Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 72.7% → 83.3%

Time: 23.7s

Alternatives: 24

Speedup: 0.5×

• 58.2% 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: 72.7% 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: 83.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(i * N[(N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] - N[(y * 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 92.5%

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

   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 i around inf 30.3%

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

   5. Simplified 43.0%

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

   6. Taylor expanded in t around 0 59.0%

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

      1. +-commutative 59.0%

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

      2. mul-1-neg 59.0%

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

      3. sub-neg 59.0%

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

      4. *-commutative 59.0%

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

   8. Simplified 59.0%

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

4. Final simplification 84.2%

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

Alternative 2: 64.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.7 \cdot 10^{+248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.55 \cdot 10^{+57}:\\ \;\;\;\;i \cdot \left(\frac{z \cdot \left(x \cdot y - b \cdot c\right)}{i} + \left(a \cdot b - y \cdot j\right)\right)\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-222}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-84}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - \left(i \cdot \left(y \cdot j\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(t \cdot \left(y \cdot \frac{z}{t} - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -1.7e+248)
     t_1
     (if (<= c -2.55e+57)
       (* i (+ (/ (* z (- (* x y) (* b c))) i) (- (* a b) (* y j))))
       (if (<= c -1.2e-222)
         (+ (* y (- (* x z) (* i j))) (* b (- (* a i) (* z c))))
         (if (<= c 4.5e-84)
           (- (* a (* b i)) (+ (* i (* y j)) (* x (- (* t a) (* y z)))))
           (if (<= c 1.1e+155)
             (+ (* j (- (* t c) (* y i))) (* x (* t (- (* y (/ z t)) a))))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.7e+248) {
		tmp = t_1;
	} else if (c <= -2.55e+57) {
		tmp = i * (((z * ((x * y) - (b * c))) / i) + ((a * b) - (y * j)));
	} else if (c <= -1.2e-222) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	} else if (c <= 4.5e-84) {
		tmp = (a * (b * i)) - ((i * (y * j)) + (x * ((t * a) - (y * z))));
	} else if (c <= 1.1e+155) {
		tmp = (j * ((t * c) - (y * i))) + (x * (t * ((y * (z / t)) - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-1.7d+248)) then
        tmp = t_1
    else if (c <= (-2.55d+57)) then
        tmp = i * (((z * ((x * y) - (b * c))) / i) + ((a * b) - (y * j)))
    else if (c <= (-1.2d-222)) then
        tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)))
    else if (c <= 4.5d-84) then
        tmp = (a * (b * i)) - ((i * (y * j)) + (x * ((t * a) - (y * z))))
    else if (c <= 1.1d+155) then
        tmp = (j * ((t * c) - (y * i))) + (x * (t * ((y * (z / t)) - a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.7e+248) {
		tmp = t_1;
	} else if (c <= -2.55e+57) {
		tmp = i * (((z * ((x * y) - (b * c))) / i) + ((a * b) - (y * j)));
	} else if (c <= -1.2e-222) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	} else if (c <= 4.5e-84) {
		tmp = (a * (b * i)) - ((i * (y * j)) + (x * ((t * a) - (y * z))));
	} else if (c <= 1.1e+155) {
		tmp = (j * ((t * c) - (y * i))) + (x * (t * ((y * (z / t)) - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1.7e+248:
		tmp = t_1
	elif c <= -2.55e+57:
		tmp = i * (((z * ((x * y) - (b * c))) / i) + ((a * b) - (y * j)))
	elif c <= -1.2e-222:
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)))
	elif c <= 4.5e-84:
		tmp = (a * (b * i)) - ((i * (y * j)) + (x * ((t * a) - (y * z))))
	elif c <= 1.1e+155:
		tmp = (j * ((t * c) - (y * i))) + (x * (t * ((y * (z / t)) - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.7e+248)
		tmp = t_1;
	elseif (c <= -2.55e+57)
		tmp = Float64(i * Float64(Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) / i) + Float64(Float64(a * b) - Float64(y * j))));
	elseif (c <= -1.2e-222)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (c <= 4.5e-84)
		tmp = Float64(Float64(a * Float64(b * i)) - Float64(Float64(i * Float64(y * j)) + Float64(x * Float64(Float64(t * a) - Float64(y * z)))));
	elseif (c <= 1.1e+155)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(t * Float64(Float64(y * Float64(z / t)) - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.7e+248)
		tmp = t_1;
	elseif (c <= -2.55e+57)
		tmp = i * (((z * ((x * y) - (b * c))) / i) + ((a * b) - (y * j)));
	elseif (c <= -1.2e-222)
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	elseif (c <= 4.5e-84)
		tmp = (a * (b * i)) - ((i * (y * j)) + (x * ((t * a) - (y * z))));
	elseif (c <= 1.1e+155)
		tmp = (j * ((t * c) - (y * i))) + (x * (t * ((y * (z / t)) - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.7e+248], t$95$1, If[LessEqual[c, -2.55e+57], N[(i * N[(N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.2e-222], 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], If[LessEqual[c, 4.5e-84], N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.1e+155], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(t * N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.7e248 or 1.1000000000000001e155 < c

   1. Initial program 42.2%

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

   3. Taylor expanded in c around inf 78.5%

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

      1. *-commutative 78.5%

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

   5. Simplified 78.5%

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

   if -1.7e248 < c < -2.55000000000000011e57

   1. Initial program 56.1%

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

   3. Taylor expanded in i around inf 78.1%

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

   5. Simplified 59.6%

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

   6. Taylor expanded in t around 0 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. sub-neg 65.6%

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

      4. *-commutative 65.6%

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

   8. Simplified 65.6%

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

   if -2.55000000000000011e57 < c < -1.19999999999999997e-222

   1. Initial program 77.3%

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

   3. Taylor expanded in y around inf 74.0%

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

      1. +-commutative 74.0%

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

      2. mul-1-neg 74.0%

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

      3. unsub-neg 74.0%

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

      4. *-commutative 74.0%

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

      5. associate-/l* 72.4%

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

      6. *-commutative 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in t around 0 71.1%

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

      1. associate-*r* 72.5%

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

      2. associate-*r* 72.5%

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

      3. *-commutative 72.5%

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

      4. associate-*r* 75.7%

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

      5. distribute-rgt-in 77.4%

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

      6. +-commutative 77.4%

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

      7. mul-1-neg 77.4%

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

      8. unsub-neg 77.4%

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

      9. *-commutative 77.4%

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

      10. *-commutative 77.4%

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

   8. Simplified 77.4%

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

   if -1.19999999999999997e-222 < c < 4.50000000000000016e-84

   1. Initial program 81.5%

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

   3. Taylor expanded in c around 0 78.4%

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

   if 4.50000000000000016e-84 < c < 1.1000000000000001e155

   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 b around 0 74.7%

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

   4. Taylor expanded in t around inf 78.8%

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

      1. associate-/l* 76.8%

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

   6. Simplified 76.8%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.7 \cdot 10^{+248}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.55 \cdot 10^{+57}:\\ \;\;\;\;i \cdot \left(\frac{z \cdot \left(x \cdot y - b \cdot c\right)}{i} + \left(a \cdot b - y \cdot j\right)\right)\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-222}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-84}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - \left(i \cdot \left(y \cdot j\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(t \cdot \left(y \cdot \frac{z}{t} - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 41.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.9 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-60}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{-270}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-264}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 4.55 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -5.9e+51)
     t_2
     (if (<= b -2.1e-60)
       (* j (* t c))
       (if (<= b -4.1e-78)
         (* z (* x y))
         (if (<= b -1.25e-144)
           t_1
           (if (<= b -4.7e-270)
             (* (* x t) (- a))
             (if (<= b 4.8e-264)
               (* x (* y z))
               (if (<= b 4.55e-7) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (i * -j);
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.9e+51) {
		tmp = t_2;
	} else if (b <= -2.1e-60) {
		tmp = j * (t * c);
	} else if (b <= -4.1e-78) {
		tmp = z * (x * y);
	} else if (b <= -1.25e-144) {
		tmp = t_1;
	} else if (b <= -4.7e-270) {
		tmp = (x * t) * -a;
	} else if (b <= 4.8e-264) {
		tmp = x * (y * z);
	} else if (b <= 4.55e-7) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (i * -j)
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-5.9d+51)) then
        tmp = t_2
    else if (b <= (-2.1d-60)) then
        tmp = j * (t * c)
    else if (b <= (-4.1d-78)) then
        tmp = z * (x * y)
    else if (b <= (-1.25d-144)) then
        tmp = t_1
    else if (b <= (-4.7d-270)) then
        tmp = (x * t) * -a
    else if (b <= 4.8d-264) then
        tmp = x * (y * z)
    else if (b <= 4.55d-7) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (i * -j);
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.9e+51) {
		tmp = t_2;
	} else if (b <= -2.1e-60) {
		tmp = j * (t * c);
	} else if (b <= -4.1e-78) {
		tmp = z * (x * y);
	} else if (b <= -1.25e-144) {
		tmp = t_1;
	} else if (b <= -4.7e-270) {
		tmp = (x * t) * -a;
	} else if (b <= 4.8e-264) {
		tmp = x * (y * z);
	} else if (b <= 4.55e-7) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -5.9e+51:
		tmp = t_2
	elif b <= -2.1e-60:
		tmp = j * (t * c)
	elif b <= -4.1e-78:
		tmp = z * (x * y)
	elif b <= -1.25e-144:
		tmp = t_1
	elif b <= -4.7e-270:
		tmp = (x * t) * -a
	elif b <= 4.8e-264:
		tmp = x * (y * z)
	elif b <= 4.55e-7:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-j)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.9e+51)
		tmp = t_2;
	elseif (b <= -2.1e-60)
		tmp = Float64(j * Float64(t * c));
	elseif (b <= -4.1e-78)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= -1.25e-144)
		tmp = t_1;
	elseif (b <= -4.7e-270)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (b <= 4.8e-264)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 4.55e-7)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (i * -j);
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.9e+51)
		tmp = t_2;
	elseif (b <= -2.1e-60)
		tmp = j * (t * c);
	elseif (b <= -4.1e-78)
		tmp = z * (x * y);
	elseif (b <= -1.25e-144)
		tmp = t_1;
	elseif (b <= -4.7e-270)
		tmp = (x * t) * -a;
	elseif (b <= 4.8e-264)
		tmp = x * (y * z);
	elseif (b <= 4.55e-7)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.9e+51], t$95$2, If[LessEqual[b, -2.1e-60], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.1e-78], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.25e-144], t$95$1, If[LessEqual[b, -4.7e-270], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[b, 4.8e-264], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.55e-7], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -5.89999999999999983e51 or 4.5499999999999998e-7 < b

