Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.1% → 82.3%

Time: 20.0s

Alternatives: 19

Speedup: 0.5×

• 57.5% 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: 74.1% accurate, 1.0× speedup

Math

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

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: 82.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.2%

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

   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 t around inf 53.1%

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

      1. +-commutative 53.1%

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

      2. mul-1-neg 53.1%

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

      3. unsub-neg 53.1%

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

   5. Simplified 53.1%

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

4. Final simplification 84.6%

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

Alternative 2: 57.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;b \leq -6.2 \cdot 10^{+21}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-296}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-277}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{-104}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* z (* x y)))))
   (if (<= b -6.2e+21)
     (* b (* z (- (* a (/ i z)) c)))
     (if (<= b -3e-296)
       t_1
       (if (<= b 2.15e-296)
         (- (* c (* t j)) (* a (* x t)))
         (if (<= b 1.6e-277)
           t_1
           (if (<= b 2.35e-104)
             (* t (- (* c j) (* x a)))
             (if (<= b 1e+57) t_1 (* b (- (* a i) (* z c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (z * (x * y));
	double tmp;
	if (b <= -6.2e+21) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (b <= -3e-296) {
		tmp = t_1;
	} else if (b <= 2.15e-296) {
		tmp = (c * (t * j)) - (a * (x * t));
	} else if (b <= 1.6e-277) {
		tmp = t_1;
	} else if (b <= 2.35e-104) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 1e+57) {
		tmp = t_1;
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) + (z * (x * y))
    if (b <= (-6.2d+21)) then
        tmp = b * (z * ((a * (i / z)) - c))
    else if (b <= (-3d-296)) then
        tmp = t_1
    else if (b <= 2.15d-296) then
        tmp = (c * (t * j)) - (a * (x * t))
    else if (b <= 1.6d-277) then
        tmp = t_1
    else if (b <= 2.35d-104) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 1d+57) then
        tmp = t_1
    else
        tmp = b * ((a * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (z * (x * y));
	double tmp;
	if (b <= -6.2e+21) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (b <= -3e-296) {
		tmp = t_1;
	} else if (b <= 2.15e-296) {
		tmp = (c * (t * j)) - (a * (x * t));
	} else if (b <= 1.6e-277) {
		tmp = t_1;
	} else if (b <= 2.35e-104) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 1e+57) {
		tmp = t_1;
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (z * (x * y))
	tmp = 0
	if b <= -6.2e+21:
		tmp = b * (z * ((a * (i / z)) - c))
	elif b <= -3e-296:
		tmp = t_1
	elif b <= 2.15e-296:
		tmp = (c * (t * j)) - (a * (x * t))
	elif b <= 1.6e-277:
		tmp = t_1
	elif b <= 2.35e-104:
		tmp = t * ((c * j) - (x * a))
	elif b <= 1e+57:
		tmp = t_1
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(z * Float64(x * y)))
	tmp = 0.0
	if (b <= -6.2e+21)
		tmp = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)));
	elseif (b <= -3e-296)
		tmp = t_1;
	elseif (b <= 2.15e-296)
		tmp = Float64(Float64(c * Float64(t * j)) - Float64(a * Float64(x * t)));
	elseif (b <= 1.6e-277)
		tmp = t_1;
	elseif (b <= 2.35e-104)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 1e+57)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + (z * (x * y));
	tmp = 0.0;
	if (b <= -6.2e+21)
		tmp = b * (z * ((a * (i / z)) - c));
	elseif (b <= -3e-296)
		tmp = t_1;
	elseif (b <= 2.15e-296)
		tmp = (c * (t * j)) - (a * (x * t));
	elseif (b <= 1.6e-277)
		tmp = t_1;
	elseif (b <= 2.35e-104)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 1e+57)
		tmp = t_1;
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.2e+21], N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3e-296], t$95$1, If[LessEqual[b, 2.15e-296], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e-277], t$95$1, If[LessEqual[b, 2.35e-104], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+57], t$95$1, N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.2e21

   1. Initial program 71.7%

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

   3. Taylor expanded in b around inf 60.6%

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

   4. Taylor expanded in z around inf 62.3%

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

      1. associate-/l* 62.4%

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

   6. Simplified 62.4%

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

   if -6.2e21 < b < -2.9999999999999997e-296 or 2.14999999999999989e-296 < b < 1.5999999999999999e-277 or 2.35e-104 < b < 1.00000000000000005e57

   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 y around inf 61.9%

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

      1. *-commutative 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-*r* 62.7%

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

   5. Simplified 62.7%

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

   if -2.9999999999999997e-296 < b < 2.14999999999999989e-296

   1. Initial program 40.0%

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

   3. Taylor expanded in t around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. distribute-rgt-neg-in 60.0%

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

      3. distribute-rgt-neg-in 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in i around 0 80.5%

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

      1. +-commutative 80.5%

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

      2. mul-1-neg 80.5%

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

      3. unsub-neg 80.5%

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

   8. Simplified 80.5%

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

   if 1.5999999999999999e-277 < b < 2.35e-104

   1. Initial program 70.7%

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

   3. Taylor expanded in t around inf 71.6%

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

      1. +-commutative 71.6%

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

      2. mul-1-neg 71.6%

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

      3. unsub-neg 71.6%

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

   5. Simplified 71.6%

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

   if 1.00000000000000005e57 < b

   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 b around inf 76.3%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+21}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-296}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-296}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-277}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{-104}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 10^{+57}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{-24}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-208}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-304}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-277}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* t (- (* c j) (* x a))))
        (t_3 (* b (- (* a i) (* z c)))))
   (if (<= b -5e-24)
     t_3
     (if (<= b -3.4e-57)
       (* x (- (* y z) (* t a)))
       (if (<= b -3.1e-208)
         (* j (- (* t c) (* y i)))
         (if (<= b -6.5e-304)
           t_2
           (if (<= b 1.7e-277)
             t_1
             (if (<= b 4.2e-101) t_2 (if (<= b 1.35e+57) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5e-24) {
		tmp = t_3;
	} else if (b <= -3.4e-57) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= -3.1e-208) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= -6.5e-304) {
		tmp = t_2;
	} else if (b <= 1.7e-277) {
		tmp = t_1;
	} else if (b <= 4.2e-101) {
		tmp = t_2;
	} else if (b <= 1.35e+57) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = t * ((c * j) - (x * a))
    t_3 = b * ((a * i) - (z * c))
    if (b <= (-5d-24)) then
        tmp = t_3
    else if (b <= (-3.4d-57)) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= (-3.1d-208)) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= (-6.5d-304)) then
        tmp = t_2
    else if (b <= 1.7d-277) then
        tmp = t_1
    else if (b <= 4.2d-101) then
        tmp = t_2
    else if (b <= 1.35d+57) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5e-24) {
		tmp = t_3;
	} else if (b <= -3.4e-57) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= -3.1e-208) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= -6.5e-304) {
		tmp = t_2;
	} else if (b <= 1.7e-277) {
		tmp = t_1;
	} else if (b <= 4.2e-101) {
		tmp = t_2;
	} else if (b <= 1.35e+57) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = t * ((c * j) - (x * a))
	t_3 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -5e-24:
		tmp = t_3
	elif b <= -3.4e-57:
		tmp = x * ((y * z) - (t * a))
	elif b <= -3.1e-208:
		tmp = j * ((t * c) - (y * i))
	elif b <= -6.5e-304:
		tmp = t_2
	elif b <= 1.7e-277:
		tmp = t_1
	elif b <= 4.2e-101:
		tmp = t_2
	elif b <= 1.35e+57:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5e-24)
		tmp = t_3;
	elseif (b <= -3.4e-57)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= -3.1e-208)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= -6.5e-304)
		tmp = t_2;
	elseif (b <= 1.7e-277)
		tmp = t_1;
	elseif (b <= 4.2e-101)
		tmp = t_2;
	elseif (b <= 1.35e+57)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = t * ((c * j) - (x * a));
	t_3 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -5e-24)
		tmp = t_3;
	elseif (b <= -3.4e-57)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= -3.1e-208)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= -6.5e-304)
		tmp = t_2;
	elseif (b <= 1.7e-277)
		tmp = t_1;
	elseif (b <= 4.2e-101)
		tmp = t_2;
	elseif (b <= 1.35e+57)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e-24], t$95$3, If[LessEqual[b, -3.4e-57], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.1e-208], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.5e-304], t$95$2, If[LessEqual[b, 1.7e-277], t$95$1, If[LessEqual[b, 4.2e-101], t$95$2, If[LessEqual[b, 1.35e+57], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.9999999999999998e-24 or 1.3499999999999999e57 < b

