Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.5% → 82.9%

Time: 19.6s

Alternatives: 22

Speedup: 0.7×

• 58.1% 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: 73.5% 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: 82.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) - ((b * ((z * c) - (a * i))) + (x * ((t * a) - (y * z))))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)))
	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(b * Float64(Float64(z * c) - Float64(a * i))) + Float64(x * Float64(Float64(t * a) - Float64(y * z)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	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))) - ((b * ((z * c) - (a * i))) + (x * ((t * a) - (y * z))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	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[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.7%

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

   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 y around 0 20.2%

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

   5. Simplified 18.2%

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

   6. Taylor expanded in b around 0 56.1%

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

4. Final simplification 85.6%

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

Alternative 2: 69.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t\_2 + t\_1\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+53}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-43}:\\ \;\;\;\;t\_2 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 80000000000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+39}:\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (+ t_2 t_1)))
   (if (<= x -4.5e+53)
     t_3
     (if (<= x 1.25e-43)
       (+ t_2 (* b (- (* a i) (* z c))))
       (if (<= x 80000000000.0)
         (+ (* t (- (* c j) (* x a))) (* y (- (* x z) (* i j))))
         (if (<= x 9.8e+39) (+ t_1 (* b (* a i))) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = t_2 + t_1;
	double tmp;
	if (x <= -4.5e+53) {
		tmp = t_3;
	} else if (x <= 1.25e-43) {
		tmp = t_2 + (b * ((a * i) - (z * c)));
	} else if (x <= 80000000000.0) {
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	} else if (x <= 9.8e+39) {
		tmp = t_1 + (b * (a * i));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = j * ((t * c) - (y * i))
    t_3 = t_2 + t_1
    if (x <= (-4.5d+53)) then
        tmp = t_3
    else if (x <= 1.25d-43) then
        tmp = t_2 + (b * ((a * i) - (z * c)))
    else if (x <= 80000000000.0d0) then
        tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)))
    else if (x <= 9.8d+39) then
        tmp = t_1 + (b * (a * i))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = t_2 + t_1;
	double tmp;
	if (x <= -4.5e+53) {
		tmp = t_3;
	} else if (x <= 1.25e-43) {
		tmp = t_2 + (b * ((a * i) - (z * c)));
	} else if (x <= 80000000000.0) {
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	} else if (x <= 9.8e+39) {
		tmp = t_1 + (b * (a * i));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((t * c) - (y * i))
	t_3 = t_2 + t_1
	tmp = 0
	if x <= -4.5e+53:
		tmp = t_3
	elif x <= 1.25e-43:
		tmp = t_2 + (b * ((a * i) - (z * c)))
	elif x <= 80000000000.0:
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)))
	elif x <= 9.8e+39:
		tmp = t_1 + (b * (a * i))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(t_2 + t_1)
	tmp = 0.0
	if (x <= -4.5e+53)
		tmp = t_3;
	elseif (x <= 1.25e-43)
		tmp = Float64(t_2 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (x <= 80000000000.0)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	elseif (x <= 9.8e+39)
		tmp = Float64(t_1 + Float64(b * Float64(a * i)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = j * ((t * c) - (y * i));
	t_3 = t_2 + t_1;
	tmp = 0.0;
	if (x <= -4.5e+53)
		tmp = t_3;
	elseif (x <= 1.25e-43)
		tmp = t_2 + (b * ((a * i) - (z * c)));
	elseif (x <= 80000000000.0)
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	elseif (x <= 9.8e+39)
		tmp = t_1 + (b * (a * i));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, If[LessEqual[x, -4.5e+53], t$95$3, If[LessEqual[x, 1.25e-43], N[(t$95$2 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 80000000000.0], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e+39], N[(t$95$1 + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.5000000000000002e53 or 9.79999999999999974e39 < x

   1. Initial program 79.6%

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

   3. Taylor expanded in b around 0 81.2%

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

   if -4.5000000000000002e53 < x < 1.25000000000000005e-43

   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 x around 0 76.3%

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

   if 1.25000000000000005e-43 < x < 8e10

   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 y around 0 66.7%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in b around 0 93.1%

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

   if 8e10 < x < 9.79999999999999974e39

   1. Initial program 47.6%

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

   3. Taylor expanded in j around 0 81.5%

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

      1. *-commutative 81.5%

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

      2. sub-neg 81.5%

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

      3. +-commutative 81.5%

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

      4. neg-mul-1 81.5%

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

      5. *-commutative 81.5%

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

   5. Simplified 81.5%

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

   6. Taylor expanded in c around 0 90.6%

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

      1. neg-mul-1 90.6%

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

      2. distribute-rgt-neg-in 90.6%

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

   8. Simplified 90.6%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-43}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 80000000000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+185} \lor \neg \left(c \leq 5.1 \cdot 10^{+109}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + \left(y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.9e+185) (not (<= c 5.1e+109)))
   (* c (- (* t j) (* z b)))
   (+
    (* t (- (* c j) (* x a)))
    (+ (* y (- (* x z) (* i j))) (* 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 tmp;
	if ((c <= -1.9e+185) || !(c <= 5.1e+109)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = (t * ((c * j) - (x * a))) + ((y * ((x * z) - (i * j))) + (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) :: tmp
    if ((c <= (-1.9d+185)) .or. (.not. (c <= 5.1d+109))) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = (t * ((c * j) - (x * a))) + ((y * ((x * z) - (i * j))) + (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 tmp;
	if ((c <= -1.9e+185) || !(c <= 5.1e+109)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = (t * ((c * j) - (x * a))) + ((y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -1.9e+185) or not (c <= 5.1e+109):
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = (t * ((c * j) - (x * a))) + ((y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -1.9e+185) || !(c <= 5.1e+109))
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + 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)
	tmp = 0.0;
	if ((c <= -1.9e+185) || ~((c <= 5.1e+109)))
		tmp = c * ((t * j) - (z * b));
	else
		tmp = (t * ((c * j) - (x * a))) + ((y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -1.9e+185], N[Not[LessEqual[c, 5.1e+109]], $MachinePrecision]], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.8999999999999999e185 or 5.0999999999999999e109 < c