   1. Initial program 70.3%

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

   3. Taylor expanded in b around inf 63.8%

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

   if -5.89999999999999983e51 < b < -2.09999999999999991e-60

   1. Initial program 74.9%

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

   3. Taylor expanded in b around 0 71.6%

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

   4. Taylor expanded in c around inf 37.4%

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

      1. associate-*r* 40.7%

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

      2. *-commutative 40.7%

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

      3. associate-*r* 40.7%

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

   6. Simplified 40.7%

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

   if -2.09999999999999991e-60 < b < -4.0999999999999998e-78

   1. Initial program 51.3%

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

   3. Taylor expanded in z around inf 67.0%

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

   4. Taylor expanded in x around inf 67.2%

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

   if -4.0999999999999998e-78 < b < -1.2499999999999999e-144 or 4.7999999999999997e-264 < b < 4.5499999999999998e-7

   1. Initial program 59.9%

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

   3. Taylor expanded in c around 0 59.7%

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

   4. Taylor expanded in j around inf 40.1%

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

      1. neg-mul-1 40.1%

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

      2. *-commutative 40.1%

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

      3. distribute-rgt-neg-in 40.1%

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

      4. *-commutative 40.1%

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

      5. associate-*l* 45.3%

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

   6. Simplified 45.3%

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

   if -1.2499999999999999e-144 < b < -4.6999999999999997e-270

   1. Initial program 83.2%

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

   3. Taylor expanded in c around 0 78.8%

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

   4. Taylor expanded in t around inf 55.0%

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

      1. associate-*r* 55.0%

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

      2. mul-1-neg 55.0%

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

      3. *-commutative 55.0%

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

   6. Simplified 55.0%

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

   if -4.6999999999999997e-270 < b < 4.7999999999999997e-264

   1. Initial program 75.0%

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

   3. Taylor expanded in b around 0 77.2%

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

   4. Taylor expanded in j around 0 53.8%

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

   5. Taylor expanded in y around inf 49.5%

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

      1. *-commutative 49.5%

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

   7. Simplified 49.5%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.9 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-60}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{-270}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-264}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 4.55 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-270}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 0.0016:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -2.6e+52)
     t_2
     (if (<= b -1.9e-151)
       t_1
       (if (<= b -3.2e-270)
         (* (* x t) (- a))
         (if (<= b -5.4e-285)
           (* x (* y z))
           (if (<= b 1.05e-85)
             t_1
             (if (<= b 6.5e-30)
               (* z (* x y))
               (if (<= b 0.0016) (* i (- (* a b) (* y j))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.6e+52) {
		tmp = t_2;
	} else if (b <= -1.9e-151) {
		tmp = t_1;
	} else if (b <= -3.2e-270) {
		tmp = (x * t) * -a;
	} else if (b <= -5.4e-285) {
		tmp = x * (y * z);
	} else if (b <= 1.05e-85) {
		tmp = t_1;
	} else if (b <= 6.5e-30) {
		tmp = z * (x * y);
	} else if (b <= 0.0016) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-2.6d+52)) then
        tmp = t_2
    else if (b <= (-1.9d-151)) then
        tmp = t_1
    else if (b <= (-3.2d-270)) then
        tmp = (x * t) * -a
    else if (b <= (-5.4d-285)) then
        tmp = x * (y * z)
    else if (b <= 1.05d-85) then
        tmp = t_1
    else if (b <= 6.5d-30) then
        tmp = z * (x * y)
    else if (b <= 0.0016d0) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.6e+52) {
		tmp = t_2;
	} else if (b <= -1.9e-151) {
		tmp = t_1;
	} else if (b <= -3.2e-270) {
		tmp = (x * t) * -a;
	} else if (b <= -5.4e-285) {
		tmp = x * (y * z);
	} else if (b <= 1.05e-85) {
		tmp = t_1;
	} else if (b <= 6.5e-30) {
		tmp = z * (x * y);
	} else if (b <= 0.0016) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -2.6e+52:
		tmp = t_2
	elif b <= -1.9e-151:
		tmp = t_1
	elif b <= -3.2e-270:
		tmp = (x * t) * -a
	elif b <= -5.4e-285:
		tmp = x * (y * z)
	elif b <= 1.05e-85:
		tmp = t_1
	elif b <= 6.5e-30:
		tmp = z * (x * y)
	elif b <= 0.0016:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.6e+52)
		tmp = t_2;
	elseif (b <= -1.9e-151)
		tmp = t_1;
	elseif (b <= -3.2e-270)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (b <= -5.4e-285)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 1.05e-85)
		tmp = t_1;
	elseif (b <= 6.5e-30)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 0.0016)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.6e+52)
		tmp = t_2;
	elseif (b <= -1.9e-151)
		tmp = t_1;
	elseif (b <= -3.2e-270)
		tmp = (x * t) * -a;
	elseif (b <= -5.4e-285)
		tmp = x * (y * z);
	elseif (b <= 1.05e-85)
		tmp = t_1;
	elseif (b <= 6.5e-30)
		tmp = z * (x * y);
	elseif (b <= 0.0016)
		tmp = i * ((a * b) - (y * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.6e+52], t$95$2, If[LessEqual[b, -1.9e-151], t$95$1, If[LessEqual[b, -3.2e-270], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[b, -5.4e-285], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e-85], t$95$1, If[LessEqual[b, 6.5e-30], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.0016], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.6e52 or 0.00160000000000000008 < b

   1. Initial program 70.1%

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

   3. Taylor expanded in b around inf 64.3%

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

   if -2.6e52 < b < -1.89999999999999985e-151 or -5.3999999999999997e-285 < b < 1.05e-85

   1. Initial program 64.8%

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

   3. Taylor expanded in j around inf 57.6%

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

   if -1.89999999999999985e-151 < b < -3.19999999999999988e-270

   1. Initial program 83.2%

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

   3. Taylor expanded in c around 0 78.8%

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

   4. Taylor expanded in t around inf 55.0%

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

      1. associate-*r* 55.0%

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

      2. mul-1-neg 55.0%

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

      3. *-commutative 55.0%

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

   6. Simplified 55.0%

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

   if -3.19999999999999988e-270 < b < -5.3999999999999997e-285

   1. Initial program 88.4%

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

   3. Taylor expanded in b around 0 80.2%

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

   4. Taylor expanded in j around 0 80.4%

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

   5. Taylor expanded in y around inf 70.8%

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

      1. *-commutative 70.8%

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

   7. Simplified 70.8%

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

   if 1.05e-85 < b < 6.5000000000000005e-30

   1. Initial program 50.0%

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

   3. Taylor expanded in z around inf 65.6%

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

   4. Taylor expanded in x around inf 64.2%

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

   if 6.5000000000000005e-30 < b < 0.00160000000000000008

   1. Initial program 81.3%

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

   3. Taylor expanded in i around inf 100.0%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in i around inf 61.4%

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

      1. distribute-lft-in 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. neg-mul-1 61.4%