   1. Initial program 76.6%

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

   3. Taylor expanded in b around inf 66.4%

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

   if -4.9999999999999998e-24 < b < -3.40000000000000016e-57

   1. Initial program 62.3%

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

   3. Taylor expanded in x around inf 87.6%

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

      1. *-commutative 87.6%

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

   5. Simplified 87.6%

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

   if -3.40000000000000016e-57 < b < -3.0999999999999998e-208

   1. Initial program 66.7%

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

   3. Taylor expanded in c around 0 63.0%

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

   4. Taylor expanded in j around inf 59.2%

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

      1. mul-1-neg 59.2%

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

      2. distribute-lft-neg-out 59.2%

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

      3. +-commutative 59.2%

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

      4. cancel-sign-sub-inv 59.2%

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

   6. Simplified 59.2%

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

   if -3.0999999999999998e-208 < b < -6.50000000000000011e-304 or 1.69999999999999991e-277 < b < 4.20000000000000031e-101

   1. Initial program 70.4%

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

   3. Taylor expanded in t around inf 72.8%

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

      1. +-commutative 72.8%

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

      2. mul-1-neg 72.8%

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

      3. unsub-neg 72.8%

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

   5. Simplified 72.8%

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

   if -6.50000000000000011e-304 < b < 1.69999999999999991e-277 or 4.20000000000000031e-101 < b < 1.3499999999999999e57

   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 y around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

      4. *-commutative 60.0%

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

   5. Simplified 60.0%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-24}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-208}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-304}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{-22}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{-208}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-306}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-277}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= b -3.2e-22)
     (* b (* z (- (* a (/ i z)) c)))
     (if (<= b -3.8e-53)
       (* x (- (* y z) (* t a)))
       (if (<= b -6.4e-208)
         (* j (- (* t c) (* y i)))
         (if (<= b -5.5e-306)
           t_2
           (if (<= b 1.55e-277)
             t_1
             (if (<= b 1.5e-106)
               t_2
               (if (<= b 3.8e+56) t_1 (* b (- (* a i) (* z c))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (b <= -3.2e-22) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (b <= -3.8e-53) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= -6.4e-208) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= -5.5e-306) {
		tmp = t_2;
	} else if (b <= 1.55e-277) {
		tmp = t_1;
	} else if (b <= 1.5e-106) {
		tmp = t_2;
	} else if (b <= 3.8e+56) {
		tmp = t_1;
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = t * ((c * j) - (x * a))
    if (b <= (-3.2d-22)) then
        tmp = b * (z * ((a * (i / z)) - c))
    else if (b <= (-3.8d-53)) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= (-6.4d-208)) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= (-5.5d-306)) then
        tmp = t_2
    else if (b <= 1.55d-277) then
        tmp = t_1
    else if (b <= 1.5d-106) then
        tmp = t_2
    else if (b <= 3.8d+56) then
        tmp = t_1
    else
        tmp = b * ((a * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (b <= -3.2e-22) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (b <= -3.8e-53) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= -6.4e-208) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= -5.5e-306) {
		tmp = t_2;
	} else if (b <= 1.55e-277) {
		tmp = t_1;
	} else if (b <= 1.5e-106) {
		tmp = t_2;
	} else if (b <= 3.8e+56) {
		tmp = t_1;
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if b <= -3.2e-22:
		tmp = b * (z * ((a * (i / z)) - c))
	elif b <= -3.8e-53:
		tmp = x * ((y * z) - (t * a))
	elif b <= -6.4e-208:
		tmp = j * ((t * c) - (y * i))
	elif b <= -5.5e-306:
		tmp = t_2
	elif b <= 1.55e-277:
		tmp = t_1
	elif b <= 1.5e-106:
		tmp = t_2
	elif b <= 3.8e+56:
		tmp = t_1
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (b <= -3.2e-22)
		tmp = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)));
	elseif (b <= -3.8e-53)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= -6.4e-208)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= -5.5e-306)
		tmp = t_2;
	elseif (b <= 1.55e-277)
		tmp = t_1;
	elseif (b <= 1.5e-106)
		tmp = t_2;
	elseif (b <= 3.8e+56)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (b <= -3.2e-22)
		tmp = b * (z * ((a * (i / z)) - c));
	elseif (b <= -3.8e-53)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= -6.4e-208)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= -5.5e-306)
		tmp = t_2;
	elseif (b <= 1.55e-277)
		tmp = t_1;
	elseif (b <= 1.5e-106)
		tmp = t_2;
	elseif (b <= 3.8e+56)
		tmp = t_1;
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e-22], N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.8e-53], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.4e-208], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.5e-306], t$95$2, If[LessEqual[b, 1.55e-277], t$95$1, If[LessEqual[b, 1.5e-106], t$95$2, If[LessEqual[b, 3.8e+56], t$95$1, N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -3.19999999999999987e-22

   1. Initial program 72.7%

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

   3. Taylor expanded in b around inf 59.7%

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

   4. Taylor expanded in z around inf 59.9%

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

      1. associate-/l* 59.9%

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

   6. Simplified 59.9%

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

   if -3.19999999999999987e-22 < b < -3.7999999999999998e-53

   1. Initial program 62.3%

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

   3. Taylor expanded in x around inf 87.6%

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

      1. *-commutative 87.6%

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

   5. Simplified 87.6%

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

   if -3.7999999999999998e-53 < b < -6.4000000000000003e-208

   1. Initial program 66.7%

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

   3. Taylor expanded in c around 0 63.0%

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

   4. Taylor expanded in j around inf 59.2%

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

      1. mul-1-neg 59.2%

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

      2. distribute-lft-neg-out 59.2%

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

      3. +-commutative 59.2%

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

      4. cancel-sign-sub-inv 59.2%

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

   6. Simplified 59.2%

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

   if -6.4000000000000003e-208 < b < -5.49999999999999992e-306 or 1.5499999999999999e-277 < b < 1.50000000000000009e-106

