (b <= 1d-21) then
        tmp = (y * i) * -j
    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 * (t * j);
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.75e+42) {
		tmp = t_2;
	} else if (b <= -1.2e-6) {
		tmp = t_1;
	} else if (b <= -4e-61) {
		tmp = t_2;
	} else if (b <= 5.5e-291) {
		tmp = a * (t * -x);
	} else if (b <= 9.5e-125) {
		tmp = t_1;
	} else if (b <= 1e-21) {
		tmp = (y * i) * -j;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -2.75e+42:
		tmp = t_2
	elif b <= -1.2e-6:
		tmp = t_1
	elif b <= -4e-61:
		tmp = t_2
	elif b <= 5.5e-291:
		tmp = a * (t * -x)
	elif b <= 9.5e-125:
		tmp = t_1
	elif b <= 1e-21:
		tmp = (y * i) * -j
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.75e+42)
		tmp = t_2;
	elseif (b <= -1.2e-6)
		tmp = t_1;
	elseif (b <= -4e-61)
		tmp = t_2;
	elseif (b <= 5.5e-291)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (b <= 9.5e-125)
		tmp = t_1;
	elseif (b <= 1e-21)
		tmp = Float64(Float64(y * i) * Float64(-j));
	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 * (t * j);
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.75e+42)
		tmp = t_2;
	elseif (b <= -1.2e-6)
		tmp = t_1;
	elseif (b <= -4e-61)
		tmp = t_2;
	elseif (b <= 5.5e-291)
		tmp = a * (t * -x);
	elseif (b <= 9.5e-125)
		tmp = t_1;
	elseif (b <= 1e-21)
		tmp = (y * i) * -j;
	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[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.75e+42], t$95$2, If[LessEqual[b, -1.2e-6], t$95$1, If[LessEqual[b, -4e-61], t$95$2, If[LessEqual[b, 5.5e-291], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e-125], t$95$1, If[LessEqual[b, 1e-21], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.75000000000000001e42 or -1.1999999999999999e-6 < b < -4.0000000000000002e-61 or 9.99999999999999908e-22 < b

   1. Initial program 78.5%

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

   3. Taylor expanded in b around inf 68.7%

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

      1. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   if -2.75000000000000001e42 < b < -1.1999999999999999e-6 or 5.5000000000000002e-291 < b < 9.50000000000000031e-125

   1. Initial program 81.2%

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

   3. Taylor expanded in x around 0 54.8%

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

      1. *-commutative 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in t around inf 41.0%

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

   if -4.0000000000000002e-61 < b < 5.5000000000000002e-291

   1. Initial program 72.6%

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

   3. Taylor expanded in z around 0 64.0%

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

   4. Taylor expanded in x around inf 40.5%

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

      1. *-commutative 40.5%

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

      2. neg-mul-1 40.5%

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

      3. distribute-rgt-neg-in 40.5%

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

      4. *-commutative 40.5%

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

      5. mul-1-neg 40.5%

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

      6. associate-*r* 40.5%

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

      7. mul-1-neg 40.5%

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

   6. Simplified 40.5%

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

   if 9.50000000000000031e-125 < b < 9.99999999999999908e-22

   1. Initial program 60.2%

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

   3. Taylor expanded in x around 0 48.0%

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

      1. *-commutative 48.0%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in j around inf 47.8%

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

   7. Taylor expanded in c around 0 37.9%

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

      1. mul-1-neg 37.9%

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

      2. distribute-lft-neg-out 37.9%

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

      3. *-commutative 37.9%

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

   9. Simplified 37.9%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.75 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-61}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-291}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 10^{-21}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(-x\right)\right)\\ t_2 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;c \leq -6.8 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2.35 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-205}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* t (- x)))) (t_2 (* j (* t c))))
   (if (<= c -6.8e+62)
     t_2
     (if (<= c -2.35e-272)
       t_1
       (if (<= c 6e-205)
         (* b (* a i))
         (if (<= c 1.75e-81)
           t_1
           (if (<= c 2.8e-57)
             (* a (* b i))
             (if (<= c 3e+101) (* y (* i (- j))) 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 * (t * -x);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -6.8e+62) {
		tmp = t_2;
	} else if (c <= -2.35e-272) {
		tmp = t_1;
	} else if (c <= 6e-205) {
		tmp = b * (a * i);
	} else if (c <= 1.75e-81) {
		tmp = t_1;
	} else if (c <= 2.8e-57) {
		tmp = a * (b * i);
	} else if (c <= 3e+101) {
		tmp = y * (i * -j);
	} 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 * (t * -x)
    t_2 = j * (t * c)
    if (c <= (-6.8d+62)) then
        tmp = t_2
    else if (c <= (-2.35d-272)) then
        tmp = t_1
    else if (c <= 6d-205) then
        tmp = b * (a * i)
    else if (c <= 1.75d-81) then
        tmp = t_1
    else if (c <= 2.8d-57) then
        tmp = a * (b * i)
    else if (c <= 3d+101) then
        tmp = y * (i * -j)
    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 * (t * -x);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -6.8e+62) {
		tmp = t_2;
	} else if (c <= -2.35e-272) {
		tmp = t_1;
	} else if (c <= 6e-205) {
		tmp = b * (a * i);
	} else if (c <= 1.75e-81) {
		tmp = t_1;
	} else if (c <= 2.8e-57) {
		tmp = a * (b * i);
	} else if (c <= 3e+101) {
		tmp = y * (i * -j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (t * -x)
	t_2 = j * (t * c)
	tmp = 0
	if c <= -6.8e+62:
		tmp = t_2
	elif c <= -2.35e-272:
		tmp = t_1
	elif c <= 6e-205:
		tmp = b * (a * i)
	elif c <= 1.75e-81:
		tmp = t_1
	elif c <= 2.8e-57:
		tmp = a * (b * i)
	elif c <= 3e+101:
		tmp = y * (i * -j)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(t * Float64(-x)))
	t_2 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (c <= -6.8e+62)
		tmp = t_2;
	elseif (c <= -2.35e-272)
		tmp = t_1;
	elseif (c <= 6e-205)
		tmp = Float64(b * Float64(a * i));
	elseif (c <= 1.75e-81)
		tmp = t_1;
	elseif (c <= 2.8e-57)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= 3e+101)
		tmp = Float64(y * Float64(i * Float64(-j)));
	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 * (t * -x);
	t_2 = j * (t * c);
	tmp = 0.0;
	if (c <= -6.8e+62)
		tmp = t_2;
	elseif (c <= -2.35e-272)
		tmp = t_1;
	elseif (c <= 6e-205)
		tmp = b * (a * i);
	elseif (c <= 1.75e-81)
		tmp = t_1;
	elseif (c <= 2.8e-57)
		tmp = a * (b * i);
	elseif (c <= 3e+101)
		tmp = y * (i * -j);
	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[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.8e+62], t$95$2, If[LessEqual[c, -2.35e-272], t$95$1, If[LessEqual[c, 6e-205], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.75e-81], t$95$1, If[LessEqual[c, 2.8e-57], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3e+101], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -6.80000000000000028e62 or 2.99999999999999993e101 < c

   1. Initial program 68.1%

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

   3. Taylor expanded in x around 0 62.4%

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

      1. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in j around inf 43.4%

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

   7. Taylor expanded in c around inf 42.3%

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

   if -6.80000000000000028e62 < c < -2.3499999999999999e-272 or 6e-205 < c < 1.74999999999999993e-81

   1. Initial program 83.9%

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

   3. Taylor expanded in z around 0 60.4%

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

   4. Taylor expanded in x around inf 38.7%

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

      1. *-commutative 38.7%

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

      2. neg-mul-1 38.7%

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

      3. distribute-rgt-neg-in 38.7%

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

      4. *-commutative 38.7%

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

      5. mul-1-neg 38.7%

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

      6. associate-*r* 38.7%

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

      7. mul-1-neg 38.7%

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

   6. Simplified 38.7%

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

   if -2.3499999999999999e-272 < c < 6e-205

   1. Initial program 85.9%

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

   3. Taylor expanded in b around inf 58.9%

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

      1. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in i around inf 58.9%

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

   if 1.74999999999999993e-81 < c < 2.7999999999999999e-57

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 75.7%

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

      1. *-commutative 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in i around inf 75.7%

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

   if 2.7999999999999999e-57 < c < 2.99999999999999993e101

   1. Initial program 67.2%

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

   3. Taylor expanded in y around inf 55.3%

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

      1. +-commutative 55.3%

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

      2. mul-1-neg 55.3%

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

      3. unsub-neg 55.3%

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

      4. *-commutative 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in z around 0 41.5%