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

      5. mul-1-neg 61.4%

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

      6. remove-double-neg 61.4%

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

      7. *-commutative 61.4%

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

   8. Simplified 61.4%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+52}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-151}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-270}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-85}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-30}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 0.0016:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.1 \cdot 10^{+98}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -8.8 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq -1.65 \cdot 10^{-171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-219}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.55 \cdot 10^{-297}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-209}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{+46}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (* t (- (* c j) (* x a))))
        (t_3 (* i (- (* a b) (* y j)))))
   (if (<= i -1.1e+98)
     t_3
     (if (<= i -8.8e-45)
       (* x (- (* y z) (* t a)))
       (if (<= i -1.65e-171)
         t_1
         (if (<= i -4.5e-219)
           t_2
           (if (<= i -1.55e-297)
             t_1
             (if (<= i 1.8e-209)
               (* c (- (* t j) (* z b)))
               (if (<= i 8.2e+46) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.1e+98) {
		tmp = t_3;
	} else if (i <= -8.8e-45) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= -1.65e-171) {
		tmp = t_1;
	} else if (i <= -4.5e-219) {
		tmp = t_2;
	} else if (i <= -1.55e-297) {
		tmp = t_1;
	} else if (i <= 1.8e-209) {
		tmp = c * ((t * j) - (z * b));
	} else if (i <= 8.2e+46) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = t * ((c * j) - (x * a))
    t_3 = i * ((a * b) - (y * j))
    if (i <= (-1.1d+98)) then
        tmp = t_3
    else if (i <= (-8.8d-45)) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= (-1.65d-171)) then
        tmp = t_1
    else if (i <= (-4.5d-219)) then
        tmp = t_2
    else if (i <= (-1.55d-297)) then
        tmp = t_1
    else if (i <= 1.8d-209) then
        tmp = c * ((t * j) - (z * b))
    else if (i <= 8.2d+46) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.1e+98) {
		tmp = t_3;
	} else if (i <= -8.8e-45) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= -1.65e-171) {
		tmp = t_1;
	} else if (i <= -4.5e-219) {
		tmp = t_2;
	} else if (i <= -1.55e-297) {
		tmp = t_1;
	} else if (i <= 1.8e-209) {
		tmp = c * ((t * j) - (z * b));
	} else if (i <= 8.2e+46) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = t * ((c * j) - (x * a))
	t_3 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -1.1e+98:
		tmp = t_3
	elif i <= -8.8e-45:
		tmp = x * ((y * z) - (t * a))
	elif i <= -1.65e-171:
		tmp = t_1
	elif i <= -4.5e-219:
		tmp = t_2
	elif i <= -1.55e-297:
		tmp = t_1
	elif i <= 1.8e-209:
		tmp = c * ((t * j) - (z * b))
	elif i <= 8.2e+46:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_3 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.1e+98)
		tmp = t_3;
	elseif (i <= -8.8e-45)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= -1.65e-171)
		tmp = t_1;
	elseif (i <= -4.5e-219)
		tmp = t_2;
	elseif (i <= -1.55e-297)
		tmp = t_1;
	elseif (i <= 1.8e-209)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (i <= 8.2e+46)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = t * ((c * j) - (x * a));
	t_3 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.1e+98)
		tmp = t_3;
	elseif (i <= -8.8e-45)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= -1.65e-171)
		tmp = t_1;
	elseif (i <= -4.5e-219)
		tmp = t_2;
	elseif (i <= -1.55e-297)
		tmp = t_1;
	elseif (i <= 1.8e-209)
		tmp = c * ((t * j) - (z * b));
	elseif (i <= 8.2e+46)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.1e+98], t$95$3, If[LessEqual[i, -8.8e-45], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.65e-171], t$95$1, If[LessEqual[i, -4.5e-219], t$95$2, If[LessEqual[i, -1.55e-297], t$95$1, If[LessEqual[i, 1.8e-209], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.2e+46], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.10000000000000004e98 or 8.19999999999999999e46 < i

   1. Initial program 63.8%

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

   3. Taylor expanded in i around inf 79.5%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in i around inf 70.7%

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

      1. distribute-lft-in 70.7%

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

      2. mul-1-neg 70.7%

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

      3. unsub-neg 70.7%

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

      4. neg-mul-1 70.7%

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

      5. mul-1-neg 70.7%

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

      6. remove-double-neg 70.7%

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

      7. *-commutative 70.7%

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

   8. Simplified 70.7%

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

   if -1.10000000000000004e98 < i < -8.79999999999999974e-45

   1. Initial program 75.7%

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

   3. Taylor expanded in b around 0 64.7%

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

   4. Taylor expanded in j around 0 56.2%

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

   if -8.79999999999999974e-45 < i < -1.6500000000000001e-171 or -4.50000000000000014e-219 < i < -1.5499999999999998e-297

   1. Initial program 64.5%

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

   3. Taylor expanded in z around inf 65.4%

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

   if -1.6500000000000001e-171 < i < -4.50000000000000014e-219 or 1.80000000000000008e-209 < i < 8.19999999999999999e46

   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 b around 0 66.5%

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

   4. Taylor expanded in t around inf 59.6%

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

      1. +-commutative 59.6%

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

      2. mul-1-neg 59.6%

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

      3. unsub-neg 59.6%

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

   6. Simplified 59.6%

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

   if -1.5499999999999998e-297 < i < 1.80000000000000008e-209

   1. Initial program 86.1%

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

   3. Taylor expanded in c around inf 69.1%

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

      1. *-commutative 69.1%

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

   5. Simplified 69.1%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.1 \cdot 10^{+98}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -8.8 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq -1.65 \cdot 10^{-171}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-219}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq -1.55 \cdot 10^{-297}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-209}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.9 \cdot 10^{+210}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{+138}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -5 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{-121}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{+154}:\\ \;\;\;\;t\_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -4.9e+210)
     t_2
     (if (<= c -4.8e+138)
       (* i (- (* a b) (* y j)))
       (if (<= c -5e+81)
         t_1
         (if (<= c -5.8e-121)
           (+ (* y (- (* x z) (* i j))) (* b (- (* a i) (* z c))))
           (if (<= c 5.2e+154) (- t_1 (* x (- (* t a) (* y z)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.9e+210) {
		tmp = t_2;
	} else if (c <= -4.8e+138) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= -5e+81) {
		tmp = t_1;
	} else if (c <= -5.8e-121) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	} else if (c <= 5.2e+154) {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-4.9d+210)) then
        tmp = t_2
    else if (c <= (-4.8d+138)) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= (-5d+81)) then
        tmp = t_1
    else if (c <= (-5.8d-121)) then
        tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)))
    else if (c <= 5.2d+154) then
        tmp = t_1 - (x * ((t * a) - (y * z)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.9e+210) {
		tmp = t_2;
	} else if (c <= -4.8e+138) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= -5e+81) {
		tmp = t_1;
	} else if (c <= -5.8e-121) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	} else if (c <= 5.2e+154) {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -4.9e+210:
		tmp = t_2
	elif c <= -4.8e+138:
		tmp = i * ((a * b) - (y * j))
	elif c <= -5e+81:
		tmp = t_1
	elif c <= -5.8e-121:
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)))
	elif c <= 5.2e+154:
		tmp = t_1 - (x * ((t * a) - (y * z)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -4.9e+210)
		tmp = t_2;
	elseif (c <= -4.8e+138)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= -5e+81)
		tmp = t_1;
	elseif (c <= -5.8e-121)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (c <= 5.2e+154)
		tmp = Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -4.9e+210)
		tmp = t_2;
	elseif (c <= -4.8e+138)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= -5e+81)
		tmp = t_1;
	elseif (c <= -5.8e-121)
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	elseif (c <= 5.2e+154)
		tmp = t_1 - (x * ((t * a) - (y * z)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.9e+210], t$95$2, If[LessEqual[c, -4.8e+138], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5e+81], t$95$1, If[LessEqual[c, -5.8e-121], 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], If[LessEqual[c, 5.2e+154], N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -4.90000000000000007e210 or 5.19999999999999978e154 < c

   1. Initial program 44.4%

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

   3. Taylor expanded in c around inf 78.1%

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

      1. *-commutative 78.1%

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

   5. Simplified 78.1%

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

   if -4.90000000000000007e210 < c < -4.8000000000000002e138

   1. Initial program 39.2%

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

   3. Taylor expanded in i around inf 54.7%

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

   5. Simplified 23.9%

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

   6. Taylor expanded in i around inf 59.9%

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

      1. distribute-lft-in 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

      4. neg-mul-1 59.9%

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

      5. mul-1-neg 59.9%

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

      6. remove-double-neg 59.9%

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

      7. *-commutative 59.9%

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

   8. Simplified 59.9%

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

   if -4.8000000000000002e138 < c < -4.9999999999999998e81

   1. Initial program 72.3%

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

   3. Taylor expanded in j around inf 73.7%

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

   if -4.9999999999999998e81 < c < -5.8e-121

   1. Initial program 71.0%

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

   3. Taylor expanded in y around inf 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. unsub-neg 70.8%

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

      4. *-commutative 70.8%

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

      5. associate-/l* 68.8%

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

      6. *-commutative 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in t around 0 68.3%