   1. Initial program 70.4%

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

   3. Taylor expanded in t around inf 72.8%

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

      1. +-commutative 72.8%

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

      2. mul-1-neg 72.8%

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

      3. unsub-neg 72.8%

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

   5. Simplified 72.8%

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

   if -5.49999999999999992e-306 < b < 1.5499999999999999e-277 or 1.50000000000000009e-106 < b < 3.79999999999999996e56

   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 y around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

      4. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   if 3.79999999999999996e56 < b

   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 b around inf 76.3%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{-22}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{-208}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-306}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+182}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{-23}:\\ \;\;\;\;a \cdot \left(i \cdot \left(b - t \cdot \frac{x}{i}\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-215}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 8500:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t (- (* c j) (* x a))) (* y (* i j))))
        (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -2.05e+182)
     t_2
     (if (<= b -2e+150)
       t_1
       (if (<= b -8.6e-23)
         (* a (* i (- b (* t (/ x i)))))
         (if (<= b -1.7e-215)
           (- (* j (- (* t c) (* y i))) (* a (* x t)))
           (if (<= b 8500.0) 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 * ((c * j) - (x * a))) - (y * (i * j));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.05e+182) {
		tmp = t_2;
	} else if (b <= -2e+150) {
		tmp = t_1;
	} else if (b <= -8.6e-23) {
		tmp = a * (i * (b - (t * (x / i))));
	} else if (b <= -1.7e-215) {
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t));
	} else if (b <= 8500.0) {
		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 * ((c * j) - (x * a))) - (y * (i * j))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-2.05d+182)) then
        tmp = t_2
    else if (b <= (-2d+150)) then
        tmp = t_1
    else if (b <= (-8.6d-23)) then
        tmp = a * (i * (b - (t * (x / i))))
    else if (b <= (-1.7d-215)) then
        tmp = (j * ((t * c) - (y * i))) - (a * (x * t))
    else if (b <= 8500.0d0) 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 * ((c * j) - (x * a))) - (y * (i * j));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.05e+182) {
		tmp = t_2;
	} else if (b <= -2e+150) {
		tmp = t_1;
	} else if (b <= -8.6e-23) {
		tmp = a * (i * (b - (t * (x / i))));
	} else if (b <= -1.7e-215) {
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t));
	} else if (b <= 8500.0) {
		tmp = t_1;
	} 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))) - (y * (i * j))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -2.05e+182:
		tmp = t_2
	elif b <= -2e+150:
		tmp = t_1
	elif b <= -8.6e-23:
		tmp = a * (i * (b - (t * (x / i))))
	elif b <= -1.7e-215:
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t))
	elif b <= 8500.0:
		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 * Float64(Float64(c * j) - Float64(x * a))) - Float64(y * Float64(i * j)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.05e+182)
		tmp = t_2;
	elseif (b <= -2e+150)
		tmp = t_1;
	elseif (b <= -8.6e-23)
		tmp = Float64(a * Float64(i * Float64(b - Float64(t * Float64(x / i)))));
	elseif (b <= -1.7e-215)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(a * Float64(x * t)));
	elseif (b <= 8500.0)
		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 * ((c * j) - (x * a))) - (y * (i * j));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.05e+182)
		tmp = t_2;
	elseif (b <= -2e+150)
		tmp = t_1;
	elseif (b <= -8.6e-23)
		tmp = a * (i * (b - (t * (x / i))));
	elseif (b <= -1.7e-215)
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t));
	elseif (b <= 8500.0)
		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 * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.05e+182], t$95$2, If[LessEqual[b, -2e+150], t$95$1, If[LessEqual[b, -8.6e-23], N[(a * N[(i * N[(b - N[(t * N[(x / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.7e-215], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8500.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.05000000000000001e182 or 8500 < b

   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 68.2%

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

   if -2.05000000000000001e182 < b < -1.99999999999999996e150 or -1.70000000000000001e-215 < b < 8500

   1. Initial program 72.2%

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

   3. Taylor expanded in t around inf 69.1%

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

      1. mul-1-neg 69.1%

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

      2. distribute-rgt-neg-in 69.1%

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

      3. distribute-rgt-neg-in 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in t around 0 75.5%

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

      1. +-commutative 75.5%

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

      2. mul-1-neg 75.5%

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

      3. unsub-neg 75.5%

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

      4. +-commutative 75.5%

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

      5. mul-1-neg 75.5%

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

      6. unsub-neg 75.5%

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

      7. *-commutative 75.5%

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

      8. associate-*r* 74.7%

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

   8. Simplified 74.7%

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

   if -1.99999999999999996e150 < b < -8.60000000000000004e-23

   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 a around inf 55.9%

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

      1. distribute-lft-out-- 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in i around inf 65.3%

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

      1. associate-/l* 62.0%

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

   8. Simplified 62.0%

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

   if -8.60000000000000004e-23 < b < -1.70000000000000001e-215

   1. Initial program 63.8%

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

   3. Taylor expanded in t around inf 69.5%

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

      1. mul-1-neg 69.5%

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

      2. distribute-rgt-neg-in 69.5%

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

      3. distribute-rgt-neg-in 69.5%

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

   5. Simplified 69.5%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+182}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{-23}:\\ \;\;\;\;a \cdot \left(i \cdot \left(b - t \cdot \frac{x}{i}\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-215}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 8500:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot t\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -3.8 \cdot 10^{+40}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - t\_1\\ \mathbf{elif}\;j \leq -1020000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-20}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(c \cdot \frac{t}{i} - y\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x t)))
        (t_2 (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))))
   (if (<= j -3.8e+40)
     (- (* j (- (* t c) (* y i))) t_1)
     (if (<= j -1020000.0)
       t_2
       (if (<= j -8e-20)
         (* c (- (* t j) (* z b)))
         (if (<= j 1.45e+93) t_2 (- (* j (* i (- (* c (/ t i)) y))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * t);
	double t_2 = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	double tmp;
	if (j <= -3.8e+40) {
		tmp = (j * ((t * c) - (y * i))) - t_1;
	} else if (j <= -1020000.0) {
		tmp = t_2;
	} else if (j <= -8e-20) {
		tmp = c * ((t * j) - (z * b));
	} else if (j <= 1.45e+93) {
		tmp = t_2;
	} else {
		tmp = (j * (i * ((c * (t / i)) - y))) - 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 = a * (x * t)
    t_2 = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    if (j <= (-3.8d+40)) then
        tmp = (j * ((t * c) - (y * i))) - t_1
    else if (j <= (-1020000.0d0)) then
        tmp = t_2
    else if (j <= (-8d-20)) then
        tmp = c * ((t * j) - (z * b))
    else if (j <= 1.45d+93) then
        tmp = t_2
    else
        tmp = (j * (i * ((c * (t / i)) - y))) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * t);
	double t_2 = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	double tmp;
	if (j <= -3.8e+40) {
		tmp = (j * ((t * c) - (y * i))) - t_1;
	} else if (j <= -1020000.0) {
		tmp = t_2;
	} else if (j <= -8e-20) {
		tmp = c * ((t * j) - (z * b));
	} else if (j <= 1.45e+93) {
		tmp = t_2;
	} else {
		tmp = (j * (i * ((c * (t / i)) - y))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * t)
	t_2 = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	tmp = 0
	if j <= -3.8e+40:
		tmp = (j * ((t * c) - (y * i))) - t_1
	elif j <= -1020000.0:
		tmp = t_2
	elif j <= -8e-20:
		tmp = c * ((t * j) - (z * b))
	elif j <= 1.45e+93:
		tmp = t_2
	else:
		tmp = (j * (i * ((c * (t / i)) - y))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * t))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (j <= -3.8e+40)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - t_1);
	elseif (j <= -1020000.0)
		tmp = t_2;
	elseif (j <= -8e-20)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (j <= 1.45e+93)
		tmp = t_2;
	else
		tmp = Float64(Float64(j * Float64(i * Float64(Float64(c * Float64(t / i)) - y))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (x * t);
	t_2 = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	tmp = 0.0;
	if (j <= -3.8e+40)
		tmp = (j * ((t * c) - (y * i))) - t_1;
	elseif (j <= -1020000.0)
		tmp = t_2;
	elseif (j <= -8e-20)
		tmp = c * ((t * j) - (z * b));
	elseif (j <= 1.45e+93)
		tmp = t_2;
	else
		tmp = (j * (i * ((c * (t / i)) - y))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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, -3.8e+40], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[j, -1020000.0], t$95$2, If[LessEqual[j, -8e-20], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.45e+93], t$95$2, N[(N[(j * N[(i * N[(N[(c * N[(t / i), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.80000000000000004e40