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

      1. neg-mul-1 41.5%

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

      2. distribute-rgt-neg-in 41.5%

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

   8. Simplified 41.5%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.8 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -2.35 \cdot 10^{-272}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-205}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-81}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(-x\right)\right)\\ t_2 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;c \leq -6 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 9.8 \cdot 10^{-203}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+102}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* t (- x)))) (t_2 (* j (* t c))))
   (if (<= c -6e+61)
     t_2
     (if (<= c -4.5e-272)
       t_1
       (if (<= c 9.8e-203)
         (* b (* a i))
         (if (<= c 1.7e-80)
           t_1
           (if (<= c 1.95e-59)
             (* a (* b i))
             (if (<= c 3.4e+102) (* (* y i) (- j)) 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 * (t * -x);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -6e+61) {
		tmp = t_2;
	} else if (c <= -4.5e-272) {
		tmp = t_1;
	} else if (c <= 9.8e-203) {
		tmp = b * (a * i);
	} else if (c <= 1.7e-80) {
		tmp = t_1;
	} else if (c <= 1.95e-59) {
		tmp = a * (b * i);
	} else if (c <= 3.4e+102) {
		tmp = (y * i) * -j;
	} 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 * (t * -x)
    t_2 = j * (t * c)
    if (c <= (-6d+61)) then
        tmp = t_2
    else if (c <= (-4.5d-272)) then
        tmp = t_1
    else if (c <= 9.8d-203) then
        tmp = b * (a * i)
    else if (c <= 1.7d-80) then
        tmp = t_1
    else if (c <= 1.95d-59) then
        tmp = a * (b * i)
    else if (c <= 3.4d+102) then
        tmp = (y * i) * -j
    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 * (t * -x);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -6e+61) {
		tmp = t_2;
	} else if (c <= -4.5e-272) {
		tmp = t_1;
	} else if (c <= 9.8e-203) {
		tmp = b * (a * i);
	} else if (c <= 1.7e-80) {
		tmp = t_1;
	} else if (c <= 1.95e-59) {
		tmp = a * (b * i);
	} else if (c <= 3.4e+102) {
		tmp = (y * i) * -j;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (t * -x)
	t_2 = j * (t * c)
	tmp = 0
	if c <= -6e+61:
		tmp = t_2
	elif c <= -4.5e-272:
		tmp = t_1
	elif c <= 9.8e-203:
		tmp = b * (a * i)
	elif c <= 1.7e-80:
		tmp = t_1
	elif c <= 1.95e-59:
		tmp = a * (b * i)
	elif c <= 3.4e+102:
		tmp = (y * i) * -j
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(t * Float64(-x)))
	t_2 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (c <= -6e+61)
		tmp = t_2;
	elseif (c <= -4.5e-272)
		tmp = t_1;
	elseif (c <= 9.8e-203)
		tmp = Float64(b * Float64(a * i));
	elseif (c <= 1.7e-80)
		tmp = t_1;
	elseif (c <= 1.95e-59)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= 3.4e+102)
		tmp = Float64(Float64(y * i) * Float64(-j));
	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 * (t * -x);
	t_2 = j * (t * c);
	tmp = 0.0;
	if (c <= -6e+61)
		tmp = t_2;
	elseif (c <= -4.5e-272)
		tmp = t_1;
	elseif (c <= 9.8e-203)
		tmp = b * (a * i);
	elseif (c <= 1.7e-80)
		tmp = t_1;
	elseif (c <= 1.95e-59)
		tmp = a * (b * i);
	elseif (c <= 3.4e+102)
		tmp = (y * i) * -j;
	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[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6e+61], t$95$2, If[LessEqual[c, -4.5e-272], t$95$1, If[LessEqual[c, 9.8e-203], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.7e-80], t$95$1, If[LessEqual[c, 1.95e-59], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.4e+102], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -6e61 or 3.4e102 < c

   1. Initial program 68.1%

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

   3. Taylor expanded in x around 0 62.4%

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

      1. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in j around inf 43.4%

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

   7. Taylor expanded in c around inf 42.3%

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

   if -6e61 < c < -4.4999999999999998e-272 or 9.7999999999999999e-203 < c < 1.7e-80

   1. Initial program 83.9%

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

   3. Taylor expanded in z around 0 60.4%

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

   4. Taylor expanded in x around inf 38.7%

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

      1. *-commutative 38.7%

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

      2. neg-mul-1 38.7%

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

      3. distribute-rgt-neg-in 38.7%

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

      4. *-commutative 38.7%

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

      5. mul-1-neg 38.7%

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

      6. associate-*r* 38.7%

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

      7. mul-1-neg 38.7%

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

   6. Simplified 38.7%

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

   if -4.4999999999999998e-272 < c < 9.7999999999999999e-203

   1. Initial program 85.9%

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

   3. Taylor expanded in b around inf 58.9%

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

      1. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in i around inf 58.9%

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

   if 1.7e-80 < c < 1.95000000000000009e-59

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in i around inf 100.0%

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

   if 1.95000000000000009e-59 < c < 3.4e102

   1. Initial program 68.4%

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

   3. Taylor expanded in x around 0 60.8%

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

      1. *-commutative 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in j around inf 50.5%

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

   7. Taylor expanded in c around 0 40.1%

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

      1. mul-1-neg 40.1%

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

      2. distribute-lft-neg-out 40.1%

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

      3. *-commutative 40.1%

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

   9. Simplified 40.1%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6 \cdot 10^{+61}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-272}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 9.8 \cdot 10^{-203}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+102}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{+38}:\\ \;\;\;\;t\_2 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-279}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 7800000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+133}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(a \cdot \frac{b}{j} - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (* t c)) (* b (- (* a i) (* z c)))))
        (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -7e+38)
     (- t_2 (* b (* z c)))
     (if (<= x -9.2e-270)
       t_1
       (if (<= x 5.2e-279)
         (- (* j (- (* t c) (* y i))) (* a (* x t)))
         (if (<= x 7800000000000.0)
           t_1
           (if (<= x 1.9e+133) (* (* i j) (- (* a (/ b j)) y)) 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 * (t * c)) + (b * ((a * i) - (z * c)));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -7e+38) {
		tmp = t_2 - (b * (z * c));
	} else if (x <= -9.2e-270) {
		tmp = t_1;
	} else if (x <= 5.2e-279) {
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t));
	} else if (x <= 7800000000000.0) {
		tmp = t_1;
	} else if (x <= 1.9e+133) {
		tmp = (i * j) * ((a * (b / j)) - y);
	} 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 * (t * c)) + (b * ((a * i) - (z * c)))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-7d+38)) then
        tmp = t_2 - (b * (z * c))
    else if (x <= (-9.2d-270)) then
        tmp = t_1
    else if (x <= 5.2d-279) then
        tmp = (j * ((t * c) - (y * i))) - (a * (x * t))
    else if (x <= 7800000000000.0d0) then
        tmp = t_1
    else if (x <= 1.9d+133) then
        tmp = (i * j) * ((a * (b / j)) - y)
    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 * (t * c)) + (b * ((a * i) - (z * c)));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -7e+38) {
		tmp = t_2 - (b * (z * c));
	} else if (x <= -9.2e-270) {
		tmp = t_1;
	} else if (x <= 5.2e-279) {
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t));
	} else if (x <= 7800000000000.0) {
		tmp = t_1;
	} else if (x <= 1.9e+133) {
		tmp = (i * j) * ((a * (b / j)) - y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * (t * c)) + (b * ((a * i) - (z * c)))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -7e+38:
		tmp = t_2 - (b * (z * c))
	elif x <= -9.2e-270:
		tmp = t_1
	elif x <= 5.2e-279:
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t))
	elif x <= 7800000000000.0:
		tmp = t_1
	elif x <= 1.9e+133:
		tmp = (i * j) * ((a * (b / j)) - y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(t * c)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -7e+38)
		tmp = Float64(t_2 - Float64(b * Float64(z * c)));
	elseif (x <= -9.2e-270)
		tmp = t_1;
	elseif (x <= 5.2e-279)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(a * Float64(x * t)));
	elseif (x <= 7800000000000.0)
		tmp = t_1;
	elseif (x <= 1.9e+133)
		tmp = Float64(Float64(i * j) * Float64(Float64(a * Float64(b / j)) - y));
	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 * (t * c)) + (b * ((a * i) - (z * c)));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -7e+38)
		tmp = t_2 - (b * (z * c));
	elseif (x <= -9.2e-270)
		tmp = t_1;
	elseif (x <= 5.2e-279)
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t));
	elseif (x <= 7800000000000.0)
		tmp = t_1;
	elseif (x <= 1.9e+133)
		tmp = (i * j) * ((a * (b / j)) - y);
	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[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e+38], N[(t$95$2 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.2e-270], t$95$1, If[LessEqual[x, 5.2e-279], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7800000000000.0], t$95$1, If[LessEqual[x, 1.9e+133], N[(N[(i * j), $MachinePrecision] * N[(N[(a * N[(b / j), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -7.00000000000000003e38

   1. Initial program 69.9%

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

   3. Taylor expanded in j around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. *-commutative 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in c around inf 77.5%

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

   if -7.00000000000000003e38 < x < -9.2000000000000006e-270 or 5.2000000000000004e-279 < x < 7.8e12

   1. Initial program 80.0%

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

   3. Taylor expanded in x around 0 73.2%

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

      1. *-commutative 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in c around inf 66.2%