   1. Initial program 56.2%

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

   3. Taylor expanded in c around inf 81.7%

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

      1. *-commutative 81.7%

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

   5. Simplified 81.7%

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

   if -1.8999999999999999e185 < c < 5.0999999999999999e109

   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 y around 0 73.8%

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

   5. Simplified 79.3%

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

      1. associate--l+ 79.3%

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

   7. Applied egg-rr 79.3%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+185} \lor \neg \left(c \leq 5.1 \cdot 10^{+109}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + \left(y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.5 \cdot 10^{+170}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{-76}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + \left(z \cdot \left(x \cdot y\right) + t\_1\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-28}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3 + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* t c) (* y i)))))
   (if (<= j -3.5e+170)
     t_3
     (if (<= j -1.7e-76)
       (+ (* t (- (* c j) (* x a))) (+ (* z (* x y)) t_1))
       (if (<= j 7e-28) (+ t_2 t_1) (+ t_3 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -3.5e+170) {
		tmp = t_3;
	} else if (j <= -1.7e-76) {
		tmp = (t * ((c * j) - (x * a))) + ((z * (x * y)) + t_1);
	} else if (j <= 7e-28) {
		tmp = t_2 + t_1;
	} else {
		tmp = t_3 + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((t * c) - (y * i))
    if (j <= (-3.5d+170)) then
        tmp = t_3
    else if (j <= (-1.7d-76)) then
        tmp = (t * ((c * j) - (x * a))) + ((z * (x * y)) + t_1)
    else if (j <= 7d-28) then
        tmp = t_2 + t_1
    else
        tmp = t_3 + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -3.5e+170) {
		tmp = t_3;
	} else if (j <= -1.7e-76) {
		tmp = (t * ((c * j) - (x * a))) + ((z * (x * y)) + t_1);
	} else if (j <= 7e-28) {
		tmp = t_2 + t_1;
	} else {
		tmp = t_3 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -3.5e+170:
		tmp = t_3
	elif j <= -1.7e-76:
		tmp = (t * ((c * j) - (x * a))) + ((z * (x * y)) + t_1)
	elif j <= 7e-28:
		tmp = t_2 + t_1
	else:
		tmp = t_3 + t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3.5e+170)
		tmp = t_3;
	elseif (j <= -1.7e-76)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(Float64(z * Float64(x * y)) + t_1));
	elseif (j <= 7e-28)
		tmp = Float64(t_2 + t_1);
	else
		tmp = Float64(t_3 + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -3.5e+170)
		tmp = t_3;
	elseif (j <= -1.7e-76)
		tmp = (t * ((c * j) - (x * a))) + ((z * (x * y)) + t_1);
	elseif (j <= 7e-28)
		tmp = t_2 + t_1;
	else
		tmp = t_3 + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.5e+170], t$95$3, If[LessEqual[j, -1.7e-76], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7e-28], N[(t$95$2 + t$95$1), $MachinePrecision], N[(t$95$3 + t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.50000000000000005e170

   1. Initial program 62.5%

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

   3. Taylor expanded in y around 0 53.1%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in j around inf 84.7%

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

      1. neg-mul-1 84.7%

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

      2. +-commutative 84.7%

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

      3. sub-neg 84.7%

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

   8. Simplified 84.7%

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

   if -3.50000000000000005e170 < j < -1.7e-76

   1. Initial program 81.1%

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

   3. Taylor expanded in y around 0 81.1%

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

   5. Simplified 84.5%

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

      1. associate--l+ 84.6%

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

   7. Applied egg-rr 84.6%

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

   8. Taylor expanded in z around inf 80.2%

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

      1. associate-*r* 82.0%

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

   10. Simplified 82.0%

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

   if -1.7e-76 < j < 6.9999999999999999e-28

   1. Initial program 75.6%

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

   3. Taylor expanded in j around 0 79.4%

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

      1. *-commutative 79.4%

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

      2. sub-neg 79.4%

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

      3. +-commutative 79.4%

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

      4. neg-mul-1 79.4%

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

      5. *-commutative 79.4%

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

   5. Simplified 79.4%

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

   if 6.9999999999999999e-28 < j

   1. Initial program 73.6%

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

   3. Taylor expanded in b around 0 77.6%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.5 \cdot 10^{+170}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{-76}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + \left(z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x - b \cdot \frac{c}{y}\right)\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(c \cdot j - \left(x \cdot a + \frac{i \cdot \left(y \cdot j\right)}{t}\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -5.6e+38)
   (* z (* y (- x (* b (/ c y)))))
   (if (<= z 4.5e-114)
     (* t (- (* c j) (+ (* x a) (/ (* i (* y j)) t))))
     (if (<= z 1.7e+55)
       (+ (* x (- (* y z) (* t a))) (* b (* a i)))
       (- (* y (- (* x z) (* i j))) (* z (* b c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -5.6e+38) {
		tmp = z * (y * (x - (b * (c / y))));
	} else if (z <= 4.5e-114) {
		tmp = t * ((c * j) - ((x * a) + ((i * (y * j)) / t)));
	} else if (z <= 1.7e+55) {
		tmp = (x * ((y * z) - (t * a))) + (b * (a * i));
	} else {
		tmp = (y * ((x * z) - (i * j))) - (z * (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-5.6d+38)) then
        tmp = z * (y * (x - (b * (c / y))))
    else if (z <= 4.5d-114) then
        tmp = t * ((c * j) - ((x * a) + ((i * (y * j)) / t)))
    else if (z <= 1.7d+55) then
        tmp = (x * ((y * z) - (t * a))) + (b * (a * i))
    else
        tmp = (y * ((x * z) - (i * j))) - (z * (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -5.6e+38) {
		tmp = z * (y * (x - (b * (c / y))));
	} else if (z <= 4.5e-114) {
		tmp = t * ((c * j) - ((x * a) + ((i * (y * j)) / t)));
	} else if (z <= 1.7e+55) {
		tmp = (x * ((y * z) - (t * a))) + (b * (a * i));
	} else {
		tmp = (y * ((x * z) - (i * j))) - (z * (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -5.6e+38:
		tmp = z * (y * (x - (b * (c / y))))
	elif z <= 4.5e-114:
		tmp = t * ((c * j) - ((x * a) + ((i * (y * j)) / t)))
	elif z <= 1.7e+55:
		tmp = (x * ((y * z) - (t * a))) + (b * (a * i))
	else:
		tmp = (y * ((x * z) - (i * j))) - (z * (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -5.6e+38)
		tmp = Float64(z * Float64(y * Float64(x - Float64(b * Float64(c / y)))));
	elseif (z <= 4.5e-114)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(Float64(x * a) + Float64(Float64(i * Float64(y * j)) / t))));
	elseif (z <= 1.7e+55)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(a * i)));
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(z * Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -5.6e+38)
		tmp = z * (y * (x - (b * (c / y))));
	elseif (z <= 4.5e-114)
		tmp = t * ((c * j) - ((x * a) + ((i * (y * j)) / t)));
	elseif (z <= 1.7e+55)
		tmp = (x * ((y * z) - (t * a))) + (b * (a * i));
	else
		tmp = (y * ((x * z) - (i * j))) - (z * (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -5.6e+38], N[(z * N[(y * N[(x - N[(b * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-114], N[(t * N[(N[(c * j), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] + N[(N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+55], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.6e38