   1. Initial program 74.4%

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

   3. Taylor expanded in t around inf 69.9%

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

      1. mul-1-neg 69.9%

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

      2. distribute-rgt-neg-in 69.9%

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

      3. distribute-rgt-neg-in 69.9%

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

   5. Simplified 69.9%

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

   if -3.80000000000000004e40 < j < -1.02e6 or -7.99999999999999956e-20 < j < 1.4499999999999999e93

   1. Initial program 74.7%

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

   3. Taylor expanded in j around 0 76.8%

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

      1. *-commutative 76.8%

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

   5. Simplified 76.8%

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

   if -1.02e6 < j < -7.99999999999999956e-20

   1. Initial program 84.7%

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

   3. Taylor expanded in c around inf 99.3%

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

   if 1.4499999999999999e93 < j

   1. Initial program 66.5%

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

   3. Taylor expanded in t around inf 65.3%

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

      1. mul-1-neg 65.3%

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

      2. distribute-rgt-neg-in 65.3%

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

      3. distribute-rgt-neg-in 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in i around inf 67.2%

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

      1. associate-/l* 71.2%

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

   8. Simplified 71.2%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.8 \cdot 10^{+40}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq -1020000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -8 \cdot 10^{-20}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(c \cdot \frac{t}{i} - y\right)\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.15 \cdot 10^{+182}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(i \cdot \left(b - t \cdot \frac{x}{i}\right)\right)\\ \mathbf{elif}\;b \leq 112:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t (- (* c j) (* x a))) (* y (* i j))))
        (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -2.15e+182)
     t_2
     (if (<= b -1.2e+150)
       t_1
       (if (<= b -1.1e-21)
         (* a (* i (- b (* t (/ x i)))))
         (if (<= b 112.0) 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 * ((c * j) - (x * a))) - (y * (i * j));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.15e+182) {
		tmp = t_2;
	} else if (b <= -1.2e+150) {
		tmp = t_1;
	} else if (b <= -1.1e-21) {
		tmp = a * (i * (b - (t * (x / i))));
	} else if (b <= 112.0) {
		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 * ((c * j) - (x * a))) - (y * (i * j))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-2.15d+182)) then
        tmp = t_2
    else if (b <= (-1.2d+150)) then
        tmp = t_1
    else if (b <= (-1.1d-21)) then
        tmp = a * (i * (b - (t * (x / i))))
    else if (b <= 112.0d0) 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 * ((c * j) - (x * a))) - (y * (i * j));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.15e+182) {
		tmp = t_2;
	} else if (b <= -1.2e+150) {
		tmp = t_1;
	} else if (b <= -1.1e-21) {
		tmp = a * (i * (b - (t * (x / i))));
	} else if (b <= 112.0) {
		tmp = t_1;
	} 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))) - (y * (i * j))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -2.15e+182:
		tmp = t_2
	elif b <= -1.2e+150:
		tmp = t_1
	elif b <= -1.1e-21:
		tmp = a * (i * (b - (t * (x / i))))
	elif b <= 112.0:
		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 * Float64(Float64(c * j) - Float64(x * a))) - Float64(y * Float64(i * j)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.15e+182)
		tmp = t_2;
	elseif (b <= -1.2e+150)
		tmp = t_1;
	elseif (b <= -1.1e-21)
		tmp = Float64(a * Float64(i * Float64(b - Float64(t * Float64(x / i)))));
	elseif (b <= 112.0)
		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 * ((c * j) - (x * a))) - (y * (i * j));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.15e+182)
		tmp = t_2;
	elseif (b <= -1.2e+150)
		tmp = t_1;
	elseif (b <= -1.1e-21)
		tmp = a * (i * (b - (t * (x / i))));
	elseif (b <= 112.0)
		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 * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.15e+182], t$95$2, If[LessEqual[b, -1.2e+150], t$95$1, If[LessEqual[b, -1.1e-21], N[(a * N[(i * N[(b - N[(t * N[(x / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 112.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.1500000000000001e182 or 112 < b

   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 68.2%

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

   if -2.1500000000000001e182 < b < -1.20000000000000001e150 or -1.1e-21 < b < 112

   1. Initial program 70.1%

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

   3. Taylor expanded in t around inf 69.2%

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

      1. mul-1-neg 69.2%

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

      2. distribute-rgt-neg-in 69.2%

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

      3. distribute-rgt-neg-in 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in t around 0 71.3%

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

      1. +-commutative 71.3%

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

      2. mul-1-neg 71.3%

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

      3. unsub-neg 71.3%

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

      4. +-commutative 71.3%

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

      5. mul-1-neg 71.3%

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

      6. unsub-neg 71.3%

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

      7. *-commutative 71.3%

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

      8. associate-*r* 69.2%

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

   8. Simplified 69.2%

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

   if -1.20000000000000001e150 < b < -1.1e-21

   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 a around inf 55.9%

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

      1. distribute-lft-out-- 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in i around inf 65.3%