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

      1. associate-*r* 68.3%

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

      2. associate-*r* 68.3%

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

      3. *-commutative 68.3%

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

      4. associate-*r* 72.1%

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

      5. distribute-rgt-in 76.0%

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

      6. +-commutative 76.0%

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

      7. mul-1-neg 76.0%

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

      8. unsub-neg 76.0%

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

      9. *-commutative 76.0%

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

      10. *-commutative 76.0%

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

   8. Simplified 76.0%

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

   if -5.8e-121 < c < 5.19999999999999978e154

   1. Initial program 82.0%

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

   3. Taylor expanded in b around 0 71.8%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.9 \cdot 10^{+210}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{+138}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -5 \cdot 10^{+81}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{-121}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{+154}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right) + t\_1\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{+183}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+167}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{+42}:\\ \;\;\;\;i \cdot \left(\frac{z \cdot \left(x \cdot y - b \cdot c\right)}{i} + \left(a \cdot b - y \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-72}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (- (* j (- (* t c) (* y i))) (* x (- (* t a) (* y z)))))
        (t_3 (+ (* y (- (* x z) (* i j))) t_1)))
   (if (<= b -1.3e+195)
     t_1
     (if (<= b -8.2e+183)
       t_2
       (if (<= b -6.6e+167)
         t_3
         (if (<= b -2.2e+42)
           (* i (+ (/ (* z (- (* x y) (* b c))) i) (- (* a b) (* y j))))
           (if (<= b 5.8e-72) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double t_3 = (y * ((x * z) - (i * j))) + t_1;
	double tmp;
	if (b <= -1.3e+195) {
		tmp = t_1;
	} else if (b <= -8.2e+183) {
		tmp = t_2;
	} else if (b <= -6.6e+167) {
		tmp = t_3;
	} else if (b <= -2.2e+42) {
		tmp = i * (((z * ((x * y) - (b * c))) / i) + ((a * b) - (y * j)));
	} else if (b <= 5.8e-72) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
    t_3 = (y * ((x * z) - (i * j))) + t_1
    if (b <= (-1.3d+195)) then
        tmp = t_1
    else if (b <= (-8.2d+183)) then
        tmp = t_2
    else if (b <= (-6.6d+167)) then
        tmp = t_3
    else if (b <= (-2.2d+42)) then
        tmp = i * (((z * ((x * y) - (b * c))) / i) + ((a * b) - (y * j)))
    else if (b <= 5.8d-72) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double t_3 = (y * ((x * z) - (i * j))) + t_1;
	double tmp;
	if (b <= -1.3e+195) {
		tmp = t_1;
	} else if (b <= -8.2e+183) {
		tmp = t_2;
	} else if (b <= -6.6e+167) {
		tmp = t_3;
	} else if (b <= -2.2e+42) {
		tmp = i * (((z * ((x * y) - (b * c))) / i) + ((a * b) - (y * j)));
	} else if (b <= 5.8e-72) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
	t_3 = (y * ((x * z) - (i * j))) + t_1
	tmp = 0
	if b <= -1.3e+195:
		tmp = t_1
	elif b <= -8.2e+183:
		tmp = t_2
	elif b <= -6.6e+167:
		tmp = t_3
	elif b <= -2.2e+42:
		tmp = i * (((z * ((x * y) - (b * c))) / i) + ((a * b) - (y * j)))
	elif b <= 5.8e-72:
		tmp = t_2
	else:
		tmp = t_3
	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(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	t_3 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_1)
	tmp = 0.0
	if (b <= -1.3e+195)
		tmp = t_1;
	elseif (b <= -8.2e+183)
		tmp = t_2;
	elseif (b <= -6.6e+167)
		tmp = t_3;
	elseif (b <= -2.2e+42)
		tmp = Float64(i * Float64(Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) / i) + Float64(Float64(a * b) - Float64(y * j))));
	elseif (b <= 5.8e-72)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	t_3 = (y * ((x * z) - (i * j))) + t_1;
	tmp = 0.0;
	if (b <= -1.3e+195)
		tmp = t_1;
	elseif (b <= -8.2e+183)
		tmp = t_2;
	elseif (b <= -6.6e+167)
		tmp = t_3;
	elseif (b <= -2.2e+42)
		tmp = i * (((z * ((x * y) - (b * c))) / i) + ((a * b) - (y * j)));
	elseif (b <= 5.8e-72)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[b, -1.3e+195], t$95$1, If[LessEqual[b, -8.2e+183], t$95$2, If[LessEqual[b, -6.6e+167], t$95$3, If[LessEqual[b, -2.2e+42], N[(i * N[(N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e-72], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.30000000000000001e195

   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 b around inf 90.6%

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

   if -1.30000000000000001e195 < b < -8.20000000000000029e183 or -2.2000000000000001e42 < b < 5.79999999999999995e-72

   1. Initial program 69.7%

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

   3. Taylor expanded in b around 0 72.3%

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

   if -8.20000000000000029e183 < b < -6.60000000000000036e167 or 5.79999999999999995e-72 < b

   1. Initial program 70.9%

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

   3. Taylor expanded in y around inf 70.9%

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

      1. +-commutative 70.9%

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

      2. mul-1-neg 70.9%

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

      3. unsub-neg 70.9%

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

      4. *-commutative 70.9%

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

      5. associate-/l* 69.7%

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

      6. *-commutative 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in t around 0 67.6%

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

      1. associate-*r* 70.1%

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

      2. associate-*r* 70.1%

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

      3. *-commutative 70.1%

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

      4. associate-*r* 73.8%

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

      5. distribute-rgt-in 76.4%

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

      6. +-commutative 76.4%

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

      7. mul-1-neg 76.4%

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

      8. unsub-neg 76.4%

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

      9. *-commutative 76.4%

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

      10. *-commutative 76.4%

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

   8. Simplified 76.4%

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

   if -6.60000000000000036e167 < b < -2.2000000000000001e42

   1. Initial program 65.7%

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

   3. Taylor expanded in i around inf 59.9%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in t around 0 78.6%

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

      1. +-commutative 78.6%

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

      2. mul-1-neg 78.6%

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

      3. sub-neg 78.6%

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

      4. *-commutative 78.6%

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

   8. Simplified 78.6%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+195}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{+183}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+167}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{+42}:\\ \;\;\;\;i \cdot \left(\frac{z \cdot \left(x \cdot y - b \cdot c\right)}{i} + \left(a \cdot b - y \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-278}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(x \cdot \frac{z}{i} - j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= y -3.6e+87)
     (* y (- (* x z) (* i j)))
     (if (<= y -1.85e-54)
       (* b (- (* a i) (* z c)))
       (if (<= y -1.6e-287)
         t_1
         (if (<= y 1.3e-278)
           t_2
           (if (<= y 4.7e-211)
             t_1
             (if (<= y 1.8e-20) t_2 (* (* y i) (- (* 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 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (y <= -3.6e+87) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -1.85e-54) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= -1.6e-287) {
		tmp = t_1;
	} else if (y <= 1.3e-278) {
		tmp = t_2;
	} else if (y <= 4.7e-211) {
		tmp = t_1;
	} else if (y <= 1.8e-20) {
		tmp = t_2;
	} else {
		tmp = (y * i) * ((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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = c * ((t * j) - (z * b))
    if (y <= (-3.6d+87)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= (-1.85d-54)) then
        tmp = b * ((a * i) - (z * c))
    else if (y <= (-1.6d-287)) then
        tmp = t_1
    else if (y <= 1.3d-278) then
        tmp = t_2
    else if (y <= 4.7d-211) then
        tmp = t_1
    else if (y <= 1.8d-20) then
        tmp = t_2
    else
        tmp = (y * i) * ((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 t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (y <= -3.6e+87) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -1.85e-54) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= -1.6e-287) {
		tmp = t_1;
	} else if (y <= 1.3e-278) {
		tmp = t_2;
	} else if (y <= 4.7e-211) {
		tmp = t_1;
	} else if (y <= 1.8e-20) {
		tmp = t_2;
	} else {
		tmp = (y * i) * ((x * (z / i)) - j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if y <= -3.6e+87:
		tmp = y * ((x * z) - (i * j))
	elif y <= -1.85e-54:
		tmp = b * ((a * i) - (z * c))
	elif y <= -1.6e-287:
		tmp = t_1
	elif y <= 1.3e-278:
		tmp = t_2
	elif y <= 4.7e-211:
		tmp = t_1
	elif y <= 1.8e-20:
		tmp = t_2
	else:
		tmp = (y * i) * ((x * (z / i)) - j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (y <= -3.6e+87)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= -1.85e-54)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (y <= -1.6e-287)
		tmp = t_1;
	elseif (y <= 1.3e-278)
		tmp = t_2;
	elseif (y <= 4.7e-211)
		tmp = t_1;
	elseif (y <= 1.8e-20)
		tmp = t_2;
	else
		tmp = Float64(Float64(y * i) * Float64(Float64(x * Float64(z / i)) - j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (y <= -3.6e+87)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= -1.85e-54)
		tmp = b * ((a * i) - (z * c));
	elseif (y <= -1.6e-287)
		tmp = t_1;
	elseif (y <= 1.3e-278)
		tmp = t_2;
	elseif (y <= 4.7e-211)
		tmp = t_1;
	elseif (y <= 1.8e-20)
		tmp = t_2;
	else
		tmp = (y * i) * ((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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+87], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.85e-54], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e-287], t$95$1, If[LessEqual[y, 1.3e-278], t$95$2, If[LessEqual[y, 4.7e-211], t$95$1, If[LessEqual[y, 1.8e-20], t$95$2, N[(N[(y * i), $MachinePrecision] * N[(N[(x * N[(z / i), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.59999999999999994e87

   1. Initial program 50.8%

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

   3. Taylor expanded in y around inf 74.6%

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

      1. +-commutative 74.6%

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

      2. mul-1-neg 74.6%

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

      3. unsub-neg 74.6%

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

      4. *-commutative 74.6%

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

   5. Simplified 74.6%

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

   if -3.59999999999999994e87 < y < -1.8500000000000001e-54

   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 b around inf 62.6%

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

   if -1.8500000000000001e-54 < y < -1.60000000000000009e-287 or 1.2999999999999999e-278 < y < 4.6999999999999997e-211

   1. Initial program 71.9%

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

   3. Taylor expanded in a around inf 68.7%

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

      1. distribute-lft-out-- 68.7%

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

      2. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   if -1.60000000000000009e-287 < y < 1.2999999999999999e-278 or 4.6999999999999997e-211 < y < 1.79999999999999987e-20

   1. Initial program 84.2%

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

   3. Taylor expanded in c around inf 65.8%

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

      1. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   if 1.79999999999999987e-20 < y