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

      1. *-commutative 66.2%

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

      2. associate-*l* 63.2%

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

      3. *-commutative 63.2%

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

   8. Simplified 63.2%

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

   if -9.2000000000000006e-270 < x < 5.2000000000000004e-279

   1. Initial program 75.7%

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

   3. Taylor expanded in z around 0 80.2%

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

   4. Taylor expanded in b around 0 85.4%

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

      1. +-commutative 85.4%

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

      2. *-commutative 85.4%

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

      3. *-commutative 85.4%

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

      4. mul-1-neg 85.4%

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

      5. unsub-neg 85.4%

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

      6. *-commutative 85.4%

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

      7. *-commutative 85.4%

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

      8. *-commutative 85.4%

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

   6. Simplified 85.4%

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

   if 7.8e12 < x < 1.9000000000000001e133

   1. Initial program 76.3%

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

   3. Taylor expanded in j around -inf 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in i around -inf 54.0%

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

      1. associate-*r* 58.7%

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

      2. +-commutative 58.7%

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

      3. mul-1-neg 58.7%

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

      4. unsub-neg 58.7%

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

      5. associate-/l* 58.7%

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

   8. Simplified 58.7%

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

   if 1.9000000000000001e133 < x

   1. Initial program 74.9%

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

   3. Taylor expanded in x around inf 75.7%

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

      1. *-commutative 75.7%

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

   5. Simplified 75.7%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-270}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-279}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 7800000000000:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+133}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(a \cdot \frac{b}{j} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+135}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-279}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 410000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+133}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(a \cdot \frac{b}{j} - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (* t c)) (* b (- (* a i) (* z c)))))
        (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -9.5e+135)
     t_2
     (if (<= x -1.35e-270)
       t_1
       (if (<= x 1.1e-279)
         (* j (- (* t c) (* y i)))
         (if (<= x 410000000000.0)
           t_1
           (if (<= x 3.8e+133) (* (* i j) (- (* a (/ b j)) y)) 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 * (t * c)) + (b * ((a * i) - (z * c)));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -9.5e+135) {
		tmp = t_2;
	} else if (x <= -1.35e-270) {
		tmp = t_1;
	} else if (x <= 1.1e-279) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= 410000000000.0) {
		tmp = t_1;
	} else if (x <= 3.8e+133) {
		tmp = (i * j) * ((a * (b / j)) - y);
	} 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 * (t * c)) + (b * ((a * i) - (z * c)))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-9.5d+135)) then
        tmp = t_2
    else if (x <= (-1.35d-270)) then
        tmp = t_1
    else if (x <= 1.1d-279) then
        tmp = j * ((t * c) - (y * i))
    else if (x <= 410000000000.0d0) then
        tmp = t_1
    else if (x <= 3.8d+133) then
        tmp = (i * j) * ((a * (b / j)) - y)
    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 * (t * c)) + (b * ((a * i) - (z * c)));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -9.5e+135) {
		tmp = t_2;
	} else if (x <= -1.35e-270) {
		tmp = t_1;
	} else if (x <= 1.1e-279) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= 410000000000.0) {
		tmp = t_1;
	} else if (x <= 3.8e+133) {
		tmp = (i * j) * ((a * (b / j)) - y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * (t * c)) + (b * ((a * i) - (z * c)))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -9.5e+135:
		tmp = t_2
	elif x <= -1.35e-270:
		tmp = t_1
	elif x <= 1.1e-279:
		tmp = j * ((t * c) - (y * i))
	elif x <= 410000000000.0:
		tmp = t_1
	elif x <= 3.8e+133:
		tmp = (i * j) * ((a * (b / j)) - y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(t * c)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -9.5e+135)
		tmp = t_2;
	elseif (x <= -1.35e-270)
		tmp = t_1;
	elseif (x <= 1.1e-279)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (x <= 410000000000.0)
		tmp = t_1;
	elseif (x <= 3.8e+133)
		tmp = Float64(Float64(i * j) * Float64(Float64(a * Float64(b / j)) - y));
	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 * (t * c)) + (b * ((a * i) - (z * c)));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -9.5e+135)
		tmp = t_2;
	elseif (x <= -1.35e-270)
		tmp = t_1;
	elseif (x <= 1.1e-279)
		tmp = j * ((t * c) - (y * i));
	elseif (x <= 410000000000.0)
		tmp = t_1;
	elseif (x <= 3.8e+133)
		tmp = (i * j) * ((a * (b / j)) - y);
	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[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.5e+135], t$95$2, If[LessEqual[x, -1.35e-270], t$95$1, If[LessEqual[x, 1.1e-279], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 410000000000.0], t$95$1, If[LessEqual[x, 3.8e+133], N[(N[(i * j), $MachinePrecision] * N[(N[(a * N[(b / j), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.50000000000000036e135 or 3.8000000000000002e133 < x

   1. Initial program 72.8%

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

   3. Taylor expanded in x around inf 76.0%

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

      1. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   if -9.50000000000000036e135 < x < -1.35000000000000004e-270 or 1.1e-279 < x < 4.1e11

   1. Initial program 78.6%

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

   3. Taylor expanded in x around 0 68.9%

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

      1. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in c around inf 64.1%

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

      1. *-commutative 64.1%

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

      2. associate-*l* 60.7%

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

      3. *-commutative 60.7%

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

   8. Simplified 60.7%

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

   if -1.35000000000000004e-270 < x < 1.1e-279

   1. Initial program 75.7%

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

   3. Taylor expanded in x around 0 79.2%

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

      1. *-commutative 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in j around inf 84.2%

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

   if 4.1e11 < x < 3.8000000000000002e133

   1. Initial program 76.3%

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

   3. Taylor expanded in j around -inf 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in i around -inf 54.0%

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

      1. associate-*r* 58.7%

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

      2. +-commutative 58.7%

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

      3. mul-1-neg 58.7%

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

      4. unsub-neg 58.7%

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

      5. associate-/l* 58.7%

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

   8. Simplified 58.7%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-270}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-279}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 410000000000:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+133}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(a \cdot \frac{b}{j} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -9.4 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{+74} \lor \neg \left(b \leq -9.2 \cdot 10^{-57}\right) \land b \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -9.4e+145)
     t_1
     (if (or (<= b -5.5e+74) (and (not (<= b -9.2e-57)) (<= b 1.4e-9)))
       (- (* j (- (* t c) (* y i))) (* a (* x t)))
       (+ (* j (* t c)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -9.4e+145) {
		tmp = t_1;
	} else if ((b <= -5.5e+74) || (!(b <= -9.2e-57) && (b <= 1.4e-9))) {
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t));
	} else {
		tmp = (j * (t * c)) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-9.4d+145)) then
        tmp = t_1
    else if ((b <= (-5.5d+74)) .or. (.not. (b <= (-9.2d-57))) .and. (b <= 1.4d-9)) then
        tmp = (j * ((t * c) - (y * i))) - (a * (x * t))
    else
        tmp = (j * (t * c)) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -9.4e+145) {
		tmp = t_1;
	} else if ((b <= -5.5e+74) || (!(b <= -9.2e-57) && (b <= 1.4e-9))) {
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t));
	} else {
		tmp = (j * (t * c)) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -9.4e+145:
		tmp = t_1
	elif (b <= -5.5e+74) or (not (b <= -9.2e-57) and (b <= 1.4e-9)):
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t))
	else:
		tmp = (j * (t * c)) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -9.4e+145)
		tmp = t_1;
	elseif ((b <= -5.5e+74) || (!(b <= -9.2e-57) && (b <= 1.4e-9)))
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(a * Float64(x * t)));
	else
		tmp = Float64(Float64(j * Float64(t * c)) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -9.4e+145)
		tmp = t_1;
	elseif ((b <= -5.5e+74) || (~((b <= -9.2e-57)) && (b <= 1.4e-9)))
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t));
	else
		tmp = (j * (t * c)) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.4e+145], t$95$1, If[Or[LessEqual[b, -5.5e+74], And[N[Not[LessEqual[b, -9.2e-57]], $MachinePrecision], LessEqual[b, 1.4e-9]]], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.4000000000000004e145

   1. Initial program 91.1%

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

   3. Taylor expanded in b around inf 78.9%

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

      1. *-commutative 78.9%

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

   5. Simplified 78.9%

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

   if -9.4000000000000004e145 < b < -5.5000000000000003e74 or -9.2000000000000001e-57 < b < 1.39999999999999992e-9

   1. Initial program 74.3%

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

   3. Taylor expanded in z around 0 66.1%

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

   4. Taylor expanded in b around 0 62.3%

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

      1. +-commutative 62.3%

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

      2. *-commutative 62.3%

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

      3. *-commutative 62.3%

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

      4. mul-1-neg 62.3%

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

      5. unsub-neg 62.3%

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

      6. *-commutative 62.3%

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

      7. *-commutative 62.3%

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

      8. *-commutative 62.3%

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

   6. Simplified 62.3%

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

   if -5.5000000000000003e74 < b < -9.2000000000000001e-57 or 1.39999999999999992e-9 < b