   1. Initial program 69.6%

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

   3. Taylor expanded in z around inf 77.1%

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

   4. Taylor expanded in y around inf 75.6%

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

      1. mul-1-neg 75.6%

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

      2. unsub-neg 75.6%

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

      3. associate-/l* 78.5%

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

   6. Simplified 78.5%

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

   if -5.6e38 < z < 4.49999999999999969e-114

   1. Initial program 78.2%

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

   3. Taylor expanded in t around -inf 73.7%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in j around inf 69.1%

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

      1. associate-*r/ 69.1%

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

      2. associate-*r* 69.1%

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

      3. neg-mul-1 69.1%

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

      4. *-commutative 69.1%

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

   8. Simplified 69.1%

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

   if 4.49999999999999969e-114 < z < 1.6999999999999999e55

   1. Initial program 77.2%

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

   3. Taylor expanded in j around 0 59.6%

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

      1. *-commutative 59.6%

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

      2. sub-neg 59.6%

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

      3. +-commutative 59.6%

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

      4. neg-mul-1 59.6%

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

      5. *-commutative 59.6%

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

   5. Simplified 59.6%

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

   6. Taylor expanded in c around 0 62.4%

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

      1. neg-mul-1 62.4%

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

      2. distribute-rgt-neg-in 62.4%

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

   8. Simplified 62.4%

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

   if 1.6999999999999999e55 < z

   1. Initial program 71.8%

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

   3. Taylor expanded in y around 0 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in t around 0 73.9%

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

   7. Taylor expanded in a around 0 67.5%

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

      1. sub-neg 67.5%

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

      2. *-commutative 67.5%

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

      3. +-commutative 67.5%

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

      4. +-commutative 67.5%

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

      5. sub-neg 67.5%

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

      6. associate-*r* 71.6%

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

   9. Simplified 71.6%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x - b \cdot \frac{c}{y}\right)\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(c \cdot j - \left(x \cdot a + \frac{i \cdot \left(y \cdot j\right)}{t}\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -2.4 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-28}:\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= j -2.4e-59)
     (+ (* t (- (* c j) (* x a))) (* y (- (* x z) (* i j))))
     (if (<= j 7.8e-28)
       (+ t_1 (* b (- (* a i) (* z c))))
       (+ (* j (- (* t c) (* y i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -2.4e-59) {
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	} else if (j <= 7.8e-28) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (j <= (-2.4d-59)) then
        tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)))
    else if (j <= 7.8d-28) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else
        tmp = (j * ((t * c) - (y * i))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -2.4e-59) {
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	} else if (j <= 7.8e-28) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -2.4e-59:
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)))
	elif j <= 7.8e-28:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	else:
		tmp = (j * ((t * c) - (y * i))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -2.4e-59)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	elseif (j <= 7.8e-28)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -2.4e-59)
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	elseif (j <= 7.8e-28)
		tmp = t_1 + (b * ((a * i) - (z * c)));
	else
		tmp = (j * ((t * c) - (y * i))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.4e-59], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.8e-28], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.40000000000000015e-59

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0 70.2%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in b around 0 75.1%