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

      1. associate-/l* 62.0%

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

   8. Simplified 62.0%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+182}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(i \cdot \left(b - t \cdot \frac{x}{i}\right)\right)\\ \mathbf{elif}\;b \leq 112:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 42.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -6.9 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-163}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 0.021:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -6.9e-31)
     t_1
     (if (<= b 3e-163)
       (* c (* t j))
       (if (<= b 1.05e-72)
         (* x (* t (- a)))
         (if (<= b 9.5e-37)
           (* y (* x z))
           (if (<= b 0.021) (* y (* 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -6.9e-31) {
		tmp = t_1;
	} else if (b <= 3e-163) {
		tmp = c * (t * j);
	} else if (b <= 1.05e-72) {
		tmp = x * (t * -a);
	} else if (b <= 9.5e-37) {
		tmp = y * (x * z);
	} else if (b <= 0.021) {
		tmp = y * (i * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-6.9d-31)) then
        tmp = t_1
    else if (b <= 3d-163) then
        tmp = c * (t * j)
    else if (b <= 1.05d-72) then
        tmp = x * (t * -a)
    else if (b <= 9.5d-37) then
        tmp = y * (x * z)
    else if (b <= 0.021d0) then
        tmp = y * (i * -j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -6.9e-31) {
		tmp = t_1;
	} else if (b <= 3e-163) {
		tmp = c * (t * j);
	} else if (b <= 1.05e-72) {
		tmp = x * (t * -a);
	} else if (b <= 9.5e-37) {
		tmp = y * (x * z);
	} else if (b <= 0.021) {
		tmp = y * (i * -j);
	} 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 <= -6.9e-31:
		tmp = t_1
	elif b <= 3e-163:
		tmp = c * (t * j)
	elif b <= 1.05e-72:
		tmp = x * (t * -a)
	elif b <= 9.5e-37:
		tmp = y * (x * z)
	elif b <= 0.021:
		tmp = y * (i * -j)
	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 <= -6.9e-31)
		tmp = t_1;
	elseif (b <= 3e-163)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 1.05e-72)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (b <= 9.5e-37)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 0.021)
		tmp = Float64(y * Float64(i * Float64(-j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -6.9e-31)
		tmp = t_1;
	elseif (b <= 3e-163)
		tmp = c * (t * j);
	elseif (b <= 1.05e-72)
		tmp = x * (t * -a);
	elseif (b <= 9.5e-37)
		tmp = y * (x * z);
	elseif (b <= 0.021)
		tmp = y * (i * -j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.9e-31], t$95$1, If[LessEqual[b, 3e-163], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e-72], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e-37], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.021], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.9000000000000004e-31 or 0.0210000000000000013 < b

   1. Initial program 77.3%

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

   3. Taylor expanded in b around inf 63.3%

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

   if -6.9000000000000004e-31 < b < 3.0000000000000002e-163

   1. Initial program 66.7%

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

   3. Taylor expanded in t around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. distribute-rgt-neg-in 67.2%

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

      3. distribute-rgt-neg-in 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in c around inf 41.7%

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

   if 3.0000000000000002e-163 < b < 1.05e-72

   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 x around inf 46.3%

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

      1. *-commutative 46.3%

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

   5. Simplified 46.3%

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

   6. Taylor expanded in z around 0 46.4%

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

      1. mul-1-neg 46.4%

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

      2. distribute-lft-neg-out 46.4%

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

      3. *-commutative 46.4%

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

   8. Simplified 46.4%

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

   if 1.05e-72 < b < 9.49999999999999927e-37

   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 y around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. unsub-neg 67.1%

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

      4. *-commutative 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in z around inf 45.9%

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

      1. *-commutative 45.9%

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

      2. associate-*r* 56.5%

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

   8. Simplified 56.5%

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

   if 9.49999999999999927e-37 < b < 0.0210000000000000013

   1. Initial program 70.7%

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

   3. Taylor expanded in y around inf 42.9%

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

      1. +-commutative 42.9%

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

      2. mul-1-neg 42.9%

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

      3. unsub-neg 42.9%

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

      4. *-commutative 42.9%

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

   5. Simplified 42.9%

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

   6. Taylor expanded in z around 0 52.6%

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

      1. mul-1-neg 52.6%

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

      2. *-commutative 52.6%

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

      3. distribute-rgt-neg-in 52.6%

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

      4. *-commutative 52.6%

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

      5. associate-*r* 52.8%

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

   8. Simplified 52.8%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.9 \cdot 10^{-31}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-163}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 0.021:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 44.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-162}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 0.00029:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -3.6e-13)
     t_1
     (if (<= b 1.3e-162)
       (* c (- (* t j) (* z b)))
       (if (<= b 2.7e-72)
         (* x (* t (- a)))
         (if (<= b 5.5e-37)
           (* y (* x z))
           (if (<= b 0.00029) (* y (* 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.6e-13) {
		tmp = t_1;
	} else if (b <= 1.3e-162) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 2.7e-72) {
		tmp = x * (t * -a);
	} else if (b <= 5.5e-37) {
		tmp = y * (x * z);
	} else if (b <= 0.00029) {
		tmp = y * (i * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-3.6d-13)) then
        tmp = t_1
    else if (b <= 1.3d-162) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= 2.7d-72) then
        tmp = x * (t * -a)
    else if (b <= 5.5d-37) then
        tmp = y * (x * z)
    else if (b <= 0.00029d0) then
        tmp = y * (i * -j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.6e-13) {
		tmp = t_1;
	} else if (b <= 1.3e-162) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 2.7e-72) {
		tmp = x * (t * -a);
	} else if (b <= 5.5e-37) {
		tmp = y * (x * z);
	} else if (b <= 0.00029) {
		tmp = y * (i * -j);
	} 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 <= -3.6e-13:
		tmp = t_1
	elif b <= 1.3e-162:
		tmp = c * ((t * j) - (z * b))
	elif b <= 2.7e-72:
		tmp = x * (t * -a)
	elif b <= 5.5e-37:
		tmp = y * (x * z)
	elif b <= 0.00029:
		tmp = y * (i * -j)
	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 <= -3.6e-13)
		tmp = t_1;
	elseif (b <= 1.3e-162)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= 2.7e-72)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (b <= 5.5e-37)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 0.00029)
		tmp = Float64(y * Float64(i * Float64(-j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.6e-13)
		tmp = t_1;
	elseif (b <= 1.3e-162)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= 2.7e-72)
		tmp = x * (t * -a);
	elseif (b <= 5.5e-37)
		tmp = y * (x * z);
	elseif (b <= 0.00029)
		tmp = y * (i * -j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.6e-13], t$95$1, If[LessEqual[b, 1.3e-162], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e-72], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e-37], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.00029], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.5999999999999998e-13 or 2.9e-4 < b

   1. Initial program 77.8%

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

   3. Taylor expanded in b around inf 63.5%

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

   if -3.5999999999999998e-13 < b < 1.3e-162

   1. Initial program 66.3%

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

   3. Taylor expanded in c around inf 46.1%

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

   if 1.3e-162 < b < 2.7e-72

   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 x around inf 46.3%

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

      1. *-commutative 46.3%

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

   5. Simplified 46.3%

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

   6. Taylor expanded in z around 0 46.4%

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

      1. mul-1-neg 46.4%

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

      2. distribute-lft-neg-out 46.4%

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

      3. *-commutative 46.4%

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

   8. Simplified 46.4%

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

   if 2.7e-72 < b < 5.4999999999999998e-37

   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 y around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. unsub-neg 67.1%

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

      4. *-commutative 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in z around inf 45.9%