   1. Initial program 73.8%

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

   3. Taylor expanded in x around 0 67.9%

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

      1. *-commutative 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in c around inf 70.9%

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

      1. *-commutative 70.9%

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

      2. associate-*l* 70.2%

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

      3. *-commutative 70.2%

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

   8. Simplified 70.2%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.4 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{+74} \lor \neg \left(b \leq -9.2 \cdot 10^{-57}\right) \land b \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.7 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+86}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -3.7e+62)
     t_2
     (if (<= c 5.8e-176)
       t_1
       (if (<= c 3.1e-144)
         (* y (- (* x z) (* i j)))
         (if (<= c 1.35e-59)
           t_1
           (if (<= c 7.5e+86) (* j (- (* t c) (* y i))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.7e+62) {
		tmp = t_2;
	} else if (c <= 5.8e-176) {
		tmp = t_1;
	} else if (c <= 3.1e-144) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1.35e-59) {
		tmp = t_1;
	} else if (c <= 7.5e+86) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-3.7d+62)) then
        tmp = t_2
    else if (c <= 5.8d-176) then
        tmp = t_1
    else if (c <= 3.1d-144) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 1.35d-59) then
        tmp = t_1
    else if (c <= 7.5d+86) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.7e+62) {
		tmp = t_2;
	} else if (c <= 5.8e-176) {
		tmp = t_1;
	} else if (c <= 3.1e-144) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1.35e-59) {
		tmp = t_1;
	} else if (c <= 7.5e+86) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3.7e+62:
		tmp = t_2
	elif c <= 5.8e-176:
		tmp = t_1
	elif c <= 3.1e-144:
		tmp = y * ((x * z) - (i * j))
	elif c <= 1.35e-59:
		tmp = t_1
	elif c <= 7.5e+86:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.7e+62)
		tmp = t_2;
	elseif (c <= 5.8e-176)
		tmp = t_1;
	elseif (c <= 3.1e-144)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 1.35e-59)
		tmp = t_1;
	elseif (c <= 7.5e+86)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.7e+62)
		tmp = t_2;
	elseif (c <= 5.8e-176)
		tmp = t_1;
	elseif (c <= 3.1e-144)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 1.35e-59)
		tmp = t_1;
	elseif (c <= 7.5e+86)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.7e+62], t$95$2, If[LessEqual[c, 5.8e-176], t$95$1, If[LessEqual[c, 3.1e-144], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.35e-59], t$95$1, If[LessEqual[c, 7.5e+86], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.70000000000000014e62 or 7.4999999999999997e86 < c

   1. Initial program 66.2%

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

   3. Taylor expanded in c around inf 70.3%

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

   if -3.70000000000000014e62 < c < 5.80000000000000012e-176 or 3.1000000000000001e-144 < c < 1.3499999999999999e-59

   1. Initial program 83.4%

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

   3. Taylor expanded in a around inf 62.0%

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

      1. distribute-lft-out-- 62.0%

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

      2. *-commutative 62.0%

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

   5. Simplified 62.0%

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

   if 5.80000000000000012e-176 < c < 3.1000000000000001e-144

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 74.0%

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

      1. +-commutative 74.0%

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

      2. mul-1-neg 74.0%

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

      3. unsub-neg 74.0%

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

      4. *-commutative 74.0%

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

   5. Simplified 74.0%

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

   if 1.3499999999999999e-59 < c < 7.4999999999999997e86

   1. Initial program 76.4%

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

   3. Taylor expanded in x around 0 63.9%

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

      1. *-commutative 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in j around inf 56.2%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.7 \cdot 10^{+62}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-176}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+86}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 43.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.8 \cdot 10^{+63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.12 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-148}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -2.8e+63)
     t_2
     (if (<= c -1.12e-88)
       t_1
       (if (<= c -2.7e-148)
         (* z (* x y))
         (if (<= c 5.5e-58) t_1 (if (<= c 5.8e+86) (* y (* i (- j))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.8e+63) {
		tmp = t_2;
	} else if (c <= -1.12e-88) {
		tmp = t_1;
	} else if (c <= -2.7e-148) {
		tmp = z * (x * y);
	} else if (c <= 5.5e-58) {
		tmp = t_1;
	} else if (c <= 5.8e+86) {
		tmp = y * (i * -j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-2.8d+63)) then
        tmp = t_2
    else if (c <= (-1.12d-88)) then
        tmp = t_1
    else if (c <= (-2.7d-148)) then
        tmp = z * (x * y)
    else if (c <= 5.5d-58) then
        tmp = t_1
    else if (c <= 5.8d+86) then
        tmp = y * (i * -j)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.8e+63) {
		tmp = t_2;
	} else if (c <= -1.12e-88) {
		tmp = t_1;
	} else if (c <= -2.7e-148) {
		tmp = z * (x * y);
	} else if (c <= 5.5e-58) {
		tmp = t_1;
	} else if (c <= 5.8e+86) {
		tmp = y * (i * -j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -2.8e+63:
		tmp = t_2
	elif c <= -1.12e-88:
		tmp = t_1
	elif c <= -2.7e-148:
		tmp = z * (x * y)
	elif c <= 5.5e-58:
		tmp = t_1
	elif c <= 5.8e+86:
		tmp = y * (i * -j)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.8e+63)
		tmp = t_2;
	elseif (c <= -1.12e-88)
		tmp = t_1;
	elseif (c <= -2.7e-148)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 5.5e-58)
		tmp = t_1;
	elseif (c <= 5.8e+86)
		tmp = Float64(y * Float64(i * Float64(-j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.8e+63)
		tmp = t_2;
	elseif (c <= -1.12e-88)
		tmp = t_1;
	elseif (c <= -2.7e-148)
		tmp = z * (x * y);
	elseif (c <= 5.5e-58)
		tmp = t_1;
	elseif (c <= 5.8e+86)
		tmp = y * (i * -j);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.8e+63], t$95$2, If[LessEqual[c, -1.12e-88], t$95$1, If[LessEqual[c, -2.7e-148], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.5e-58], t$95$1, If[LessEqual[c, 5.8e+86], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.79999999999999987e63 or 5.79999999999999981e86 < c

   1. Initial program 66.2%

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

   3. Taylor expanded in c around inf 70.3%

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

   if -2.79999999999999987e63 < c < -1.12e-88 or -2.69999999999999988e-148 < c < 5.49999999999999996e-58

   1. Initial program 84.4%

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

   3. Taylor expanded in b around inf 45.3%

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

      1. *-commutative 45.3%

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

   5. Simplified 45.3%

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

   if -1.12e-88 < c < -2.69999999999999988e-148

   1. Initial program 91.2%

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

   3. Taylor expanded in y around inf 46.7%

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

      1. +-commutative 46.7%

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

      2. mul-1-neg 46.7%

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

      3. unsub-neg 46.7%

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

      4. *-commutative 46.7%

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

   5. Simplified 46.7%

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

   6. Taylor expanded in z around inf 38.3%

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

      1. associate-*r* 46.8%

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

   8. Simplified 46.8%

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

   if 5.49999999999999996e-58 < c < 5.79999999999999981e86

   1. Initial program 75.4%

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

   3. Taylor expanded in y around inf 57.9%

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

      1. +-commutative 57.9%

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

      2. mul-1-neg 57.9%

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

      3. unsub-neg 57.9%

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

      4. *-commutative 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in z around 0 46.4%