   1. Initial program 66.4%

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

   3. Taylor expanded in i around inf 57.7%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in y around inf 54.4%

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

      1. associate-*r* 58.1%

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

      2. *-commutative 58.1%

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

      3. associate-/l* 58.1%

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

   8. Simplified 58.1%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-287}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-278}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-20}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(x \cdot \frac{z}{i} - j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+253}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+95}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= t -2.25e+253)
     (* (* x t) (- a))
     (if (<= t -2.6e+95)
       t_2
       (if (<= t -1.08e-45)
         t_1
         (if (<= t -7.2e-97)
           t_2
           (if (<= t 1e+99) t_1 (if (<= t 2.7e+197) (* x (* y z)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (t <= -2.25e+253) {
		tmp = (x * t) * -a;
	} else if (t <= -2.6e+95) {
		tmp = t_2;
	} else if (t <= -1.08e-45) {
		tmp = t_1;
	} else if (t <= -7.2e-97) {
		tmp = t_2;
	} else if (t <= 1e+99) {
		tmp = t_1;
	} else if (t <= 2.7e+197) {
		tmp = x * (y * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = c * ((t * j) - (z * b))
    if (t <= (-2.25d+253)) then
        tmp = (x * t) * -a
    else if (t <= (-2.6d+95)) then
        tmp = t_2
    else if (t <= (-1.08d-45)) then
        tmp = t_1
    else if (t <= (-7.2d-97)) then
        tmp = t_2
    else if (t <= 1d+99) then
        tmp = t_1
    else if (t <= 2.7d+197) then
        tmp = x * (y * z)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (t <= -2.25e+253) {
		tmp = (x * t) * -a;
	} else if (t <= -2.6e+95) {
		tmp = t_2;
	} else if (t <= -1.08e-45) {
		tmp = t_1;
	} else if (t <= -7.2e-97) {
		tmp = t_2;
	} else if (t <= 1e+99) {
		tmp = t_1;
	} else if (t <= 2.7e+197) {
		tmp = x * (y * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if t <= -2.25e+253:
		tmp = (x * t) * -a
	elif t <= -2.6e+95:
		tmp = t_2
	elif t <= -1.08e-45:
		tmp = t_1
	elif t <= -7.2e-97:
		tmp = t_2
	elif t <= 1e+99:
		tmp = t_1
	elif t <= 2.7e+197:
		tmp = x * (y * z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (t <= -2.25e+253)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (t <= -2.6e+95)
		tmp = t_2;
	elseif (t <= -1.08e-45)
		tmp = t_1;
	elseif (t <= -7.2e-97)
		tmp = t_2;
	elseif (t <= 1e+99)
		tmp = t_1;
	elseif (t <= 2.7e+197)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (t <= -2.25e+253)
		tmp = (x * t) * -a;
	elseif (t <= -2.6e+95)
		tmp = t_2;
	elseif (t <= -1.08e-45)
		tmp = t_1;
	elseif (t <= -7.2e-97)
		tmp = t_2;
	elseif (t <= 1e+99)
		tmp = t_1;
	elseif (t <= 2.7e+197)
		tmp = x * (y * z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.25e+253], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[t, -2.6e+95], t$95$2, If[LessEqual[t, -1.08e-45], t$95$1, If[LessEqual[t, -7.2e-97], t$95$2, If[LessEqual[t, 1e+99], t$95$1, If[LessEqual[t, 2.7e+197], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.24999999999999986e253

   1. Initial program 54.4%

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

   3. Taylor expanded in c around 0 70.0%

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

   4. Taylor expanded in t around inf 70.2%

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

      1. associate-*r* 70.2%

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

      2. mul-1-neg 70.2%

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

      3. *-commutative 70.2%

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

   6. Simplified 70.2%

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

   if -2.24999999999999986e253 < t < -2.5999999999999999e95 or -1.08e-45 < t < -7.19999999999999995e-97 or 2.7e197 < t

   1. Initial program 61.8%

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

   3. Taylor expanded in c around inf 62.3%

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

      1. *-commutative 62.3%

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

   5. Simplified 62.3%

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

   if -2.5999999999999999e95 < t < -1.08e-45 or -7.19999999999999995e-97 < t < 9.9999999999999997e98

   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 b around inf 50.0%

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

   if 9.9999999999999997e98 < t < 2.7e197

   1. Initial program 61.3%

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

   3. Taylor expanded in b around 0 56.4%

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

   4. Taylor expanded in j around 0 56.7%

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

   5. Taylor expanded in y around inf 57.1%

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

      1. *-commutative 57.1%

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

   7. Simplified 57.1%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+253}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+95}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-97}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 10^{+99}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.1 \cdot 10^{+98}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -1.85 \cdot 10^{-175}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{-223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -5.4 \cdot 10^{-299}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-210}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* i (- (* a b) (* y j)))))
   (if (<= i -1.1e+98)
     t_3
     (if (<= i -1.85e-175)
       t_2
       (if (<= i -2.15e-223)
         t_1
         (if (<= i -5.4e-299)
           t_2
           (if (<= i 1.05e-210)
             (* c (- (* t j) (* z b)))
             (if (<= i 5e+45) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.1e+98) {
		tmp = t_3;
	} else if (i <= -1.85e-175) {
		tmp = t_2;
	} else if (i <= -2.15e-223) {
		tmp = t_1;
	} else if (i <= -5.4e-299) {
		tmp = t_2;
	} else if (i <= 1.05e-210) {
		tmp = c * ((t * j) - (z * b));
	} else if (i <= 5e+45) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = x * ((y * z) - (t * a))
    t_3 = i * ((a * b) - (y * j))
    if (i <= (-1.1d+98)) then
        tmp = t_3
    else if (i <= (-1.85d-175)) then
        tmp = t_2
    else if (i <= (-2.15d-223)) then
        tmp = t_1
    else if (i <= (-5.4d-299)) then
        tmp = t_2
    else if (i <= 1.05d-210) then
        tmp = c * ((t * j) - (z * b))
    else if (i <= 5d+45) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.1e+98) {
		tmp = t_3;
	} else if (i <= -1.85e-175) {
		tmp = t_2;
	} else if (i <= -2.15e-223) {
		tmp = t_1;
	} else if (i <= -5.4e-299) {
		tmp = t_2;
	} else if (i <= 1.05e-210) {
		tmp = c * ((t * j) - (z * b));
	} else if (i <= 5e+45) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = x * ((y * z) - (t * a))
	t_3 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -1.1e+98:
		tmp = t_3
	elif i <= -1.85e-175:
		tmp = t_2
	elif i <= -2.15e-223:
		tmp = t_1
	elif i <= -5.4e-299:
		tmp = t_2
	elif i <= 1.05e-210:
		tmp = c * ((t * j) - (z * b))
	elif i <= 5e+45:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.1e+98)
		tmp = t_3;
	elseif (i <= -1.85e-175)
		tmp = t_2;
	elseif (i <= -2.15e-223)
		tmp = t_1;
	elseif (i <= -5.4e-299)
		tmp = t_2;
	elseif (i <= 1.05e-210)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (i <= 5e+45)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = x * ((y * z) - (t * a));
	t_3 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.1e+98)
		tmp = t_3;
	elseif (i <= -1.85e-175)
		tmp = t_2;
	elseif (i <= -2.15e-223)
		tmp = t_1;
	elseif (i <= -5.4e-299)
		tmp = t_2;
	elseif (i <= 1.05e-210)
		tmp = c * ((t * j) - (z * b));
	elseif (i <= 5e+45)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.1e+98], t$95$3, If[LessEqual[i, -1.85e-175], t$95$2, If[LessEqual[i, -2.15e-223], t$95$1, If[LessEqual[i, -5.4e-299], t$95$2, If[LessEqual[i, 1.05e-210], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5e+45], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.10000000000000004e98 or 5e45 < i

   1. Initial program 63.8%

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

   3. Taylor expanded in i around inf 79.5%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in i around inf 70.7%

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

      1. distribute-lft-in 70.7%

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

      2. mul-1-neg 70.7%

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

      3. unsub-neg 70.7%

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

      4. neg-mul-1 70.7%

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

      5. mul-1-neg 70.7%

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

      6. remove-double-neg 70.7%

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

      7. *-commutative 70.7%

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

   8. Simplified 70.7%

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

   if -1.10000000000000004e98 < i < -1.84999999999999999e-175 or -2.15e-223 < i < -5.40000000000000004e-299

   1. Initial program 71.1%

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

   3. Taylor expanded in b around 0 65.2%

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

   4. Taylor expanded in j around 0 53.8%

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

   if -1.84999999999999999e-175 < i < -2.15e-223 or 1.05000000000000008e-210 < i < 5e45