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

      1. *-commutative 45.9%

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

      2. associate-*r* 56.5%

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

   8. Simplified 56.5%

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

   if 5.4999999999999998e-37 < b < 2.9e-4

   1. Initial program 70.7%

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

   3. Taylor expanded in y around inf 42.9%

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

      1. +-commutative 42.9%

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

      2. mul-1-neg 42.9%

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

      3. unsub-neg 42.9%

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

      4. *-commutative 42.9%

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

   5. Simplified 42.9%

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

   6. Taylor expanded in z around 0 52.6%

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

      1. mul-1-neg 52.6%

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

      2. *-commutative 52.6%

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

      3. distribute-rgt-neg-in 52.6%

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

      4. *-commutative 52.6%

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

      5. associate-*r* 52.8%

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

   8. Simplified 52.8%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-162}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 0.00029:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{-23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-202}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7800:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -8e-23)
     t_2
     (if (<= b -6e-116)
       t_1
       (if (<= b -4.2e-202)
         (* c (- (* t j) (* z b)))
         (if (<= b 4.2e-103)
           t_1
           (if (<= b 7800.0) (* 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 <= -8e-23) {
		tmp = t_2;
	} else if (b <= -6e-116) {
		tmp = t_1;
	} else if (b <= -4.2e-202) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 4.2e-103) {
		tmp = t_1;
	} else if (b <= 7800.0) {
		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 <= (-8d-23)) then
        tmp = t_2
    else if (b <= (-6d-116)) then
        tmp = t_1
    else if (b <= (-4.2d-202)) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= 4.2d-103) then
        tmp = t_1
    else if (b <= 7800.0d0) 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 <= -8e-23) {
		tmp = t_2;
	} else if (b <= -6e-116) {
		tmp = t_1;
	} else if (b <= -4.2e-202) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 4.2e-103) {
		tmp = t_1;
	} else if (b <= 7800.0) {
		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 <= -8e-23:
		tmp = t_2
	elif b <= -6e-116:
		tmp = t_1
	elif b <= -4.2e-202:
		tmp = c * ((t * j) - (z * b))
	elif b <= 4.2e-103:
		tmp = t_1
	elif b <= 7800.0:
		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 <= -8e-23)
		tmp = t_2;
	elseif (b <= -6e-116)
		tmp = t_1;
	elseif (b <= -4.2e-202)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= 4.2e-103)
		tmp = t_1;
	elseif (b <= 7800.0)
		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 <= -8e-23)
		tmp = t_2;
	elseif (b <= -6e-116)
		tmp = t_1;
	elseif (b <= -4.2e-202)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= 4.2e-103)
		tmp = t_1;
	elseif (b <= 7800.0)
		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, -8e-23], t$95$2, If[LessEqual[b, -6e-116], t$95$1, If[LessEqual[b, -4.2e-202], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e-103], t$95$1, If[LessEqual[b, 7800.0], 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 < -7.99999999999999968e-23 or 7800 < b

   1. Initial program 77.1%

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

   3. Taylor expanded in b around inf 63.8%

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

   if -7.99999999999999968e-23 < b < -6.00000000000000053e-116 or -4.1999999999999997e-202 < b < 4.20000000000000009e-103

   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 t around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. unsub-neg 67.1%

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

   5. Simplified 67.1%

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

   if -6.00000000000000053e-116 < b < -4.1999999999999997e-202

   1. Initial program 76.6%

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

   3. Taylor expanded in c around inf 62.8%

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

   if 4.20000000000000009e-103 < b < 7800

   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 c around 0 82.4%

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

   4. Taylor expanded in j around inf 49.4%

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

      1. mul-1-neg 49.4%

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

      2. distribute-lft-neg-out 49.4%

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

      3. +-commutative 49.4%

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

      4. cancel-sign-sub-inv 49.4%

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

   6. Simplified 49.4%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{-23}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-202}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-103}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 7800:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -4.9 \cdot 10^{-207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-105}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 8500:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -1.15e-26)
     t_2
     (if (<= b -7.8e-56)
       (* x (- (* y z) (* t a)))
       (if (<= b -4.9e-207)
         t_1
         (if (<= b 4.2e-105)
           (* t (- (* c j) (* x a)))
           (if (<= b 8500.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.15e-26) {
		tmp = t_2;
	} else if (b <= -7.8e-56) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= -4.9e-207) {
		tmp = t_1;
	} else if (b <= 4.2e-105) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 8500.0) {
		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 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-1.15d-26)) then
        tmp = t_2
    else if (b <= (-7.8d-56)) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= (-4.9d-207)) then
        tmp = t_1
    else if (b <= 4.2d-105) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 8500.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.15e-26) {
		tmp = t_2;
	} else if (b <= -7.8e-56) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= -4.9e-207) {
		tmp = t_1;
	} else if (b <= 4.2e-105) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 8500.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.15e-26:
		tmp = t_2
	elif b <= -7.8e-56:
		tmp = x * ((y * z) - (t * a))
	elif b <= -4.9e-207:
		tmp = t_1
	elif b <= 4.2e-105:
		tmp = t * ((c * j) - (x * a))
	elif b <= 8500.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.15e-26)
		tmp = t_2;
	elseif (b <= -7.8e-56)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= -4.9e-207)
		tmp = t_1;
	elseif (b <= 4.2e-105)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 8500.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.15e-26)
		tmp = t_2;
	elseif (b <= -7.8e-56)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= -4.9e-207)
		tmp = t_1;
	elseif (b <= 4.2e-105)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 8500.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.15e-26], t$95$2, If[LessEqual[b, -7.8e-56], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.9e-207], t$95$1, If[LessEqual[b, 4.2e-105], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8500.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.15000000000000004e-26 or 8500 < b

   1. Initial program 77.1%

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

   3. Taylor expanded in b around inf 63.8%

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

   if -1.15000000000000004e-26 < b < -7.8e-56

   1. Initial program 62.3%

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

   3. Taylor expanded in x around inf 87.6%

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

      1. *-commutative 87.6%

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

   5. Simplified 87.6%

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

   if -7.8e-56 < b < -4.9e-207 or 4.2e-105 < b < 8500

   1. Initial program 72.3%

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

   3. Taylor expanded in c around 0 72.1%

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

   4. Taylor expanded in j around inf 54.6%

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

      1. mul-1-neg 54.6%

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

      2. distribute-lft-neg-out 54.6%

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

      3. +-commutative 54.6%

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

      4. cancel-sign-sub-inv 54.6%

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

   6. Simplified 54.6%

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

   if -4.9e-207 < b < 4.2e-105

   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 t around inf 67.6%

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

      1. +-commutative 67.6%

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

      2. mul-1-neg 67.6%

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

      3. unsub-neg 67.6%

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

   5. Simplified 67.6%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -4.9 \cdot 10^{-207}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-105}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 8500:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -5.8e+250)
     t_1
     (if (<= y -7.5e-17)
       (+ (* j (- (* t c) (* y i))) (* z (* x y)))
       (if (<= y 9.8e+148)
         (+ (* t (- (* c j) (* x a))) (* 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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -5.8e+250) {
		tmp = t_1;
	} else if (y <= -7.5e-17) {
		tmp = (j * ((t * c) - (y * i))) + (z * (x * y));
	} else if (y <= 9.8e+148) {
		tmp = (t * ((c * j) - (x * a))) + (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 = y * ((x * z) - (i * j))
    if (y <= (-5.8d+250)) then
        tmp = t_1
    else if (y <= (-7.5d-17)) then
        tmp = (j * ((t * c) - (y * i))) + (z * (x * y))
    else if (y <= 9.8d+148) then
        tmp = (t * ((c * j) - (x * a))) + (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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -5.8e+250) {
		tmp = t_1;
	} else if (y <= -7.5e-17) {
		tmp = (j * ((t * c) - (y * i))) + (z * (x * y));
	} else if (y <= 9.8e+148) {
		tmp = (t * ((c * j) - (x * a))) + (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 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -5.8e+250:
		tmp = t_1
	elif y <= -7.5e-17:
		tmp = (j * ((t * c) - (y * i))) + (z * (x * y))
	elif y <= 9.8e+148:
		tmp = (t * ((c * j) - (x * a))) + (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(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -5.8e+250)
		tmp = t_1;
	elseif (y <= -7.5e-17)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(z * Float64(x * y)));
	elseif (y <= 9.8e+148)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + 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 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -5.8e+250)
		tmp = t_1;
	elseif (y <= -7.5e-17)
		tmp = (j * ((t * c) - (y * i))) + (z * (x * y));
	elseif (y <= 9.8e+148)
		tmp = (t * ((c * j) - (x * a))) + (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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+250], t$95$1, If[LessEqual[y, -7.5e-17], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e+148], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $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 y < -5.80000000000000018e250 or 9.8e148 < y