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

   if -2.40000000000000015e-59 < j < 7.79999999999999998e-28

   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 j around 0 79.1%

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

      1. *-commutative 79.1%

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

      2. sub-neg 79.1%

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

      3. +-commutative 79.1%

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

      4. neg-mul-1 79.1%

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

      5. *-commutative 79.1%

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

   5. Simplified 79.1%

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

   if 7.79999999999999998e-28 < j

   1. Initial program 73.6%

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

   3. Taylor expanded in b around 0 77.6%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+150}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x - b \cdot \frac{c}{y}\right)\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z \cdot \left(b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= z -2.2e+150)
     (* z (* y (- x (* b (/ c y)))))
     (if (<= z 2.8e+58)
       (+ (* t (- (* c j) (* x a))) t_1)
       (- t_1 (* z (* b c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (z <= -2.2e+150) {
		tmp = z * (y * (x - (b * (c / y))));
	} else if (z <= 2.8e+58) {
		tmp = (t * ((c * j) - (x * a))) + t_1;
	} else {
		tmp = t_1 - (z * (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (z <= (-2.2d+150)) then
        tmp = z * (y * (x - (b * (c / y))))
    else if (z <= 2.8d+58) then
        tmp = (t * ((c * j) - (x * a))) + t_1
    else
        tmp = t_1 - (z * (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (z <= -2.2e+150) {
		tmp = z * (y * (x - (b * (c / y))));
	} else if (z <= 2.8e+58) {
		tmp = (t * ((c * j) - (x * a))) + t_1;
	} else {
		tmp = t_1 - (z * (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if z <= -2.2e+150:
		tmp = z * (y * (x - (b * (c / y))))
	elif z <= 2.8e+58:
		tmp = (t * ((c * j) - (x * a))) + t_1
	else:
		tmp = t_1 - (z * (b * 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)))
	tmp = 0.0
	if (z <= -2.2e+150)
		tmp = Float64(z * Float64(y * Float64(x - Float64(b * Float64(c / y)))));
	elseif (z <= 2.8e+58)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + t_1);
	else
		tmp = Float64(t_1 - Float64(z * Float64(b * 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));
	tmp = 0.0;
	if (z <= -2.2e+150)
		tmp = z * (y * (x - (b * (c / y))));
	elseif (z <= 2.8e+58)
		tmp = (t * ((c * j) - (x * a))) + t_1;
	else
		tmp = t_1 - (z * (b * 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]}, If[LessEqual[z, -2.2e+150], N[(z * N[(y * N[(x - N[(b * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+58], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.19999999999999999e150

   1. Initial program 64.1%

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

   3. Taylor expanded in z around inf 83.9%

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

   4. Taylor expanded in y around inf 83.9%

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

      1. mul-1-neg 83.9%

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

      2. unsub-neg 83.9%

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

      3. associate-/l* 87.9%

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

   6. Simplified 87.9%

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

   if -2.19999999999999999e150 < z < 2.7999999999999998e58

   1. Initial program 78.3%

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

   3. Taylor expanded in y around 0 72.6%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in b around 0 71.4%

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

   if 2.7999999999999998e58 < z

   1. Initial program 71.8%

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

   3. Taylor expanded in y around 0 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in t around 0 73.9%

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

   7. Taylor expanded in a around 0 67.5%

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

      1. sub-neg 67.5%

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

      2. *-commutative 67.5%

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

      3. +-commutative 67.5%

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

      4. +-commutative 67.5%

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

      5. sub-neg 67.5%

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

      6. associate-*r* 71.6%

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

   9. Simplified 71.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+150}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x - b \cdot \frac{c}{y}\right)\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+107}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x - b \cdot \frac{c}{y}\right)\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.7e+107)
   (* z (* y (- x (* b (/ c y)))))
   (if (<= z 9e+55)
     (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a))))
     (- (* y (- (* x z) (* i j))) (* z (* b c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.7e+107) {
		tmp = z * (y * (x - (b * (c / y))));
	} else if (z <= 9e+55) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (y * ((x * z) - (i * j))) - (z * (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.7d+107)) then
        tmp = z * (y * (x - (b * (c / y))))
    else if (z <= 9d+55) then
        tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = (y * ((x * z) - (i * j))) - (z * (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.7e+107) {
		tmp = z * (y * (x - (b * (c / y))));
	} else if (z <= 9e+55) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (y * ((x * z) - (i * j))) - (z * (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.7e+107:
		tmp = z * (y * (x - (b * (c / y))))
	elif z <= 9e+55:
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = (y * ((x * z) - (i * j))) - (z * (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.7e+107)
		tmp = Float64(z * Float64(y * Float64(x - Float64(b * Float64(c / y)))));
	elseif (z <= 9e+55)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(z * Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.7e+107)
		tmp = z * (y * (x - (b * (c / y))));
	elseif (z <= 9e+55)
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = (y * ((x * z) - (i * j))) - (z * (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.7e+107], N[(z * N[(y * N[(x - N[(b * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+55], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7000000000000001e107

   1. Initial program 65.9%

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

   3. Taylor expanded in z around inf 80.7%

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

   4. Taylor expanded in y around inf 80.7%

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

      1. mul-1-neg 80.7%

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

      2. unsub-neg 80.7%

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

      3. associate-/l* 84.2%

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

   6. Simplified 84.2%

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

   if -2.7000000000000001e107 < z < 8.99999999999999996e55

   1. Initial program 78.5%

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

   3. Taylor expanded in b around 0 70.4%

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

   if 8.99999999999999996e55 < z

   1. Initial program 71.8%

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

   3. Taylor expanded in y around 0 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in t around 0 73.9%

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

   7. Taylor expanded in a around 0 67.5%

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

      1. sub-neg 67.5%

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

      2. *-commutative 67.5%

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

      3. +-commutative 67.5%

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

      4. +-commutative 67.5%

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

      5. sub-neg 67.5%

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

      6. associate-*r* 71.6%

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

   9. Simplified 71.6%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+107}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x - b \cdot \frac{c}{y}\right)\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 33.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-181}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+162}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= z -4.8e+69)
     t_1
     (if (<= z 1.3e-181)
       (* c (* t j))
       (if (<= z 1.3e+76)
         (* a (- (* b i) (* x t)))
         (if (<= z 5.7e+162) (* z (* b (- 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 = z * (x * y);
	double tmp;
	if (z <= -4.8e+69) {
		tmp = t_1;
	} else if (z <= 1.3e-181) {
		tmp = c * (t * j);
	} else if (z <= 1.3e+76) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 5.7e+162) {
		tmp = z * (b * -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 = z * (x * y)
    if (z <= (-4.8d+69)) then
        tmp = t_1
    else if (z <= 1.3d-181) then
        tmp = c * (t * j)
    else if (z <= 1.3d+76) then
        tmp = a * ((b * i) - (x * t))
    else if (z <= 5.7d+162) then
        tmp = z * (b * -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 = z * (x * y);
	double tmp;
	if (z <= -4.8e+69) {
		tmp = t_1;
	} else if (z <= 1.3e-181) {
		tmp = c * (t * j);
	} else if (z <= 1.3e+76) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 5.7e+162) {
		tmp = z * (b * -c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if z <= -4.8e+69:
		tmp = t_1
	elif z <= 1.3e-181:
		tmp = c * (t * j)
	elif z <= 1.3e+76:
		tmp = a * ((b * i) - (x * t))
	elif z <= 5.7e+162:
		tmp = z * (b * -c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (z <= -4.8e+69)
		tmp = t_1;
	elseif (z <= 1.3e-181)
		tmp = Float64(c * Float64(t * j));
	elseif (z <= 1.3e+76)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (z <= 5.7e+162)
		tmp = Float64(z * Float64(b * Float64(-c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	tmp = 0.0;
	if (z <= -4.8e+69)
		tmp = t_1;
	elseif (z <= 1.3e-181)
		tmp = c * (t * j);
	elseif (z <= 1.3e+76)
		tmp = a * ((b * i) - (x * t));
	elseif (z <= 5.7e+162)
		tmp = z * (b * -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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+69], t$95$1, If[LessEqual[z, 1.3e-181], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+76], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.7e+162], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.8000000000000003e69 or 5.69999999999999997e162 < z