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

      1. neg-mul-1 46.4%

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

      2. distribute-rgt-neg-in 46.4%

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

   8. Simplified 46.4%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.8 \cdot 10^{+63}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.12 \cdot 10^{-88}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-148}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-58}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 67.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot c - y \cdot i\\ \mathbf{if}\;j \leq -8 \cdot 10^{+27}:\\ \;\;\;\;j \cdot \left(t\_1 + \frac{a \cdot \left(b \cdot i\right)}{j}\right)\\ \mathbf{elif}\;j \leq 9.4 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{+169}:\\ \;\;\;\;j \cdot \left(t\_1 - \frac{a \cdot \left(x \cdot t\right)}{j}\right)\\ \mathbf{elif}\;j \leq 9.6 \cdot 10^{+204}:\\ \;\;\;\;y \cdot \left(j \cdot \left(\frac{x \cdot z}{j} - i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t c) (* y i))))
   (if (<= j -8e+27)
     (* j (+ t_1 (/ (* a (* b i)) j)))
     (if (<= j 9.4e+14)
       (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
       (if (<= j 1.7e+169)
         (* j (- t_1 (/ (* a (* x t)) j)))
         (if (<= j 9.6e+204) (* y (* j (- (/ (* x z) j) i))) (* j t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * c) - (y * i);
	double tmp;
	if (j <= -8e+27) {
		tmp = j * (t_1 + ((a * (b * i)) / j));
	} else if (j <= 9.4e+14) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (j <= 1.7e+169) {
		tmp = j * (t_1 - ((a * (x * t)) / j));
	} else if (j <= 9.6e+204) {
		tmp = y * (j * (((x * z) / j) - i));
	} else {
		tmp = j * t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * c) - (y * i)
    if (j <= (-8d+27)) then
        tmp = j * (t_1 + ((a * (b * i)) / j))
    else if (j <= 9.4d+14) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else if (j <= 1.7d+169) then
        tmp = j * (t_1 - ((a * (x * t)) / j))
    else if (j <= 9.6d+204) then
        tmp = y * (j * (((x * z) / j) - i))
    else
        tmp = j * t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * c) - (y * i);
	double tmp;
	if (j <= -8e+27) {
		tmp = j * (t_1 + ((a * (b * i)) / j));
	} else if (j <= 9.4e+14) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (j <= 1.7e+169) {
		tmp = j * (t_1 - ((a * (x * t)) / j));
	} else if (j <= 9.6e+204) {
		tmp = y * (j * (((x * z) / j) - i));
	} else {
		tmp = j * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * c) - (y * i)
	tmp = 0
	if j <= -8e+27:
		tmp = j * (t_1 + ((a * (b * i)) / j))
	elif j <= 9.4e+14:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	elif j <= 1.7e+169:
		tmp = j * (t_1 - ((a * (x * t)) / j))
	elif j <= 9.6e+204:
		tmp = y * (j * (((x * z) / j) - i))
	else:
		tmp = j * t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * c) - Float64(y * i))
	tmp = 0.0
	if (j <= -8e+27)
		tmp = Float64(j * Float64(t_1 + Float64(Float64(a * Float64(b * i)) / j)));
	elseif (j <= 9.4e+14)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 1.7e+169)
		tmp = Float64(j * Float64(t_1 - Float64(Float64(a * Float64(x * t)) / j)));
	elseif (j <= 9.6e+204)
		tmp = Float64(y * Float64(j * Float64(Float64(Float64(x * z) / j) - i)));
	else
		tmp = Float64(j * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * c) - (y * i);
	tmp = 0.0;
	if (j <= -8e+27)
		tmp = j * (t_1 + ((a * (b * i)) / j));
	elseif (j <= 9.4e+14)
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	elseif (j <= 1.7e+169)
		tmp = j * (t_1 - ((a * (x * t)) / j));
	elseif (j <= 9.6e+204)
		tmp = y * (j * (((x * z) / j) - i));
	else
		tmp = j * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8e+27], N[(j * N[(t$95$1 + N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.4e+14], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e+169], N[(j * N[(t$95$1 - N[(N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.6e+204], N[(y * N[(j * N[(N[(N[(x * z), $MachinePrecision] / j), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -8.0000000000000001e27

   1. Initial program 72.9%

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

   3. Taylor expanded in j around -inf 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in i around inf 77.1%

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

   if -8.0000000000000001e27 < j < 9.4e14

   1. Initial program 80.4%

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

   3. Taylor expanded in j around 0 78.4%

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

      1. *-commutative 78.4%

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

      2. *-commutative 78.4%

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

   5. Simplified 78.4%

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

   if 9.4e14 < j < 1.70000000000000014e169

   1. Initial program 79.1%

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

   3. Taylor expanded in j around -inf 96.4%

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

   5. Simplified 96.4%

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

   6. Taylor expanded in t around inf 76.4%

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

      1. associate-*r/ 76.4%

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

      2. *-commutative 76.4%

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

      3. neg-mul-1 76.4%

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

      4. distribute-rgt-neg-in 76.4%

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

      5. *-commutative 76.4%

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

      6. mul-1-neg 76.4%

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

      7. associate-*r* 76.4%

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

      8. mul-1-neg 76.4%

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

   8. Simplified 76.4%

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

   if 1.70000000000000014e169 < j < 9.5999999999999999e204

   1. Initial program 57.4%

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

   3. Taylor expanded in y around inf 71.5%

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

      1. +-commutative 71.5%

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

      2. mul-1-neg 71.5%

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

      3. unsub-neg 71.5%

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

      4. *-commutative 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in j around inf 71.8%

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

   if 9.5999999999999999e204 < j

   1. Initial program 53.3%

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

   3. Taylor expanded in x around 0 60.0%

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

      1. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in j around inf 80.0%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8 \cdot 10^{+27}:\\ \;\;\;\;j \cdot \left(\left(t \cdot c - y \cdot i\right) + \frac{a \cdot \left(b \cdot i\right)}{j}\right)\\ \mathbf{elif}\;j \leq 9.4 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{+169}:\\ \;\;\;\;j \cdot \left(\left(t \cdot c - y \cdot i\right) - \frac{a \cdot \left(x \cdot t\right)}{j}\right)\\ \mathbf{elif}\;j \leq 9.6 \cdot 10^{+204}:\\ \;\;\;\;y \cdot \left(j \cdot \left(\frac{x \cdot z}{j} - i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;c \leq -4.7 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -9.8 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-181}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.06 \cdot 10^{-153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 5.7 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))) (t_2 (* j (* t c))))
   (if (<= c -4.7e+61)
     t_2
     (if (<= c -9.8e-85)
       t_1
       (if (<= c -1.15e-181)
         (* z (* x y))
         (if (<= c 1.06e-153) t_1 (if (<= c 5.7e+75) (* y (* x z)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -4.7e+61) {
		tmp = t_2;
	} else if (c <= -9.8e-85) {
		tmp = t_1;
	} else if (c <= -1.15e-181) {
		tmp = z * (x * y);
	} else if (c <= 1.06e-153) {
		tmp = t_1;
	} else if (c <= 5.7e+75) {
		tmp = y * (x * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * i)
    t_2 = j * (t * c)
    if (c <= (-4.7d+61)) then
        tmp = t_2
    else if (c <= (-9.8d-85)) then
        tmp = t_1
    else if (c <= (-1.15d-181)) then
        tmp = z * (x * y)
    else if (c <= 1.06d-153) then
        tmp = t_1
    else if (c <= 5.7d+75) then
        tmp = y * (x * z)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -4.7e+61) {
		tmp = t_2;
	} else if (c <= -9.8e-85) {
		tmp = t_1;
	} else if (c <= -1.15e-181) {
		tmp = z * (x * y);
	} else if (c <= 1.06e-153) {
		tmp = t_1;
	} else if (c <= 5.7e+75) {
		tmp = y * (x * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	t_2 = j * (t * c)
	tmp = 0
	if c <= -4.7e+61:
		tmp = t_2
	elif c <= -9.8e-85:
		tmp = t_1
	elif c <= -1.15e-181:
		tmp = z * (x * y)
	elif c <= 1.06e-153:
		tmp = t_1
	elif c <= 5.7e+75:
		tmp = y * (x * z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	t_2 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (c <= -4.7e+61)
		tmp = t_2;
	elseif (c <= -9.8e-85)
		tmp = t_1;
	elseif (c <= -1.15e-181)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 1.06e-153)
		tmp = t_1;
	elseif (c <= 5.7e+75)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	t_2 = j * (t * c);
	tmp = 0.0;
	if (c <= -4.7e+61)
		tmp = t_2;
	elseif (c <= -9.8e-85)
		tmp = t_1;
	elseif (c <= -1.15e-181)
		tmp = z * (x * y);
	elseif (c <= 1.06e-153)
		tmp = t_1;
	elseif (c <= 5.7e+75)
		tmp = y * (x * z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.7e+61], t$95$2, If[LessEqual[c, -9.8e-85], t$95$1, If[LessEqual[c, -1.15e-181], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.06e-153], t$95$1, If[LessEqual[c, 5.7e+75], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -4.6999999999999998e61 or 5.7000000000000004e75 < c

   1. Initial program 65.9%

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

   3. Taylor expanded in x around 0 61.4%

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

      1. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in j around inf 43.3%

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

   7. Taylor expanded in c around inf 41.3%

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

   if -4.6999999999999998e61 < c < -9.80000000000000029e-85 or -1.14999999999999995e-181 < c < 1.06e-153

   1. Initial program 84.8%

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

   3. Taylor expanded in b around inf 51.2%

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

      1. *-commutative 51.2%

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

   5. Simplified 51.2%

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

   6. Taylor expanded in i around inf 45.5%

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

   if -9.80000000000000029e-85 < c < -1.14999999999999995e-181

   1. Initial program 84.9%

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

   3. Taylor expanded in y around inf 43.6%

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

      1. +-commutative 43.6%

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

      2. mul-1-neg 43.6%

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

      3. unsub-neg 43.6%

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

      4. *-commutative 43.6%

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

   5. Simplified 43.6%

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

   6. Taylor expanded in z around inf 28.3%

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

      1. associate-*r* 33.3%

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

   8. Simplified 33.3%

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

   if 1.06e-153 < c < 5.7000000000000004e75

   1. Initial program 81.9%

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

   3. Taylor expanded in y around inf 48.3%

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

      1. +-commutative 48.3%

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

      2. mul-1-neg 48.3%

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

      3. unsub-neg 48.3%

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

      4. *-commutative 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in z around inf 29.1%