   1. Initial program 72.9%

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

   3. Taylor expanded in b around 0 63.8%

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

   4. Taylor expanded in t around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. unsub-neg 58.8%

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

   6. Simplified 58.8%

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

   if -5.40000000000000004e-299 < i < 1.05000000000000008e-210

   1. Initial program 86.1%

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

   3. Taylor expanded in c around inf 69.1%

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

      1. *-commutative 69.1%

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

   5. Simplified 69.1%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.1 \cdot 10^{+98}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.85 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq -2.15 \cdot 10^{-223}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq -5.4 \cdot 10^{-299}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-210}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+87}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{-276}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.75 \cdot 10^{-212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-17}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t))))
        (t_2 (* c (- (* t j) (* z b))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -3.8e+87)
     t_3
     (if (<= y -7e-55)
       (* b (- (* a i) (* z c)))
       (if (<= y -1.15e-287)
         t_1
         (if (<= y 1.72e-276)
           t_2
           (if (<= y 3.75e-212) t_1 (if (<= y 3e-17) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -3.8e+87) {
		tmp = t_3;
	} else if (y <= -7e-55) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= -1.15e-287) {
		tmp = t_1;
	} else if (y <= 1.72e-276) {
		tmp = t_2;
	} else if (y <= 3.75e-212) {
		tmp = t_1;
	} else if (y <= 3e-17) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = c * ((t * j) - (z * b))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-3.8d+87)) then
        tmp = t_3
    else if (y <= (-7d-55)) then
        tmp = b * ((a * i) - (z * c))
    else if (y <= (-1.15d-287)) then
        tmp = t_1
    else if (y <= 1.72d-276) then
        tmp = t_2
    else if (y <= 3.75d-212) then
        tmp = t_1
    else if (y <= 3d-17) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -3.8e+87) {
		tmp = t_3;
	} else if (y <= -7e-55) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= -1.15e-287) {
		tmp = t_1;
	} else if (y <= 1.72e-276) {
		tmp = t_2;
	} else if (y <= 3.75e-212) {
		tmp = t_1;
	} else if (y <= 3e-17) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = c * ((t * j) - (z * b))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -3.8e+87:
		tmp = t_3
	elif y <= -7e-55:
		tmp = b * ((a * i) - (z * c))
	elif y <= -1.15e-287:
		tmp = t_1
	elif y <= 1.72e-276:
		tmp = t_2
	elif y <= 3.75e-212:
		tmp = t_1
	elif y <= 3e-17:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -3.8e+87)
		tmp = t_3;
	elseif (y <= -7e-55)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (y <= -1.15e-287)
		tmp = t_1;
	elseif (y <= 1.72e-276)
		tmp = t_2;
	elseif (y <= 3.75e-212)
		tmp = t_1;
	elseif (y <= 3e-17)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = c * ((t * j) - (z * b));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -3.8e+87)
		tmp = t_3;
	elseif (y <= -7e-55)
		tmp = b * ((a * i) - (z * c));
	elseif (y <= -1.15e-287)
		tmp = t_1;
	elseif (y <= 1.72e-276)
		tmp = t_2;
	elseif (y <= 3.75e-212)
		tmp = t_1;
	elseif (y <= 3e-17)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+87], t$95$3, If[LessEqual[y, -7e-55], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.15e-287], t$95$1, If[LessEqual[y, 1.72e-276], t$95$2, If[LessEqual[y, 3.75e-212], t$95$1, If[LessEqual[y, 3e-17], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.80000000000000011e87 or 3.00000000000000006e-17 < y

   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 inf 64.0%

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

      1. +-commutative 64.0%

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

      2. mul-1-neg 64.0%

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

      3. unsub-neg 64.0%

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

      4. *-commutative 64.0%

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

   5. Simplified 64.0%

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

   if -3.80000000000000011e87 < y < -7.00000000000000051e-55

   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 b around inf 62.6%

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

   if -7.00000000000000051e-55 < y < -1.14999999999999993e-287 or 1.71999999999999996e-276 < y < 3.75000000000000006e-212

   1. Initial program 71.9%

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

   3. Taylor expanded in a around inf 68.7%

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

      1. distribute-lft-out-- 68.7%

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

      2. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   if -1.14999999999999993e-287 < y < 1.71999999999999996e-276 or 3.75000000000000006e-212 < y < 3.00000000000000006e-17

   1. Initial program 83.3%

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

   3. Taylor expanded in c around inf 63.8%

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

      1. *-commutative 63.8%

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

   5. Simplified 63.8%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-287}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{-276}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3.75 \cdot 10^{-212}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-17}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+195}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{+130}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* t c) (* y i))) (* x (- (* t a) (* y z)))))
        (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -5.5e+195)
     t_2
     (if (<= b -3.1e+184)
       t_1
       (if (<= b -6.8e+130)
         (* c (- (* t j) (* z b)))
         (if (<= b 1.02e-85) t_1 (+ (* x (- (* y z) (* t a))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.5e+195) {
		tmp = t_2;
	} else if (b <= -3.1e+184) {
		tmp = t_1;
	} else if (b <= -6.8e+130) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 1.02e-85) {
		tmp = t_1;
	} else {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-5.5d+195)) then
        tmp = t_2
    else if (b <= (-3.1d+184)) then
        tmp = t_1
    else if (b <= (-6.8d+130)) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= 1.02d-85) then
        tmp = t_1
    else
        tmp = (x * ((y * z) - (t * a))) + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.5e+195) {
		tmp = t_2;
	} else if (b <= -3.1e+184) {
		tmp = t_1;
	} else if (b <= -6.8e+130) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 1.02e-85) {
		tmp = t_1;
	} else {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -5.5e+195:
		tmp = t_2
	elif b <= -3.1e+184:
		tmp = t_1
	elif b <= -6.8e+130:
		tmp = c * ((t * j) - (z * b))
	elif b <= 1.02e-85:
		tmp = t_1
	else:
		tmp = (x * ((y * z) - (t * a))) + t_2
	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(x * Float64(Float64(t * a) - Float64(y * z))))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.5e+195)
		tmp = t_2;
	elseif (b <= -3.1e+184)
		tmp = t_1;
	elseif (b <= -6.8e+130)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= 1.02e-85)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.5e+195)
		tmp = t_2;
	elseif (b <= -3.1e+184)
		tmp = t_1;
	elseif (b <= -6.8e+130)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= 1.02e-85)
		tmp = t_1;
	else
		tmp = (x * ((y * z) - (t * a))) + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e+195], t$95$2, If[LessEqual[b, -3.1e+184], t$95$1, If[LessEqual[b, -6.8e+130], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.02e-85], t$95$1, N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.49999999999999994e195

   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 b around inf 90.6%

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

   if -5.49999999999999994e195 < b < -3.0999999999999998e184 or -6.8000000000000001e130 < b < 1.02000000000000001e-85

   1. Initial program 70.7%

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

   3. Taylor expanded in b around 0 71.6%

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

   if -3.0999999999999998e184 < b < -6.8000000000000001e130

   1. Initial program 53.7%

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

   3. Taylor expanded in c around inf 62.2%

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

      1. *-commutative 62.2%

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

   5. Simplified 62.2%

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

   if 1.02000000000000001e-85 < b

   1. Initial program 70.2%

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

   3. Taylor expanded in j around 0 71.7%

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

      1. *-commutative 71.7%

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

   5. Simplified 71.7%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+195}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{+184}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{+130}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-85}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot \left(y - a \cdot \frac{t}{z}\right)\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.2 \cdot 10^{+98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -2.7 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-297}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-108}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* z (- y (* a (/ t z)))))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -1.2e+98)
     t_2
     (if (<= i -2.7e-95)
       t_1
       (if (<= i -1.05e-297)
         (* z (- (* x y) (* b c)))
         (if (<= i 1.05e-108)
           (* c (- (* t j) (* z b)))
           (if (<= i 6.6e-28) 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 * (z * (y - (a * (t / z))));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.2e+98) {
		tmp = t_2;
	} else if (i <= -2.7e-95) {
		tmp = t_1;
	} else if (i <= -1.05e-297) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 1.05e-108) {
		tmp = c * ((t * j) - (z * b));
	} else if (i <= 6.6e-28) {
		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 * (z * (y - (a * (t / z))))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-1.2d+98)) then
        tmp = t_2
    else if (i <= (-2.7d-95)) then
        tmp = t_1
    else if (i <= (-1.05d-297)) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 1.05d-108) then
        tmp = c * ((t * j) - (z * b))
    else if (i <= 6.6d-28) 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 * (z * (y - (a * (t / z))));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.2e+98) {
		tmp = t_2;
	} else if (i <= -2.7e-95) {
		tmp = t_1;
	} else if (i <= -1.05e-297) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 1.05e-108) {
		tmp = c * ((t * j) - (z * b));
	} else if (i <= 6.6e-28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (z * (y - (a * (t / z))))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -1.2e+98:
		tmp = t_2
	elif i <= -2.7e-95:
		tmp = t_1
	elif i <= -1.05e-297:
		tmp = z * ((x * y) - (b * c))
	elif i <= 1.05e-108:
		tmp = c * ((t * j) - (z * b))
	elif i <= 6.6e-28:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(z * Float64(y - Float64(a * Float64(t / z)))))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.2e+98)
		tmp = t_2;
	elseif (i <= -2.7e-95)
		tmp = t_1;
	elseif (i <= -1.05e-297)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 1.05e-108)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (i <= 6.6e-28)
		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 * (z * (y - (a * (t / z))));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.2e+98)
		tmp = t_2;
	elseif (i <= -2.7e-95)
		tmp = t_1;
	elseif (i <= -1.05e-297)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 1.05e-108)
		tmp = c * ((t * j) - (z * b));
	elseif (i <= 6.6e-28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(z * N[(y - N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.2e+98], t$95$2, If[LessEqual[i, -2.7e-95], t$95$1, If[LessEqual[i, -1.05e-297], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.05e-108], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.6e-28], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.1999999999999999e98 or 6.6000000000000003e-28 < i

   1. Initial program 66.3%

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

   3. Taylor expanded in i around inf 80.9%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in i around inf 68.6%

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

      1. distribute-lft-in 68.6%

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

      2. mul-1-neg 68.6%

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

      3. unsub-neg 68.6%

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

      4. neg-mul-1 68.6%

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

      5. mul-1-neg 68.6%

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

      6. remove-double-neg 68.6%

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

      7. *-commutative 68.6%

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

   8. Simplified 68.6%

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

   if -1.1999999999999999e98 < i < -2.7e-95 or 1.05e-108 < i < 6.6000000000000003e-28