   1. Initial program 67.8%

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

   3. Taylor expanded in z around inf 76.8%

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

   4. Taylor expanded in x around inf 50.4%

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

   if -4.8000000000000003e69 < z < 1.29999999999999999e-181

   1. Initial program 79.1%

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

   3. Taylor expanded in c around inf 46.8%

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

      1. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in t around inf 43.6%

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

   if 1.29999999999999999e-181 < z < 1.3e76

   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 y around 0 69.5%

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

   5. Simplified 76.3%

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

      1. associate--l+ 76.3%

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

   7. Applied egg-rr 76.3%

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

   8. Taylor expanded in a around inf 44.1%

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

      1. mul-1-neg 44.1%

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

      2. distribute-lft-neg-out 44.1%

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

      3. cancel-sign-sub 44.1%

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

      4. +-commutative 44.1%

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

      5. *-commutative 44.1%

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

      6. mul-1-neg 44.1%

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

      7. unsub-neg 44.1%

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

      8. *-commutative 44.1%

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

   10. Simplified 44.1%

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

   if 1.3e76 < z < 5.69999999999999997e162

   1. Initial program 74.5%

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

   3. Taylor expanded in z around inf 64.5%

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

   4. Taylor expanded in x around 0 48.9%

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

      1. neg-mul-1 48.9%

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

      2. distribute-rgt-neg-in 48.9%

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

   6. Simplified 48.9%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+69}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-181}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+162}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.7 \cdot 10^{+102}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(c - i \cdot \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -2.7e+102)
   (* j (- (* t c) (* y i)))
   (if (<= j 4.4e+132)
     (+ (* x (- (* y z) (* t a))) (* b (* a i)))
     (* (* t j) (- c (* i (/ y t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.7e+102) {
		tmp = j * ((t * c) - (y * i));
	} else if (j <= 4.4e+132) {
		tmp = (x * ((y * z) - (t * a))) + (b * (a * i));
	} else {
		tmp = (t * j) * (c - (i * (y / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-2.7d+102)) then
        tmp = j * ((t * c) - (y * i))
    else if (j <= 4.4d+132) then
        tmp = (x * ((y * z) - (t * a))) + (b * (a * i))
    else
        tmp = (t * j) * (c - (i * (y / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.7e+102) {
		tmp = j * ((t * c) - (y * i));
	} else if (j <= 4.4e+132) {
		tmp = (x * ((y * z) - (t * a))) + (b * (a * i));
	} else {
		tmp = (t * j) * (c - (i * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -2.7e+102:
		tmp = j * ((t * c) - (y * i))
	elif j <= 4.4e+132:
		tmp = (x * ((y * z) - (t * a))) + (b * (a * i))
	else:
		tmp = (t * j) * (c - (i * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -2.7e+102)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (j <= 4.4e+132)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(a * i)));
	else
		tmp = Float64(Float64(t * j) * Float64(c - Float64(i * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -2.7e+102)
		tmp = j * ((t * c) - (y * i));
	elseif (j <= 4.4e+132)
		tmp = (x * ((y * z) - (t * a))) + (b * (a * i));
	else
		tmp = (t * j) * (c - (i * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -2.7e+102], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e+132], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * j), $MachinePrecision] * N[(c - N[(i * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.7000000000000001e102

   1. Initial program 68.1%

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

   3. Taylor expanded in y around 0 61.7%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in j around inf 79.4%

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

      1. neg-mul-1 79.4%

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

      2. +-commutative 79.4%

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

      3. sub-neg 79.4%

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

   8. Simplified 79.4%

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

   if -2.7000000000000001e102 < j < 4.39999999999999977e132

   1. Initial program 77.4%

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

   3. Taylor expanded in j around 0 70.5%

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

      1. *-commutative 70.5%

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

      2. sub-neg 70.5%

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

      3. +-commutative 70.5%

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

      4. neg-mul-1 70.5%

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

      5. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in c around 0 61.9%

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

      1. neg-mul-1 61.9%

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

      2. distribute-rgt-neg-in 61.9%

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

   8. Simplified 61.9%

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

   if 4.39999999999999977e132 < j

   1. Initial program 71.5%

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

   3. Taylor expanded in t around -inf 53.8%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in j around inf 80.6%

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

      1. associate-*r* 78.5%

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

      2. *-commutative 78.5%

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

      3. mul-1-neg 78.5%

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

      4. unsub-neg 78.5%

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

      5. associate-/l* 80.7%

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

   8. Simplified 80.7%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.7 \cdot 10^{+102}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(c - i \cdot \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{+106}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(c - i \cdot \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -9.5e+106)
   (* j (- (* t c) (* y i)))
   (if (<= j 1.1e+88)
     (- (* x (- (* y z) (* t a))) (* b (* z c)))
     (* (* t j) (- c (* i (/ y t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -9.5e+106) {
		tmp = j * ((t * c) - (y * i));
	} else if (j <= 1.1e+88) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else {
		tmp = (t * j) * (c - (i * (y / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-9.5d+106)) then
        tmp = j * ((t * c) - (y * i))
    else if (j <= 1.1d+88) then
        tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
    else
        tmp = (t * j) * (c - (i * (y / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -9.5e+106) {
		tmp = j * ((t * c) - (y * i));
	} else if (j <= 1.1e+88) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else {
		tmp = (t * j) * (c - (i * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -9.5e+106:
		tmp = j * ((t * c) - (y * i))
	elif j <= 1.1e+88:
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
	else:
		tmp = (t * j) * (c - (i * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -9.5e+106)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (j <= 1.1e+88)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(z * c)));
	else
		tmp = Float64(Float64(t * j) * Float64(c - Float64(i * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -9.5e+106)
		tmp = j * ((t * c) - (y * i));
	elseif (j <= 1.1e+88)
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	else
		tmp = (t * j) * (c - (i * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -9.5e+106], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.1e+88], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * j), $MachinePrecision] * N[(c - N[(i * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -9.4999999999999995e106