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

      1. *-commutative 29.1%

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

   8. Simplified 29.1%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.7 \cdot 10^{+61}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -9.8 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-181}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.06 \cdot 10^{-153}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 5.7 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.75 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-46} \lor \neg \left(b \leq 8.6 \cdot 10^{-7}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -2.75e+42)
     t_1
     (if (<= b -1.8e-6)
       (* c (* t j))
       (if (or (<= b -6.2e-46) (not (<= b 8.6e-7)))
         t_1
         (* j (- (* t 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.75e+42) {
		tmp = t_1;
	} else if (b <= -1.8e-6) {
		tmp = c * (t * j);
	} else if ((b <= -6.2e-46) || !(b <= 8.6e-7)) {
		tmp = t_1;
	} else {
		tmp = j * ((t * 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 = b * ((a * i) - (z * c))
    if (b <= (-2.75d+42)) then
        tmp = t_1
    else if (b <= (-1.8d-6)) then
        tmp = c * (t * j)
    else if ((b <= (-6.2d-46)) .or. (.not. (b <= 8.6d-7))) then
        tmp = t_1
    else
        tmp = j * ((t * 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.75e+42) {
		tmp = t_1;
	} else if (b <= -1.8e-6) {
		tmp = c * (t * j);
	} else if ((b <= -6.2e-46) || !(b <= 8.6e-7)) {
		tmp = t_1;
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -2.75e+42:
		tmp = t_1
	elif b <= -1.8e-6:
		tmp = c * (t * j)
	elif (b <= -6.2e-46) or not (b <= 8.6e-7):
		tmp = t_1
	else:
		tmp = j * ((t * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.75e+42)
		tmp = t_1;
	elseif (b <= -1.8e-6)
		tmp = Float64(c * Float64(t * j));
	elseif ((b <= -6.2e-46) || !(b <= 8.6e-7))
		tmp = t_1;
	else
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.75e+42)
		tmp = t_1;
	elseif (b <= -1.8e-6)
		tmp = c * (t * j);
	elseif ((b <= -6.2e-46) || ~((b <= 8.6e-7)))
		tmp = t_1;
	else
		tmp = j * ((t * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.75e+42], t$95$1, If[LessEqual[b, -1.8e-6], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -6.2e-46], N[Not[LessEqual[b, 8.6e-7]], $MachinePrecision]], t$95$1, N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.75000000000000001e42 or -1.79999999999999992e-6 < b < -6.2000000000000002e-46 or 8.6000000000000002e-7 < b

   1. Initial program 78.4%

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

   3. Taylor expanded in b around inf 69.2%

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

      1. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   if -2.75000000000000001e42 < b < -1.79999999999999992e-6

   1. Initial program 76.8%

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

   3. Taylor expanded in x around 0 54.4%

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

      1. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in t around inf 48.1%

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

   if -6.2000000000000002e-46 < b < 8.6000000000000002e-7

   1. Initial program 73.8%

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

   3. Taylor expanded in x around 0 44.9%

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

      1. *-commutative 44.9%

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

   5. Simplified 44.9%

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

   6. Taylor expanded in j around inf 45.3%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.75 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-46} \lor \neg \left(b \leq 8.6 \cdot 10^{-7}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 48.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+109}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+211}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -3.3e-38)
     t_2
     (if (<= t 1.45e+32)
       t_1
       (if (<= t 7.5e+109) (* y (* x z)) (if (<= t 2.6e+211) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3.3e-38) {
		tmp = t_2;
	} else if (t <= 1.45e+32) {
		tmp = t_1;
	} else if (t <= 7.5e+109) {
		tmp = y * (x * z);
	} else if (t <= 2.6e+211) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-3.3d-38)) then
        tmp = t_2
    else if (t <= 1.45d+32) then
        tmp = t_1
    else if (t <= 7.5d+109) then
        tmp = y * (x * z)
    else if (t <= 2.6d+211) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3.3e-38) {
		tmp = t_2;
	} else if (t <= 1.45e+32) {
		tmp = t_1;
	} else if (t <= 7.5e+109) {
		tmp = y * (x * z);
	} else if (t <= 2.6e+211) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -3.3e-38:
		tmp = t_2
	elif t <= 1.45e+32:
		tmp = t_1
	elif t <= 7.5e+109:
		tmp = y * (x * z)
	elif t <= 2.6e+211:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -3.3e-38)
		tmp = t_2;
	elseif (t <= 1.45e+32)
		tmp = t_1;
	elseif (t <= 7.5e+109)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 2.6e+211)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -3.3e-38)
		tmp = t_2;
	elseif (t <= 1.45e+32)
		tmp = t_1;
	elseif (t <= 7.5e+109)
		tmp = y * (x * z);
	elseif (t <= 2.6e+211)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e-38], t$95$2, If[LessEqual[t, 1.45e+32], t$95$1, If[LessEqual[t, 7.5e+109], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+211], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3000000000000002e-38 or 2.5999999999999998e211 < t

   1. Initial program 72.5%

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

   3. Taylor expanded in t around inf 69.9%

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

      1. +-commutative 69.9%

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

      2. mul-1-neg 69.9%

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

      3. unsub-neg 69.9%

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

      4. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   if -3.3000000000000002e-38 < t < 1.45000000000000001e32 or 7.50000000000000018e109 < t < 2.5999999999999998e211

   1. Initial program 79.4%

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

   3. Taylor expanded in b around inf 53.1%

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

      1. *-commutative 53.1%

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

   5. Simplified 53.1%

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

   if 1.45000000000000001e32 < t < 7.50000000000000018e109

   1. Initial program 71.5%

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

   3. Taylor expanded in y around inf 63.6%

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

      1. +-commutative 63.6%

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

      2. mul-1-neg 63.6%

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

      3. unsub-neg 63.6%

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

      4. *-commutative 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in z around inf 51.7%

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

      1. *-commutative 51.7%

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

   8. Simplified 51.7%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+109}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+211}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot c - y \cdot i\\ \mathbf{if}\;j \leq -7.2 \cdot 10^{+24}:\\ \;\;\;\;j \cdot \left(t\_1 + \frac{a \cdot \left(b \cdot i\right)}{j}\right)\\ \mathbf{elif}\;j \leq 10^{+205}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t c) (* y i))))
   (if (<= j -7.2e+24)
     (* j (+ t_1 (/ (* a (* b i)) j)))
     (if (<= j 1e+205)
       (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
       (* j t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * c) - (y * i);
	double tmp;
	if (j <= -7.2e+24) {
		tmp = j * (t_1 + ((a * (b * i)) / j));
	} else if (j <= 1e+205) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = j * t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * c) - (y * i)
    if (j <= (-7.2d+24)) then
        tmp = j * (t_1 + ((a * (b * i)) / j))
    else if (j <= 1d+205) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else
        tmp = j * t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * c) - (y * i);
	double tmp;
	if (j <= -7.2e+24) {
		tmp = j * (t_1 + ((a * (b * i)) / j));
	} else if (j <= 1e+205) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = j * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * c) - (y * i)
	tmp = 0
	if j <= -7.2e+24:
		tmp = j * (t_1 + ((a * (b * i)) / j))
	elif j <= 1e+205:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	else:
		tmp = j * t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * c) - Float64(y * i))
	tmp = 0.0
	if (j <= -7.2e+24)
		tmp = Float64(j * Float64(t_1 + Float64(Float64(a * Float64(b * i)) / j)));
	elseif (j <= 1e+205)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(j * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * c) - (y * i);
	tmp = 0.0;
	if (j <= -7.2e+24)
		tmp = j * (t_1 + ((a * (b * i)) / j));
	elseif (j <= 1e+205)
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	else
		tmp = j * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.2e+24], N[(j * N[(t$95$1 + N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1e+205], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -7.19999999999999966e24

   1. Initial program 72.9%

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

   3. Taylor expanded in j around -inf 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in i around inf 77.1%

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

   if -7.19999999999999966e24 < j < 1.00000000000000002e205

   1. Initial program 79.3%

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

   3. Taylor expanded in j around 0 75.2%

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

      1. *-commutative 75.2%

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

      2. *-commutative 75.2%

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

   5. Simplified 75.2%

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

   if 1.00000000000000002e205 < j

   1. Initial program 53.3%

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

   3. Taylor expanded in x around 0 60.0%

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

      1. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in j around inf 80.0%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.2 \cdot 10^{+24}:\\ \;\;\;\;j \cdot \left(\left(t \cdot c - y \cdot i\right) + \frac{a \cdot \left(b \cdot i\right)}{j}\right)\\ \mathbf{elif}\;j \leq 10^{+205}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+46}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+157}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -1.5e+46)
     (- t_1 (* b (* z c)))
     (if (<= x 2.7e+157)
       (+ (* j (- (* t c) (* y i))) (* b (- (* a i) (* z c))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.5e+46) {
		tmp = t_1 - (b * (z * c));
	} else if (x <= 2.7e+157) {
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-1.5d+46)) then
        tmp = t_1 - (b * (z * c))
    else if (x <= 2.7d+157) then
        tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.5e+46) {
		tmp = t_1 - (b * (z * c));
	} else if (x <= 2.7e+157) {
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.5e+46:
		tmp = t_1 - (b * (z * c))
	elif x <= 2.7e+157:
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.5e+46)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	elseif (x <= 2.7e+157)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.5e+46)
		tmp = t_1 - (b * (z * c));
	elseif (x <= 2.7e+157)
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e+46], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+157], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.50000000000000012e46