   1. Initial program 71.6%

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

   3. Taylor expanded in b around 0 60.8%

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

   4. Taylor expanded in j around 0 56.3%

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

   5. Taylor expanded in z around inf 57.8%

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

      1. mul-1-neg 57.8%

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

      2. unsub-neg 57.8%

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

      3. associate-/l* 61.0%

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

   7. Simplified 61.0%

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

   if -2.7e-95 < i < -1.05000000000000007e-297

   1. Initial program 67.9%

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

   3. Taylor expanded in z around inf 55.2%

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

   if -1.05000000000000007e-297 < i < 1.05e-108

   1. Initial program 79.0%

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

   3. Taylor expanded in c around inf 59.1%

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

      1. *-commutative 59.1%

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

   5. Simplified 59.1%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.2 \cdot 10^{+98}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -2.7 \cdot 10^{-95}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - a \cdot \frac{t}{z}\right)\right)\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-297}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-108}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - a \cdot \frac{t}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -4.6 \cdot 10^{-224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+137}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -2e+50)
     t_2
     (if (<= i -4.6e-224)
       t_1
       (if (<= i -1.3e-292)
         (* z (* x y))
         (if (<= i 2.15e-58)
           t_1
           (if (<= i 4.8e+137) (* b (- (* a i) (* z c))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2e+50) {
		tmp = t_2;
	} else if (i <= -4.6e-224) {
		tmp = t_1;
	} else if (i <= -1.3e-292) {
		tmp = z * (x * y);
	} else if (i <= 2.15e-58) {
		tmp = t_1;
	} else if (i <= 4.8e+137) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-2d+50)) then
        tmp = t_2
    else if (i <= (-4.6d-224)) then
        tmp = t_1
    else if (i <= (-1.3d-292)) then
        tmp = z * (x * y)
    else if (i <= 2.15d-58) then
        tmp = t_1
    else if (i <= 4.8d+137) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2e+50) {
		tmp = t_2;
	} else if (i <= -4.6e-224) {
		tmp = t_1;
	} else if (i <= -1.3e-292) {
		tmp = z * (x * y);
	} else if (i <= 2.15e-58) {
		tmp = t_1;
	} else if (i <= 4.8e+137) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -2e+50:
		tmp = t_2
	elif i <= -4.6e-224:
		tmp = t_1
	elif i <= -1.3e-292:
		tmp = z * (x * y)
	elif i <= 2.15e-58:
		tmp = t_1
	elif i <= 4.8e+137:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_2
	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)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2e+50)
		tmp = t_2;
	elseif (i <= -4.6e-224)
		tmp = t_1;
	elseif (i <= -1.3e-292)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 2.15e-58)
		tmp = t_1;
	elseif (i <= 4.8e+137)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -2e+50)
		tmp = t_2;
	elseif (i <= -4.6e-224)
		tmp = t_1;
	elseif (i <= -1.3e-292)
		tmp = z * (x * y);
	elseif (i <= 2.15e-58)
		tmp = t_1;
	elseif (i <= 4.8e+137)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2e+50], t$95$2, If[LessEqual[i, -4.6e-224], t$95$1, If[LessEqual[i, -1.3e-292], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.15e-58], t$95$1, If[LessEqual[i, 4.8e+137], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.0000000000000002e50 or 4.79999999999999966e137 < i

   1. Initial program 65.2%

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

   3. Taylor expanded in i around inf 78.5%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in i around inf 71.9%

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

      1. distribute-lft-in 71.9%

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

      2. mul-1-neg 71.9%

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

      3. unsub-neg 71.9%

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

      4. neg-mul-1 71.9%

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

      5. mul-1-neg 71.9%

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

      6. remove-double-neg 71.9%

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

      7. *-commutative 71.9%

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

   8. Simplified 71.9%

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

   if -2.0000000000000002e50 < i < -4.59999999999999975e-224 or -1.30000000000000007e-292 < i < 2.15e-58

   1. Initial program 70.7%

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

   3. Taylor expanded in c around inf 48.5%

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

      1. *-commutative 48.5%

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

   5. Simplified 48.5%

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

   if -4.59999999999999975e-224 < i < -1.30000000000000007e-292

   1. Initial program 77.9%

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

   3. Taylor expanded in z around inf 62.6%

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

   4. Taylor expanded in x around inf 51.4%

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

   if 2.15e-58 < i < 4.79999999999999966e137

   1. Initial program 76.2%

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

   3. Taylor expanded in b around inf 57.8%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2 \cdot 10^{+50}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -4.6 \cdot 10^{-224}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 2.15 \cdot 10^{-58}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+137}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;j \leq -2.6 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-289}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 4.9 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{+206} \lor \neg \left(j \leq 2.85 \cdot 10^{+240}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))))
   (if (<= j -2.6e+79)
     t_1
     (if (<= j -1.05e-289)
       (* z (* x y))
       (if (<= j 4.9e+27)
         (* a (* b i))
         (if (or (<= j 6.5e+206) (not (<= j 2.85e+240)))
           t_1
           (* t (* c 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 = y * (i * -j);
	double tmp;
	if (j <= -2.6e+79) {
		tmp = t_1;
	} else if (j <= -1.05e-289) {
		tmp = z * (x * y);
	} else if (j <= 4.9e+27) {
		tmp = a * (b * i);
	} else if ((j <= 6.5e+206) || !(j <= 2.85e+240)) {
		tmp = t_1;
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (i * -j)
    if (j <= (-2.6d+79)) then
        tmp = t_1
    else if (j <= (-1.05d-289)) then
        tmp = z * (x * y)
    else if (j <= 4.9d+27) then
        tmp = a * (b * i)
    else if ((j <= 6.5d+206) .or. (.not. (j <= 2.85d+240))) then
        tmp = t_1
    else
        tmp = t * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (i * -j);
	double tmp;
	if (j <= -2.6e+79) {
		tmp = t_1;
	} else if (j <= -1.05e-289) {
		tmp = z * (x * y);
	} else if (j <= 4.9e+27) {
		tmp = a * (b * i);
	} else if ((j <= 6.5e+206) || !(j <= 2.85e+240)) {
		tmp = t_1;
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	tmp = 0
	if j <= -2.6e+79:
		tmp = t_1
	elif j <= -1.05e-289:
		tmp = z * (x * y)
	elif j <= 4.9e+27:
		tmp = a * (b * i)
	elif (j <= 6.5e+206) or not (j <= 2.85e+240):
		tmp = t_1
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (j <= -2.6e+79)
		tmp = t_1;
	elseif (j <= -1.05e-289)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 4.9e+27)
		tmp = Float64(a * Float64(b * i));
	elseif ((j <= 6.5e+206) || !(j <= 2.85e+240))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (i * -j);
	tmp = 0.0;
	if (j <= -2.6e+79)
		tmp = t_1;
	elseif (j <= -1.05e-289)
		tmp = z * (x * y);
	elseif (j <= 4.9e+27)
		tmp = a * (b * i);
	elseif ((j <= 6.5e+206) || ~((j <= 2.85e+240)))
		tmp = t_1;
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.6e+79], t$95$1, If[LessEqual[j, -1.05e-289], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.9e+27], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, 6.5e+206], N[Not[LessEqual[j, 2.85e+240]], $MachinePrecision]], t$95$1, N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.60000000000000015e79 or 4.90000000000000015e27 < j < 6.4999999999999995e206 or 2.84999999999999986e240 < j

   1. Initial program 75.9%

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

   3. Taylor expanded in c around 0 58.3%

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

   4. Taylor expanded in j around inf 38.8%

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

      1. neg-mul-1 38.8%

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

      2. *-commutative 38.8%

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

      3. distribute-rgt-neg-in 38.8%

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

      4. *-commutative 38.8%

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

      5. associate-*l* 44.9%

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

   6. Simplified 44.9%

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

   if -2.60000000000000015e79 < j < -1.0499999999999999e-289

   1. Initial program 64.6%

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

   3. Taylor expanded in z around inf 53.1%

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

   4. Taylor expanded in x around inf 37.6%

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

   if -1.0499999999999999e-289 < j < 4.90000000000000015e27

   1. Initial program 66.0%

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

   3. Taylor expanded in b around inf 51.5%

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

   4. Taylor expanded in a around inf 36.7%

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

   if 6.4999999999999995e206 < j < 2.84999999999999986e240

   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 i around inf 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in t around inf 75.2%