   1. Initial program 67.4%

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

   3. Taylor expanded in y around 0 60.9%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in j around inf 79.0%

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

      1. neg-mul-1 79.0%

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

      2. +-commutative 79.0%

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

      3. sub-neg 79.0%

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

   8. Simplified 79.0%

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

   if -9.4999999999999995e106 < j < 1.10000000000000004e88

   1. Initial program 77.0%

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

   3. Taylor expanded in j around 0 72.2%

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

      1. *-commutative 72.2%

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

      2. sub-neg 72.2%

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

      3. +-commutative 72.2%

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

      4. neg-mul-1 72.2%

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

      5. *-commutative 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in c around inf 60.9%

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

      1. *-commutative 60.9%

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

   8. Simplified 60.9%

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

   if 1.10000000000000004e88 < j

   1. Initial program 74.0%

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

   3. Taylor expanded in t around -inf 58.4%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in j around inf 72.8%

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

      1. associate-*r* 71.1%

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

      2. *-commutative 71.1%

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

      3. mul-1-neg 71.1%

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

      4. unsub-neg 71.1%

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

      5. associate-/l* 72.9%

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

   8. Simplified 72.9%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{+106}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot j\right) \cdot \left(c - i \cdot \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-122}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-70}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -3000000000000.0)
     t_1
     (if (<= c -1.45e-122)
       (* z (* x y))
       (if (<= c 3.6e-70) (* a (- (* b i) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3000000000000.0) {
		tmp = t_1;
	} else if (c <= -1.45e-122) {
		tmp = z * (x * y);
	} else if (c <= 3.6e-70) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-3000000000000.0d0)) then
        tmp = t_1
    else if (c <= (-1.45d-122)) then
        tmp = z * (x * y)
    else if (c <= 3.6d-70) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3000000000000.0) {
		tmp = t_1;
	} else if (c <= -1.45e-122) {
		tmp = z * (x * y);
	} else if (c <= 3.6e-70) {
		tmp = a * ((b * i) - (x * t));
	} 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 <= -3000000000000.0:
		tmp = t_1
	elif c <= -1.45e-122:
		tmp = z * (x * y)
	elif c <= 3.6e-70:
		tmp = a * ((b * i) - (x * t))
	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 <= -3000000000000.0)
		tmp = t_1;
	elseif (c <= -1.45e-122)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 3.6e-70)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3000000000000.0)
		tmp = t_1;
	elseif (c <= -1.45e-122)
		tmp = z * (x * y);
	elseif (c <= 3.6e-70)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3000000000000.0], t$95$1, If[LessEqual[c, -1.45e-122], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.6e-70], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3e12 or 3.6000000000000002e-70 < c

   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 inf 61.3%

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

      1. *-commutative 61.3%

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

   5. Simplified 61.3%

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

   if -3e12 < c < -1.4500000000000001e-122

   1. Initial program 82.1%

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

   3. Taylor expanded in z around inf 58.8%

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

   4. Taylor expanded in x around inf 48.7%

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

   if -1.4500000000000001e-122 < c < 3.6000000000000002e-70

   1. Initial program 85.3%

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

   3. Taylor expanded in y around 0 76.7%

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

   5. Simplified 84.5%

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

      1. associate--l+ 84.5%

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

   7. Applied egg-rr 84.5%

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

   8. Taylor expanded in a around inf 48.6%

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

      1. mul-1-neg 48.6%

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

      2. distribute-lft-neg-out 48.6%

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

      3. cancel-sign-sub 48.6%

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

      4. +-commutative 48.6%

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

      5. *-commutative 48.6%

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

      6. mul-1-neg 48.6%

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

      7. unsub-neg 48.6%

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

      8. *-commutative 48.6%

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

   10. Simplified 48.6%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3000000000000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-122}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-70}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 40.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+229}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= x -1.3e+56)
     t_1
     (if (<= x 6.5e-10)
       (* b (- (* a i) (* z c)))
       (if (<= x 1.16e+229) t_1 (* a (- (* b i) (* x t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -1.3e+56) {
		tmp = t_1;
	} else if (x <= 6.5e-10) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 1.16e+229) {
		tmp = t_1;
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x * y)
    if (x <= (-1.3d+56)) then
        tmp = t_1
    else if (x <= 6.5d-10) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 1.16d+229) then
        tmp = t_1
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -1.3e+56) {
		tmp = t_1;
	} else if (x <= 6.5e-10) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 1.16e+229) {
		tmp = t_1;
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if x <= -1.3e+56:
		tmp = t_1
	elif x <= 6.5e-10:
		tmp = b * ((a * i) - (z * c))
	elif x <= 1.16e+229:
		tmp = t_1
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -1.3e+56)
		tmp = t_1;
	elseif (x <= 6.5e-10)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 1.16e+229)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	tmp = 0.0;
	if (x <= -1.3e+56)
		tmp = t_1;
	elseif (x <= 6.5e-10)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 1.16e+229)
		tmp = t_1;
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e+56], t$95$1, If[LessEqual[x, 6.5e-10], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.16e+229], t$95$1, N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.30000000000000005e56 or 6.5000000000000003e-10 < x < 1.16000000000000001e229