   1. Initial program 69.9%

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

   3. Taylor expanded in j around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. *-commutative 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in c around inf 77.5%

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

   if -1.50000000000000012e46 < x < 2.7e157

   1. Initial program 79.0%

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

   3. Taylor expanded in x around 0 71.0%

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

      1. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   if 2.7e157 < x

   1. Initial program 74.2%

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

   3. Taylor expanded in x around inf 80.6%

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

      1. *-commutative 80.6%

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

   5. Simplified 80.6%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+157}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(-x\right)\right)\\ t_2 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;c \leq -1.2 \cdot 10^{+63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{-204}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* t (- x)))) (t_2 (* j (* t c))))
   (if (<= c -1.2e+63)
     t_2
     (if (<= c -1e-271)
       t_1
       (if (<= c 3.3e-204) (* b (* a i)) (if (<= c 2e+103) 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 * (t * -x);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -1.2e+63) {
		tmp = t_2;
	} else if (c <= -1e-271) {
		tmp = t_1;
	} else if (c <= 3.3e-204) {
		tmp = b * (a * i);
	} else if (c <= 2e+103) {
		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 * (t * -x)
    t_2 = j * (t * c)
    if (c <= (-1.2d+63)) then
        tmp = t_2
    else if (c <= (-1d-271)) then
        tmp = t_1
    else if (c <= 3.3d-204) then
        tmp = b * (a * i)
    else if (c <= 2d+103) 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 * (t * -x);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -1.2e+63) {
		tmp = t_2;
	} else if (c <= -1e-271) {
		tmp = t_1;
	} else if (c <= 3.3e-204) {
		tmp = b * (a * i);
	} else if (c <= 2e+103) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (t * -x)
	t_2 = j * (t * c)
	tmp = 0
	if c <= -1.2e+63:
		tmp = t_2
	elif c <= -1e-271:
		tmp = t_1
	elif c <= 3.3e-204:
		tmp = b * (a * i)
	elif c <= 2e+103:
		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(t * Float64(-x)))
	t_2 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (c <= -1.2e+63)
		tmp = t_2;
	elseif (c <= -1e-271)
		tmp = t_1;
	elseif (c <= 3.3e-204)
		tmp = Float64(b * Float64(a * i));
	elseif (c <= 2e+103)
		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 * (t * -x);
	t_2 = j * (t * c);
	tmp = 0.0;
	if (c <= -1.2e+63)
		tmp = t_2;
	elseif (c <= -1e-271)
		tmp = t_1;
	elseif (c <= 3.3e-204)
		tmp = b * (a * i);
	elseif (c <= 2e+103)
		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[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.2e+63], t$95$2, If[LessEqual[c, -1e-271], t$95$1, If[LessEqual[c, 3.3e-204], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2e+103], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.2e63 or 2e103 < c

   1. Initial program 68.1%

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

   3. Taylor expanded in x around 0 62.4%

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

      1. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in j around inf 43.4%

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

   7. Taylor expanded in c around inf 42.3%

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

   if -1.2e63 < c < -9.99999999999999963e-272 or 3.30000000000000009e-204 < c < 2e103

   1. Initial program 80.6%

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

   3. Taylor expanded in z around 0 63.5%

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

   4. Taylor expanded in x around inf 35.4%

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

      1. *-commutative 35.4%

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

      2. neg-mul-1 35.4%

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

      3. distribute-rgt-neg-in 35.4%

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

      4. *-commutative 35.4%

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

      5. mul-1-neg 35.4%

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

      6. associate-*r* 35.4%

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

      7. mul-1-neg 35.4%

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

   6. Simplified 35.4%

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

   if -9.99999999999999963e-272 < c < 3.30000000000000009e-204

   1. Initial program 85.9%

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

   3. Taylor expanded in b around inf 58.9%

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

      1. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in i around inf 58.9%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{+63}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-271}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{-204}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+103}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;c \leq -8 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))) (t_2 (* j (* t c))))
   (if (<= c -8e+62)
     t_2
     (if (<= c -2e-82)
       t_1
       (if (<= c -6.8e-183) (* x (* y z)) (if (<= c 2e-59) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -8e+62) {
		tmp = t_2;
	} else if (c <= -2e-82) {
		tmp = t_1;
	} else if (c <= -6.8e-183) {
		tmp = x * (y * z);
	} else if (c <= 2e-59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * i)
    t_2 = j * (t * c)
    if (c <= (-8d+62)) then
        tmp = t_2
    else if (c <= (-2d-82)) then
        tmp = t_1
    else if (c <= (-6.8d-183)) then
        tmp = x * (y * z)
    else if (c <= 2d-59) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -8e+62) {
		tmp = t_2;
	} else if (c <= -2e-82) {
		tmp = t_1;
	} else if (c <= -6.8e-183) {
		tmp = x * (y * z);
	} else if (c <= 2e-59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	t_2 = j * (t * c)
	tmp = 0
	if c <= -8e+62:
		tmp = t_2
	elif c <= -2e-82:
		tmp = t_1
	elif c <= -6.8e-183:
		tmp = x * (y * z)
	elif c <= 2e-59:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	t_2 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (c <= -8e+62)
		tmp = t_2;
	elseif (c <= -2e-82)
		tmp = t_1;
	elseif (c <= -6.8e-183)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 2e-59)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	t_2 = j * (t * c);
	tmp = 0.0;
	if (c <= -8e+62)
		tmp = t_2;
	elseif (c <= -2e-82)
		tmp = t_1;
	elseif (c <= -6.8e-183)
		tmp = x * (y * z);
	elseif (c <= 2e-59)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8e+62], t$95$2, If[LessEqual[c, -2e-82], t$95$1, If[LessEqual[c, -6.8e-183], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2e-59], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -8.00000000000000028e62 or 2.0000000000000001e-59 < c

   1. Initial program 68.2%

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

   3. Taylor expanded in x around 0 62.0%

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

      1. *-commutative 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in j around inf 44.9%

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

   7. Taylor expanded in c around inf 35.9%

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

   if -8.00000000000000028e62 < c < -2e-82 or -6.80000000000000029e-183 < c < 2.0000000000000001e-59

   1. Initial program 84.9%

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

   3. Taylor expanded in b around inf 48.0%

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

      1. *-commutative 48.0%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in i around inf 42.5%

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

   if -2e-82 < c < -6.80000000000000029e-183

   1. Initial program 84.9%

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

   3. Taylor expanded in y around inf 43.6%

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

      1. +-commutative 43.6%

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

      2. mul-1-neg 43.6%

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

      3. unsub-neg 43.6%

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

      4. *-commutative 43.6%

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

   5. Simplified 43.6%

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

   6. Taylor expanded in z around inf 28.3%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;c \leq -2.1 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* t c))))
   (if (<= c -2.1e+63)
     t_1
     (if (<= c 7e-157) (* b (* a i)) (if (<= c 8.5e+76) (* y (* x z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (c <= -2.1e+63) {
		tmp = t_1;
	} else if (c <= 7e-157) {
		tmp = b * (a * i);
	} else if (c <= 8.5e+76) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (t * c)
    if (c <= (-2.1d+63)) then
        tmp = t_1
    else if (c <= 7d-157) then
        tmp = b * (a * i)
    else if (c <= 8.5d+76) then
        tmp = y * (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (c <= -2.1e+63) {
		tmp = t_1;
	} else if (c <= 7e-157) {
		tmp = b * (a * i);
	} else if (c <= 8.5e+76) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (t * c)
	tmp = 0
	if c <= -2.1e+63:
		tmp = t_1
	elif c <= 7e-157:
		tmp = b * (a * i)
	elif c <= 8.5e+76:
		tmp = y * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (c <= -2.1e+63)
		tmp = t_1;
	elseif (c <= 7e-157)
		tmp = Float64(b * Float64(a * i));
	elseif (c <= 8.5e+76)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (t * c);
	tmp = 0.0;
	if (c <= -2.1e+63)
		tmp = t_1;
	elseif (c <= 7e-157)
		tmp = b * (a * i);
	elseif (c <= 8.5e+76)
		tmp = y * (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.1e+63], t$95$1, If[LessEqual[c, 7e-157], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.5e+76], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.1000000000000002e63 or 8.49999999999999992e76 < c

   1. Initial program 65.9%

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

   3. Taylor expanded in x around 0 61.4%

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

      1. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in j around inf 43.3%

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

   7. Taylor expanded in c around inf 41.3%

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

   if -2.1000000000000002e63 < c < 7.0000000000000004e-157

   1. Initial program 84.8%

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

   3. Taylor expanded in b around inf 43.3%

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

      1. *-commutative 43.3%

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

   5. Simplified 43.3%

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

   6. Taylor expanded in i around inf 37.8%

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

   if 7.0000000000000004e-157 < c < 8.49999999999999992e76

   1. Initial program 81.9%

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

   3. Taylor expanded in y around inf 48.3%

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

      1. +-commutative 48.3%

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

      2. mul-1-neg 48.3%

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

      3. unsub-neg 48.3%

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

      4. *-commutative 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in z around inf 29.1%