   1. Initial program 54.4%

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

   3. Taylor expanded in y around inf 82.4%

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

      1. +-commutative 82.4%

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

      2. mul-1-neg 82.4%

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

      3. unsub-neg 82.4%

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

      4. *-commutative 82.4%

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

   5. Simplified 82.4%

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

   if -5.80000000000000018e250 < y < -7.49999999999999984e-17

   1. Initial program 82.8%

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

   3. Taylor expanded in y around inf 70.5%

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

      1. *-commutative 70.5%

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

      2. *-commutative 70.5%

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

      3. associate-*r* 72.5%

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

   5. Simplified 72.5%

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

   if -7.49999999999999984e-17 < y < 9.8e148

   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 y around 0 70.8%

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

      1. *-commutative 70.8%

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

      2. associate-*r* 67.8%

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

      3. associate-*l* 67.8%

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

      4. associate-*r* 69.0%

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

      5. distribute-rgt-in 70.3%

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

      6. +-commutative 70.3%

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

      7. mul-1-neg 70.3%

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

      8. unsub-neg 70.3%

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

   5. Simplified 70.3%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+250}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7.6 \cdot 10^{-31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 40:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -7.6e-31)
     t_2
     (if (<= b 4.5e-245)
       t_1
       (if (<= b 6.5e-211) (* x (* y z)) (if (<= b 40.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7.6e-31) {
		tmp = t_2;
	} else if (b <= 4.5e-245) {
		tmp = t_1;
	} else if (b <= 6.5e-211) {
		tmp = x * (y * z);
	} else if (b <= 40.0) {
		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 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-7.6d-31)) then
        tmp = t_2
    else if (b <= 4.5d-245) then
        tmp = t_1
    else if (b <= 6.5d-211) then
        tmp = x * (y * z)
    else if (b <= 40.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7.6e-31) {
		tmp = t_2;
	} else if (b <= 4.5e-245) {
		tmp = t_1;
	} else if (b <= 6.5e-211) {
		tmp = x * (y * z);
	} else if (b <= 40.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -7.6e-31:
		tmp = t_2
	elif b <= 4.5e-245:
		tmp = t_1
	elif b <= 6.5e-211:
		tmp = x * (y * z)
	elif b <= 40.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -7.6e-31)
		tmp = t_2;
	elseif (b <= 4.5e-245)
		tmp = t_1;
	elseif (b <= 6.5e-211)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 40.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -7.6e-31)
		tmp = t_2;
	elseif (b <= 4.5e-245)
		tmp = t_1;
	elseif (b <= 6.5e-211)
		tmp = x * (y * z);
	elseif (b <= 40.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $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-31], t$95$2, If[LessEqual[b, 4.5e-245], t$95$1, If[LessEqual[b, 6.5e-211], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 40.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.5999999999999999e-31 or 40 < b

   1. Initial program 77.3%

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

   3. Taylor expanded in b around inf 63.3%

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

   if -7.5999999999999999e-31 < b < 4.49999999999999969e-245 or 6.4999999999999996e-211 < b < 40

   1. Initial program 69.3%

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

   3. Taylor expanded in c around 0 71.7%

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

   4. Taylor expanded in j around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. distribute-lft-neg-out 53.5%

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

      3. +-commutative 53.5%

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

      4. cancel-sign-sub-inv 53.5%

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

   6. Simplified 53.5%

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

   if 4.49999999999999969e-245 < b < 6.4999999999999996e-211

   1. Initial program 66.7%

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

   3. Taylor expanded in x around inf 89.6%

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

      1. *-commutative 89.6%

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

   5. Simplified 89.6%

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

   6. Taylor expanded in z around inf 67.8%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{-31}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-245}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 40:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -5 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-76}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{+96}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -5e+28)
     t_1
     (if (<= c -5.6e-54)
       (* y (- (* x z) (* i j)))
       (if (<= c 9.5e-76)
         (* i (- (* a b) (* y j)))
         (if (<= c 3.6e+96) (* t (- (* c j) (* x a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -5e+28) {
		tmp = t_1;
	} else if (c <= -5.6e-54) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 9.5e-76) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 3.6e+96) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-5d+28)) then
        tmp = t_1
    else if (c <= (-5.6d-54)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 9.5d-76) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= 3.6d+96) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -5e+28) {
		tmp = t_1;
	} else if (c <= -5.6e-54) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 9.5e-76) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 3.6e+96) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -5e+28:
		tmp = t_1
	elif c <= -5.6e-54:
		tmp = y * ((x * z) - (i * j))
	elif c <= 9.5e-76:
		tmp = i * ((a * b) - (y * j))
	elif c <= 3.6e+96:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -5e+28)
		tmp = t_1;
	elseif (c <= -5.6e-54)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 9.5e-76)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= 3.6e+96)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -5e+28)
		tmp = t_1;
	elseif (c <= -5.6e-54)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 9.5e-76)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= 3.6e+96)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5e+28], t$95$1, If[LessEqual[c, -5.6e-54], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.5e-76], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.6e+96], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -4.99999999999999957e28 or 3.60000000000000013e96 < c