   1. Initial program 75.4%

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

   3. Taylor expanded in z around inf 55.9%

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

   4. Taylor expanded in x around inf 49.7%

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

   if -1.30000000000000005e56 < x < 6.5000000000000003e-10

   1. Initial program 74.3%

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

   3. Taylor expanded in b around inf 48.7%

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

   if 1.16000000000000001e229 < x

   1. Initial program 71.8%

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

   3. Taylor expanded in y around 0 50.4%

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

   5. Simplified 50.4%

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

      1. associate--l+ 50.4%

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

   7. Applied egg-rr 50.4%

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

   8. Taylor expanded in a around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. distribute-lft-neg-out 57.9%

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

      3. cancel-sign-sub 57.9%

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

      4. +-commutative 57.9%

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

      5. *-commutative 57.9%

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

      6. mul-1-neg 57.9%

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

      7. unsub-neg 57.9%

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

      8. *-commutative 57.9%

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

   10. Simplified 57.9%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+229}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+77} \lor \neg \left(z \leq 1.3 \cdot 10^{+86}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -5.2e+77) (not (<= z 1.3e+86)))
   (* z (- (* x y) (* b c)))
   (* j (- (* t c) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -5.2e+77) || !(z <= 1.3e+86)) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-5.2d+77)) .or. (.not. (z <= 1.3d+86))) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = j * ((t * c) - (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -5.2e+77) || !(z <= 1.3e+86)) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -5.2e+77) or not (z <= 1.3e+86):
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = j * ((t * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -5.2e+77) || !(z <= 1.3e+86))
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -5.2e+77) || ~((z <= 1.3e+86)))
		tmp = z * ((x * y) - (b * c));
	else
		tmp = j * ((t * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -5.2e+77], N[Not[LessEqual[z, 1.3e+86]], $MachinePrecision]], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2000000000000004e77 or 1.2999999999999999e86 < z

   1. Initial program 69.1%

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

   3. Taylor expanded in z around inf 74.5%

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

   if -5.2000000000000004e77 < z < 1.2999999999999999e86

   1. Initial program 78.3%

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

   3. Taylor expanded in y around 0 70.9%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in j around inf 54.2%

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

      1. neg-mul-1 54.2%

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

      2. +-commutative 54.2%

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

      3. sub-neg 54.2%

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

   8. Simplified 54.2%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+77} \lor \neg \left(z \leq 1.3 \cdot 10^{+86}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+17} \lor \neg \left(t \leq 6800000000000\right):\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -6.6e+17) (not (<= t 6800000000000.0)))
   (* t (- (* c j) (* x a)))
   (* y (- (* x z) (* i 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 ((t <= -6.6e+17) || !(t <= 6800000000000.0)) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = y * ((x * z) - (i * 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 ((t <= (-6.6d+17)) .or. (.not. (t <= 6800000000000.0d0))) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = y * ((x * z) - (i * 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 ((t <= -6.6e+17) || !(t <= 6800000000000.0)) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -6.6e+17) or not (t <= 6800000000000.0):
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = y * ((x * z) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -6.6e+17) || !(t <= 6800000000000.0))
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -6.6e+17) || ~((t <= 6800000000000.0)))
		tmp = t * ((c * j) - (x * a));
	else
		tmp = y * ((x * z) - (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -6.6e+17], N[Not[LessEqual[t, 6800000000000.0]], $MachinePrecision]], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.6e17 or 6.8e12 < t

   1. Initial program 68.6%

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

   3. Taylor expanded in t around inf 61.5%

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

      1. +-commutative 61.5%

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

      2. mul-1-neg 61.5%

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

      3. unsub-neg 61.5%

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

   5. Simplified 61.5%

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

   if -6.6e17 < t < 6.8e12

   1. Initial program 81.1%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

      4. *-commutative 60.3%

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

   5. Simplified 60.3%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+17} \lor \neg \left(t \leq 6800000000000\right):\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+102} \lor \neg \left(j \leq 2.7 \cdot 10^{+104}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -2.9e+102) (not (<= j 2.7e+104)))
   (* j (- (* t c) (* y i)))
   (* x (- (* y z) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -2.9e+102) || !(j <= 2.7e+104)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-2.9d+102)) .or. (.not. (j <= 2.7d+104))) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = x * ((y * z) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -2.9e+102) || !(j <= 2.7e+104)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -2.9e+102) or not (j <= 2.7e+104):
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = x * ((y * z) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -2.9e+102) || !(j <= 2.7e+104))
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -2.9e+102) || ~((j <= 2.7e+104)))
		tmp = j * ((t * c) - (y * i));
	else
		tmp = x * ((y * z) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -2.9e+102], N[Not[LessEqual[j, 2.7e+104]], $MachinePrecision]], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -2.9000000000000002e102 or 2.69999999999999985e104 < j

   1. Initial program 71.2%

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

   3. Taylor expanded in y around 0 61.3%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in j around inf 76.7%

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

      1. neg-mul-1 76.7%

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

      2. +-commutative 76.7%

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

      3. sub-neg 76.7%

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

   8. Simplified 76.7%

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

   if -2.9000000000000002e102 < j < 2.69999999999999985e104

   1. Initial program 76.8%

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

   3. Taylor expanded in y around 0 73.9%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in x around inf 50.5%

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

      1. neg-mul-1 50.5%

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

      2. +-commutative 50.5%

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

      3. *-commutative 50.5%

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

      4. sub-neg 50.5%

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

   8. Simplified 50.5%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+102} \lor \neg \left(j \leq 2.7 \cdot 10^{+104}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 52.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.8 \cdot 10^{+103} \lor \neg \left(j \leq 7.6 \cdot 10^{-28}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.8e+103) (not (<= j 7.6e-28)))
   (* j (- (* t c) (* y i)))
   (* 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 tmp;
	if ((j <= -1.8e+103) || !(j <= 7.6e-28)) {
		tmp = j * ((t * c) - (y * i));
	} 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) :: tmp
    if ((j <= (-1.8d+103)) .or. (.not. (j <= 7.6d-28))) then
        tmp = j * ((t * c) - (y * i))
    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 tmp;
	if ((j <= -1.8e+103) || !(j <= 7.6e-28)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.8e+103) or not (j <= 7.6e-28):
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.8e+103) || !(j <= 7.6e-28))
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	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)
	tmp = 0.0;
	if ((j <= -1.8e+103) || ~((j <= 7.6e-28)))
		tmp = j * ((t * c) - (y * i));
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.8e+103], N[Not[LessEqual[j, 7.6e-28]], $MachinePrecision]], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.80000000000000008e103 or 7.60000000000000018e-28 < j