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

      1. *-commutative 29.1%

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

   8. Simplified 29.1%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.1 \cdot 10^{+63}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.4 \cdot 10^{+63} \lor \neg \left(c \leq 1.95 \cdot 10^{-59}\right):\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -2.4e+63) (not (<= c 1.95e-59))) (* j (* t c)) (* b (* a 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 ((c <= -2.4e+63) || !(c <= 1.95e-59)) {
		tmp = j * (t * c);
	} else {
		tmp = b * (a * 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 ((c <= (-2.4d+63)) .or. (.not. (c <= 1.95d-59))) then
        tmp = j * (t * c)
    else
        tmp = b * (a * 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 ((c <= -2.4e+63) || !(c <= 1.95e-59)) {
		tmp = j * (t * c);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -2.4e+63) or not (c <= 1.95e-59):
		tmp = j * (t * c)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -2.4e+63) || !(c <= 1.95e-59))
		tmp = Float64(j * Float64(t * c));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -2.4e+63) || ~((c <= 1.95e-59)))
		tmp = j * (t * c);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -2.4e+63], N[Not[LessEqual[c, 1.95e-59]], $MachinePrecision]], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.4e63 or 1.95000000000000009e-59 < c

   1. Initial program 68.2%

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

   3. Taylor expanded in x around 0 62.0%

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

      1. *-commutative 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in j around inf 44.9%

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

   7. Taylor expanded in c around inf 35.9%

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

   if -2.4e63 < c < 1.95000000000000009e-59

   1. Initial program 84.9%

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

   3. Taylor expanded in b around inf 41.9%

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

      1. *-commutative 41.9%

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

   5. Simplified 41.9%

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

   6. Taylor expanded in i around inf 36.6%

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

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.4 \cdot 10^{+63} \lor \neg \left(c \leq 1.95 \cdot 10^{-59}\right):\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 29.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.6 \cdot 10^{+62} \lor \neg \left(c \leq 1.85 \cdot 10^{-59}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -6.6e+62) (not (<= c 1.85e-59))) (* c (* t j)) (* b (* a 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 ((c <= -6.6e+62) || !(c <= 1.85e-59)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * 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 ((c <= (-6.6d+62)) .or. (.not. (c <= 1.85d-59))) then
        tmp = c * (t * j)
    else
        tmp = b * (a * 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 ((c <= -6.6e+62) || !(c <= 1.85e-59)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -6.6e+62) or not (c <= 1.85e-59):
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -6.6e+62) || !(c <= 1.85e-59))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -6.6e+62) || ~((c <= 1.85e-59)))
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -6.6e+62], N[Not[LessEqual[c, 1.85e-59]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -6.6e62 or 1.85e-59 < c

   1. Initial program 68.2%

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

   3. Taylor expanded in x around 0 62.0%

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

      1. *-commutative 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in t around inf 31.0%

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

   if -6.6e62 < c < 1.85e-59

   1. Initial program 84.9%

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

   3. Taylor expanded in b around inf 41.9%

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

      1. *-commutative 41.9%

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

   5. Simplified 41.9%

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

   6. Taylor expanded in i around inf 36.6%

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

4. Final simplification 33.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.6 \cdot 10^{+62} \lor \neg \left(c \leq 1.85 \cdot 10^{-59}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 20.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 4.9 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c 4.9e+86) (* b (* a i)) (* a (* x t))))

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 <= 4.9e+86) {
		tmp = b * (a * i);
	} else {
		tmp = a * (x * t);
	}
	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 <= 4.9d+86) then
        tmp = b * (a * i)
    else
        tmp = a * (x * t)
    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 <= 4.9e+86) {
		tmp = b * (a * i);
	} else {
		tmp = a * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= 4.9e+86:
		tmp = b * (a * i)
	else:
		tmp = a * (x * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= 4.9e+86)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(a * Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= 4.9e+86)
		tmp = b * (a * i);
	else
		tmp = a * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, 4.9e+86], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 4.8999999999999999e86

   1. Initial program 80.2%

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

   3. Taylor expanded in b around inf 41.1%

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

      1. *-commutative 41.1%

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

   5. Simplified 41.1%

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

   6. Taylor expanded in i around inf 29.6%

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

   if 4.8999999999999999e86 < c

   1. Initial program 58.9%

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

   3. Taylor expanded in z around 0 28.3%

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

   4. Taylor expanded in x around inf 16.3%

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

      1. *-commutative 16.3%

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

      2. neg-mul-1 16.3%

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

      3. distribute-rgt-neg-in 16.3%

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

      4. *-commutative 16.3%

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

      5. mul-1-neg 16.3%

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

      6. associate-*r* 16.3%

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

      7. mul-1-neg 16.3%

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

   6. Simplified 16.3%

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

      1. pow1 16.3%

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

      2. pow1 16.3%

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

      3. pow1 16.3%

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

      4. associate-*r* 14.3%

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

      5. add-sqr-sqrt 7.2%

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

      6. sqrt-unprod 27.5%

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

      7. sqr-neg 27.5%

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

      8. sqrt-unprod 10.3%

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

      9. add-sqr-sqrt 11.1%

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

      10. *-commutative 11.1%

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

   8. Applied egg-rr 11.1%

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

      1. unpow1 11.1%

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

      2. *-commutative 11.1%

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

      3. associate-*r* 17.1%

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

   10. Simplified 17.1%

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

4. Final simplification 27.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 4.9 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 20.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 5.5 \cdot 10^{+86}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c 5.5e+86) (* a (* b i)) (* a (* x t))))

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 <= 5.5e+86) {
		tmp = a * (b * i);
	} else {
		tmp = a * (x * t);
	}
	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 <= 5.5d+86) then
        tmp = a * (b * i)
    else
        tmp = a * (x * t)
    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 <= 5.5e+86) {
		tmp = a * (b * i);
	} else {
		tmp = a * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= 5.5e+86:
		tmp = a * (b * i)
	else:
		tmp = a * (x * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= 5.5e+86)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(a * Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= 5.5e+86)
		tmp = a * (b * i);
	else
		tmp = a * (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, 5.5e+86], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 5.5000000000000002e86

   1. Initial program 80.2%

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

   3. Taylor expanded in b around inf 41.1%

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

      1. *-commutative 41.1%

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

   5. Simplified 41.1%

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

   6. Taylor expanded in i around inf 28.2%

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

   if 5.5000000000000002e86 < c

   1. Initial program 58.9%

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

   3. Taylor expanded in z around 0 28.3%

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

   4. Taylor expanded in x around inf 16.3%

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

      1. *-commutative 16.3%

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

      2. neg-mul-1 16.3%

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

      3. distribute-rgt-neg-in 16.3%

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

      4. *-commutative 16.3%

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

      5. mul-1-neg 16.3%

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

      6. associate-*r* 16.3%

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

      7. mul-1-neg 16.3%

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

   6. Simplified 16.3%

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

      1. pow1 16.3%

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

      2. pow1 16.3%

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

      3. pow1 16.3%

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

      4. associate-*r* 14.3%

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

      5. add-sqr-sqrt 7.2%

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

      6. sqrt-unprod 27.5%

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

      7. sqr-neg 27.5%

         \[\leadsto {\left(\left(a \cdot \sqrt{\color{blue}{t \cdot t}}\right) \cdot x\right)}^{1} \]

      8. sqrt-unprod 10.3%

         \[\leadsto {\left(\left(a \cdot \color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)}\right) \cdot x\right)}^{1} \]

      9. add-sqr-sqrt 11.1%

         \[\leadsto {\left(\left(a \cdot \color{blue}{t}\right) \cdot x\right)}^{1} \]

      10. *-commutative 11.1%

          \[\leadsto {\left(\color{blue}{\left(t \cdot a\right)} \cdot x\right)}^{1} \]

   8. Applied egg-rr 11.1%

      \[\leadsto \color{blue}{{\left(\left(t \cdot a\right) \cdot x\right)}^{1}} \]
   9. Step-by-step derivation

      1. unpow1 11.1%

         \[\leadsto \color{blue}{\left(t \cdot a\right) \cdot x} \]

      2. *-commutative 11.1%

         \[\leadsto \color{blue}{\left(a \cdot t\right)} \cdot x \]

      3. associate-*r* 17.1%

         \[\leadsto \color{blue}{a \cdot \left(t \cdot x\right)} \]

   10. Simplified 17.1%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 5.5 \cdot 10^{+86}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 22.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * 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 = a * (b * 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 a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.3%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 41.7%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
4. Step-by-step derivation

   1. *-commutative 41.7%

      \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

5. Simplified 41.7%

   \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

6. Taylor expanded in i around inf 24.2%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
7. Add Preprocessing

Developer target: 69.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		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(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		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[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024106 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))