   1. Initial program 63.8%

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

   3. Taylor expanded in c around inf 69.4%

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

   if -4.99999999999999957e28 < c < -5.6000000000000004e-54

   1. Initial program 82.0%

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

   3. Taylor expanded in y around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. unsub-neg 58.8%

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

      4. *-commutative 58.8%

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

   5. Simplified 58.8%

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

   if -5.6000000000000004e-54 < c < 9.49999999999999984e-76

   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 i around inf 58.5%

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

      1. distribute-lft-out-- 58.5%

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

      2. *-commutative 58.5%

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

   5. Simplified 58.5%

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

   if 9.49999999999999984e-76 < c < 3.60000000000000013e96

   1. Initial program 71.0%

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

   3. Taylor expanded in t around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

   5. Simplified 61.0%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5 \cdot 10^{+28}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-76}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{+96}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;c \leq -1.55 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-75}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= c -1.55e+85)
     t_1
     (if (<= c -1.02e-172)
       (* x (* y z))
       (if (<= c 2.2e-75)
         (* b (* a i))
         (if (<= c 1.15e+80) (* a (* t (- x))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (c <= -1.55e+85) {
		tmp = t_1;
	} else if (c <= -1.02e-172) {
		tmp = x * (y * z);
	} else if (c <= 2.2e-75) {
		tmp = b * (a * i);
	} else if (c <= 1.15e+80) {
		tmp = a * (t * -x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (c <= (-1.55d+85)) then
        tmp = t_1
    else if (c <= (-1.02d-172)) then
        tmp = x * (y * z)
    else if (c <= 2.2d-75) then
        tmp = b * (a * i)
    else if (c <= 1.15d+80) then
        tmp = a * (t * -x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (c <= -1.55e+85) {
		tmp = t_1;
	} else if (c <= -1.02e-172) {
		tmp = x * (y * z);
	} else if (c <= 2.2e-75) {
		tmp = b * (a * i);
	} else if (c <= 1.15e+80) {
		tmp = a * (t * -x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if c <= -1.55e+85:
		tmp = t_1
	elif c <= -1.02e-172:
		tmp = x * (y * z)
	elif c <= 2.2e-75:
		tmp = b * (a * i)
	elif c <= 1.15e+80:
		tmp = a * (t * -x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (c <= -1.55e+85)
		tmp = t_1;
	elseif (c <= -1.02e-172)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 2.2e-75)
		tmp = Float64(b * Float64(a * i));
	elseif (c <= 1.15e+80)
		tmp = Float64(a * Float64(t * Float64(-x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (c <= -1.55e+85)
		tmp = t_1;
	elseif (c <= -1.02e-172)
		tmp = x * (y * z);
	elseif (c <= 2.2e-75)
		tmp = b * (a * i);
	elseif (c <= 1.15e+80)
		tmp = a * (t * -x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.55e+85], t$95$1, If[LessEqual[c, -1.02e-172], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e-75], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.15e+80], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.55000000000000006e85 or 1.15000000000000002e80 < c

   1. Initial program 60.3%

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

   3. Taylor expanded in t around inf 53.6%

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

      1. mul-1-neg 53.6%

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

      2. distribute-rgt-neg-in 53.6%

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

      3. distribute-rgt-neg-in 53.6%

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

   5. Simplified 53.6%

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

   6. Taylor expanded in c around inf 43.9%

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

   if -1.55000000000000006e85 < c < -1.02e-172

   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 x around inf 46.3%

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

      1. *-commutative 46.3%

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

   5. Simplified 46.3%

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

   6. Taylor expanded in z around inf 37.2%

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

   if -1.02e-172 < c < 2.20000000000000005e-75

   1. Initial program 85.7%

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

   3. Taylor expanded in b around inf 45.6%

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

   4. Taylor expanded in a around inf 41.0%

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

      1. *-commutative 41.0%

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

   6. Simplified 41.0%

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

   if 2.20000000000000005e-75 < c < 1.15000000000000002e80

   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 49.7%

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

      1. *-commutative 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in a around inf 42.5%

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

      1. +-commutative 42.5%

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

      2. mul-1-neg 42.5%

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

      3. unsub-neg 42.5%

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

      4. associate-/l* 44.9%

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

      5. associate-/l* 44.9%

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

   8. Simplified 44.9%

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

   9. Taylor expanded in y around 0 40.3%

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

       1. mul-1-neg 40.3%

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

       2. distribute-lft-neg-out 40.3%

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

       3. *-commutative 40.3%

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

   11. Simplified 40.3%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+85}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-75}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;c \leq -2.65 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-177}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-68}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= c -2.65e+84)
     t_1
     (if (<= c -3.7e-177)
       (* x (* y z))
       (if (<= c 2.3e-68) (* b (* a 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 = c * (t * j);
	double tmp;
	if (c <= -2.65e+84) {
		tmp = t_1;
	} else if (c <= -3.7e-177) {
		tmp = x * (y * z);
	} else if (c <= 2.3e-68) {
		tmp = b * (a * 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 = c * (t * j)
    if (c <= (-2.65d+84)) then
        tmp = t_1
    else if (c <= (-3.7d-177)) then
        tmp = x * (y * z)
    else if (c <= 2.3d-68) then
        tmp = b * (a * 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 = c * (t * j);
	double tmp;
	if (c <= -2.65e+84) {
		tmp = t_1;
	} else if (c <= -3.7e-177) {
		tmp = x * (y * z);
	} else if (c <= 2.3e-68) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if c <= -2.65e+84:
		tmp = t_1
	elif c <= -3.7e-177:
		tmp = x * (y * z)
	elif c <= 2.3e-68:
		tmp = b * (a * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (c <= -2.65e+84)
		tmp = t_1;
	elseif (c <= -3.7e-177)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 2.3e-68)
		tmp = Float64(b * Float64(a * 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 = c * (t * j);
	tmp = 0.0;
	if (c <= -2.65e+84)
		tmp = t_1;
	elseif (c <= -3.7e-177)
		tmp = x * (y * z);
	elseif (c <= 2.3e-68)
		tmp = b * (a * 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[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.65e+84], t$95$1, If[LessEqual[c, -3.7e-177], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.3e-68], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.6500000000000001e84 or 2.29999999999999997e-68 < c

   1. Initial program 64.0%

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

   3. Taylor expanded in t around inf 54.4%

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

      1. mul-1-neg 54.4%

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

      2. distribute-rgt-neg-in 54.4%

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

      3. distribute-rgt-neg-in 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in c around inf 37.8%

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

   if -2.6500000000000001e84 < c < -3.69999999999999993e-177

   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 x around inf 46.3%

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

      1. *-commutative 46.3%

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

   5. Simplified 46.3%

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

   6. Taylor expanded in z around inf 37.2%

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

   if -3.69999999999999993e-177 < c < 2.29999999999999997e-68

   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 45.1%

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

   4. Taylor expanded in a around inf 40.5%

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

      1. *-commutative 40.5%

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

   6. Simplified 40.5%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.65 \cdot 10^{+84}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-177}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-68}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-26} \lor \neg \left(b \leq 6.6 \cdot 10^{-6}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.6e-26) (not (<= b 6.6e-6))) (* a (* b i)) (* c (* t j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.6e-26) || !(b <= 6.6e-6)) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.6d-26)) .or. (.not. (b <= 6.6d-6))) then
        tmp = a * (b * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.6e-26) || !(b <= 6.6e-6)) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.6e-26) or not (b <= 6.6e-6):
		tmp = a * (b * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.6e-26) || !(b <= 6.6e-6))
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.6e-26) || ~((b <= 6.6e-6)))
		tmp = a * (b * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.6e-26], N[Not[LessEqual[b, 6.6e-6]], $MachinePrecision]], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.6000000000000001e-26 or 6.60000000000000034e-6 < b

   1. Initial program 76.1%

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

   3. Taylor expanded in b around inf 62.3%

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

   4. Taylor expanded in a around inf 35.6%

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

      1. *-commutative 35.6%

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

   6. Simplified 35.6%

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

   if -1.6000000000000001e-26 < b < 6.60000000000000034e-6

   1. Initial program 70.2%

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

   3. Taylor expanded in t around inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. distribute-rgt-neg-in 67.6%

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

      3. distribute-rgt-neg-in 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in c around inf 36.6%

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

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-26} \lor \neg \left(b \leq 6.6 \cdot 10^{-6}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 23.0% 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 73.2%

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

3. Taylor expanded in b around inf 38.1%

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

4. Taylor expanded in a around inf 20.6%

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

   1. *-commutative 20.6%

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

6. Simplified 20.6%

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

7. Final simplification 20.6%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
8. Add Preprocessing

Alternative 19: 23.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.2%

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

3. Taylor expanded in b around inf 38.1%

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

4. Taylor expanded in a around inf 21.0%

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

   1. *-commutative 21.0%

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

6. Simplified 21.0%

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

7. Final simplification 21.0%

   \[\leadsto b \cdot \left(a \cdot i\right) \]
8. Add Preprocessing

Developer target: 69.3% 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 2024115 
(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)))))