   1. Initial program 71.3%

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

   3. Taylor expanded in y around 0 59.8%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in j around inf 71.9%

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

      1. neg-mul-1 71.9%

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

      2. +-commutative 71.9%

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

      3. sub-neg 71.9%

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

   8. Simplified 71.9%

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

   if -1.80000000000000008e103 < j < 7.60000000000000018e-28

   1. Initial program 77.6%

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

   3. Taylor expanded in b around inf 48.4%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.8 \cdot 10^{+103} \lor \neg \left(j \leq 7.6 \cdot 10^{-28}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x - b \cdot \frac{c}{y}\right)\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+73}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -9.2e+66)
   (* z (* y (- x (* b (/ c y)))))
   (if (<= z 7e+73) (* j (- (* t c) (* y i))) (* z (- (* x y) (* b c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -9.2e+66) {
		tmp = z * (y * (x - (b * (c / y))));
	} else if (z <= 7e+73) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-9.2d+66)) then
        tmp = z * (y * (x - (b * (c / y))))
    else if (z <= 7d+73) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = z * ((x * y) - (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -9.2e+66) {
		tmp = z * (y * (x - (b * (c / y))));
	} else if (z <= 7e+73) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -9.2e+66:
		tmp = z * (y * (x - (b * (c / y))))
	elif z <= 7e+73:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -9.2e+66)
		tmp = Float64(z * Float64(y * Float64(x - Float64(b * Float64(c / y)))));
	elseif (z <= 7e+73)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -9.2e+66)
		tmp = z * (y * (x - (b * (c / y))));
	elseif (z <= 7e+73)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -9.2e+66], N[(z * N[(y * N[(x - N[(b * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+73], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.2e66

   1. Initial program 68.3%

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

   3. Taylor expanded in z around inf 82.1%

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

   4. Taylor expanded in y around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. unsub-neg 82.1%

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

      3. associate-/l* 85.3%

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

   6. Simplified 85.3%

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

   if -9.2e66 < z < 7.00000000000000004e73

   1. Initial program 78.3%

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

   3. Taylor expanded in y around 0 70.9%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in j around inf 54.2%

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

      1. neg-mul-1 54.2%

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

      2. +-commutative 54.2%

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

      3. sub-neg 54.2%

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

   8. Simplified 54.2%

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

   if 7.00000000000000004e73 < z

   1. Initial program 69.9%

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

   3. Taylor expanded in z around inf 65.2%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \left(y \cdot \left(x - b \cdot \frac{c}{y}\right)\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+73}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+20} \lor \neg \left(t \leq 9.5 \cdot 10^{+38}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -5e+20) (not (<= t 9.5e+38))) (* c (* t j)) (* z (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -5e+20) || !(t <= 9.5e+38)) {
		tmp = c * (t * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-5d+20)) .or. (.not. (t <= 9.5d+38))) then
        tmp = c * (t * j)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -5e+20) || !(t <= 9.5e+38)) {
		tmp = c * (t * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -5e+20) or not (t <= 9.5e+38):
		tmp = c * (t * j)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -5e+20) || !(t <= 9.5e+38))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -5e+20) || ~((t <= 9.5e+38)))
		tmp = c * (t * j);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -5e+20], N[Not[LessEqual[t, 9.5e+38]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5e20 or 9.4999999999999995e38 < t

   1. Initial program 68.7%

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

   3. Taylor expanded in c around inf 55.7%

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

      1. *-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in t around inf 45.0%

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

   if -5e20 < t < 9.4999999999999995e38

   1. Initial program 80.5%

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

   3. Taylor expanded in z around inf 53.7%

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

   4. Taylor expanded in x around inf 38.0%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+20} \lor \neg \left(t \leq 9.5 \cdot 10^{+38}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.8 \cdot 10^{+74} \lor \neg \left(i \leq 1.35 \cdot 10^{+54}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -5.8e+74) (not (<= i 1.35e+54))) (* b (* a 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 ((i <= -5.8e+74) || !(i <= 1.35e+54)) {
		tmp = b * (a * 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 ((i <= (-5.8d+74)) .or. (.not. (i <= 1.35d+54))) then
        tmp = b * (a * 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 ((i <= -5.8e+74) || !(i <= 1.35e+54)) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -5.8e+74) or not (i <= 1.35e+54):
		tmp = b * (a * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -5.8e+74) || !(i <= 1.35e+54))
		tmp = Float64(b * Float64(a * 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 ((i <= -5.8e+74) || ~((i <= 1.35e+54)))
		tmp = b * (a * 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[i, -5.8e+74], N[Not[LessEqual[i, 1.35e+54]], $MachinePrecision]], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -5.8000000000000005e74 or 1.35000000000000005e54 < i

   1. Initial program 68.3%

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

   3. Taylor expanded in b around inf 51.7%

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

   4. Taylor expanded in a around inf 45.1%

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

   if -5.8000000000000005e74 < i < 1.35000000000000005e54

   1. Initial program 78.7%

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

   3. Taylor expanded in c around inf 48.0%

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

      1. *-commutative 48.0%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in t around inf 32.7%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.8 \cdot 10^{+74} \lor \neg \left(i \leq 1.35 \cdot 10^{+54}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 22.2% 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 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 b around inf 38.2%

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

4. Taylor expanded in a around inf 21.5%

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

Alternative 22: 22.0% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 b around inf 38.2%

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

4. Taylor expanded in a around inf 20.6%

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

Developer Target 1: 68.9% 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 2024135 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1015122364899489/125000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -942510763643697/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -238547917063487/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 10535888557455487/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* 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)))))