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

      1. associate-*r* 75.2%

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

      2. *-commutative 75.2%

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

      3. +-commutative 75.2%

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

      4. mul-1-neg 75.2%

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

      5. unsub-neg 75.2%

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

      6. associate-/l* 63.4%

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

   8. Simplified 63.4%

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

   9. Taylor expanded in c around inf 75.6%

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

       1. *-commutative 75.6%

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

       2. *-commutative 75.6%

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

       3. associate-*l* 87.4%

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

   11. Simplified 87.4%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.6 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-289}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 4.9 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{+206} \lor \neg \left(j \leq 2.85 \cdot 10^{+240}\right):\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-56}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-272}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-86}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))))
   (if (<= b -5e+42)
     t_1
     (if (<= b -3.5e-56)
       (* j (* t c))
       (if (<= b -2.8e-131)
         (* x (* y z))
         (if (<= b -3e-272)
           (* (* t a) (- x))
           (if (<= b 5.3e-86) (* t (* c j)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (b <= -5e+42) {
		tmp = t_1;
	} else if (b <= -3.5e-56) {
		tmp = j * (t * c);
	} else if (b <= -2.8e-131) {
		tmp = x * (y * z);
	} else if (b <= -3e-272) {
		tmp = (t * a) * -x;
	} else if (b <= 5.3e-86) {
		tmp = t * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * i)
    if (b <= (-5d+42)) then
        tmp = t_1
    else if (b <= (-3.5d-56)) then
        tmp = j * (t * c)
    else if (b <= (-2.8d-131)) then
        tmp = x * (y * z)
    else if (b <= (-3d-272)) then
        tmp = (t * a) * -x
    else if (b <= 5.3d-86) then
        tmp = t * (c * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (b <= -5e+42) {
		tmp = t_1;
	} else if (b <= -3.5e-56) {
		tmp = j * (t * c);
	} else if (b <= -2.8e-131) {
		tmp = x * (y * z);
	} else if (b <= -3e-272) {
		tmp = (t * a) * -x;
	} else if (b <= 5.3e-86) {
		tmp = t * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	tmp = 0
	if b <= -5e+42:
		tmp = t_1
	elif b <= -3.5e-56:
		tmp = j * (t * c)
	elif b <= -2.8e-131:
		tmp = x * (y * z)
	elif b <= -3e-272:
		tmp = (t * a) * -x
	elif b <= 5.3e-86:
		tmp = t * (c * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (b <= -5e+42)
		tmp = t_1;
	elseif (b <= -3.5e-56)
		tmp = Float64(j * Float64(t * c));
	elseif (b <= -2.8e-131)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= -3e-272)
		tmp = Float64(Float64(t * a) * Float64(-x));
	elseif (b <= 5.3e-86)
		tmp = Float64(t * Float64(c * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	tmp = 0.0;
	if (b <= -5e+42)
		tmp = t_1;
	elseif (b <= -3.5e-56)
		tmp = j * (t * c);
	elseif (b <= -2.8e-131)
		tmp = x * (y * z);
	elseif (b <= -3e-272)
		tmp = (t * a) * -x;
	elseif (b <= 5.3e-86)
		tmp = t * (c * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e+42], t$95$1, If[LessEqual[b, -3.5e-56], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.8e-131], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3e-272], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[b, 5.3e-86], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5.00000000000000007e42 or 5.2999999999999997e-86 < b

   1. Initial program 69.8%

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

   3. Taylor expanded in b around inf 59.7%

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

   4. Taylor expanded in a around inf 37.6%

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

   if -5.00000000000000007e42 < b < -3.4999999999999998e-56

   1. Initial program 73.0%

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

   3. Taylor expanded in b around 0 69.4%

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

   4. Taylor expanded in c around inf 40.1%

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

      1. associate-*r* 43.7%

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

      2. *-commutative 43.7%

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

      3. associate-*r* 43.7%

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

   6. Simplified 43.7%

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

   if -3.4999999999999998e-56 < b < -2.8e-131

   1. Initial program 61.1%

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

   3. Taylor expanded in b around 0 80.6%

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

   4. Taylor expanded in j around 0 55.3%

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

   5. Taylor expanded in y around inf 48.6%

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

      1. *-commutative 48.6%

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

   7. Simplified 48.6%

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

   if -2.8e-131 < b < -3.0000000000000003e-272

   1. Initial program 83.2%

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

   3. Taylor expanded in b around 0 82.2%

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

   4. Taylor expanded in j around 0 58.5%

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

   5. Taylor expanded in y around 0 43.0%

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

      1. neg-mul-1 43.0%

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

      2. distribute-rgt-neg-in 43.0%

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

   7. Simplified 43.0%

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

   if -3.0000000000000003e-272 < b < 5.2999999999999997e-86

   1. Initial program 62.1%

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

   3. Taylor expanded in i around inf 66.6%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in t around inf 47.0%

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

      1. associate-*r* 50.8%

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

      2. *-commutative 50.8%

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

      3. +-commutative 50.8%

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

      4. mul-1-neg 50.8%

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

      5. unsub-neg 50.8%

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

      6. associate-/l* 48.7%

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

   8. Simplified 48.7%

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

   9. Taylor expanded in c around inf 39.4%

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

       1. *-commutative 39.4%

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

       2. *-commutative 39.4%

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

       3. associate-*l* 41.5%

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

   11. Simplified 41.5%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-56}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-272}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-86}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.3 \cdot 10^{+174} \lor \neg \left(i \leq 5.4 \cdot 10^{+79}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -2.3e+174) (not (<= i 5.4e+79)))
   (* i (- (* a b) (* y j)))
   (- (* j (- (* t c) (* y i))) (* x (- (* t a) (* y z))))))

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 <= -2.3e+174) || !(i <= 5.4e+79)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	}
	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 <= (-2.3d+174)) .or. (.not. (i <= 5.4d+79))) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
    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 <= -2.3e+174) || !(i <= 5.4e+79)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -2.3e+174) or not (i <= 5.4e+79):
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -2.3e+174) || !(i <= 5.4e+79))
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -2.3e+174) || ~((i <= 5.4e+79)))
		tmp = i * ((a * b) - (y * j));
	else
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -2.3e+174], N[Not[LessEqual[i, 5.4e+79]], $MachinePrecision]], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.2999999999999998e174 or 5.3999999999999999e79 < i

   1. Initial program 61.6%

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

   3. Taylor expanded in i around inf 81.8%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in i around inf 76.3%

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

      1. distribute-lft-in 76.3%

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

      2. mul-1-neg 76.3%

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

      3. unsub-neg 76.3%

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

      4. neg-mul-1 76.3%

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

      5. mul-1-neg 76.3%

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

      6. remove-double-neg 76.3%

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

      7. *-commutative 76.3%

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

   8. Simplified 76.3%

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

   if -2.2999999999999998e174 < i < 5.3999999999999999e79

   1. Initial program 73.9%

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

   3. Taylor expanded in b around 0 64.4%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.3 \cdot 10^{+174} \lor \neg \left(i \leq 5.4 \cdot 10^{+79}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;a \leq -5 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* b (* a i))))
   (if (<= a -5e+43)
     t_2
     (if (<= a 9.6e-120)
       t_1
       (if (<= a 1.1e-15) (* t (* c j)) (if (<= a 9.5e+38) 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);
	double t_2 = b * (a * i);
	double tmp;
	if (a <= -5e+43) {
		tmp = t_2;
	} else if (a <= 9.6e-120) {
		tmp = t_1;
	} else if (a <= 1.1e-15) {
		tmp = t * (c * j);
	} else if (a <= 9.5e+38) {
		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_2 = b * (a * i)
    if (a <= (-5d+43)) then
        tmp = t_2
    else if (a <= 9.6d-120) then
        tmp = t_1
    else if (a <= 1.1d-15) then
        tmp = t * (c * j)
    else if (a <= 9.5d+38) 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);
	double t_2 = b * (a * i);
	double tmp;
	if (a <= -5e+43) {
		tmp = t_2;
	} else if (a <= 9.6e-120) {
		tmp = t_1;
	} else if (a <= 1.1e-15) {
		tmp = t * (c * j);
	} else if (a <= 9.5e+38) {
		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_2 = b * (a * i)
	tmp = 0
	if a <= -5e+43:
		tmp = t_2
	elif a <= 9.6e-120:
		tmp = t_1
	elif a <= 1.1e-15:
		tmp = t * (c * j)
	elif a <= 9.5e+38:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (a <= -5e+43)
		tmp = t_2;
	elseif (a <= 9.6e-120)
		tmp = t_1;
	elseif (a <= 1.1e-15)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= 9.5e+38)
		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_2 = b * (a * i);
	tmp = 0.0;
	if (a <= -5e+43)
		tmp = t_2;
	elseif (a <= 9.6e-120)
		tmp = t_1;
	elseif (a <= 1.1e-15)
		tmp = t * (c * j);
	elseif (a <= 9.5e+38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5e+43], t$95$2, If[LessEqual[a, 9.6e-120], t$95$1, If[LessEqual[a, 1.1e-15], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+38], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.0000000000000004e43 or 9.4999999999999995e38 < a

   1. Initial program 58.9%

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

   3. Taylor expanded in b around inf 49.3%

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

   4. Taylor expanded in a around inf 45.6%

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

   if -5.0000000000000004e43 < a < 9.5999999999999998e-120 or 1.09999999999999993e-15 < a < 9.4999999999999995e38

   1. Initial program 77.8%

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

   3. Taylor expanded in b around 0 63.8%

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

   4. Taylor expanded in j around 0 38.8%

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

   5. Taylor expanded in y around inf 33.1%

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

      1. *-commutative 33.1%

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

   7. Simplified 33.1%

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

   if 9.5999999999999998e-120 < a < 1.09999999999999993e-15

   1. Initial program 79.2%

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

   3. Taylor expanded in i around inf 63.3%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in t around inf 40.8%

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

      1. associate-*r* 31.1%

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

      2. *-commutative 31.1%

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

      3. +-commutative 31.1%

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

      4. mul-1-neg 31.1%

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

      5. unsub-neg 31.1%

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

      6. associate-/l* 30.9%

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

   8. Simplified 30.9%

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

   9. Taylor expanded in c around inf 34.4%

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

       1. *-commutative 34.4%

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

       2. *-commutative 34.4%

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

       3. associate-*l* 34.4%

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

   11. Simplified 34.4%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 52.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-143}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -7.2e+52)
     t_1
     (if (<= b -1.55e-143)
       (* j (- (* t c) (* y i)))
       (if (<= b 4.1e+50) (* t (- (* c j) (* x a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7.2e+52) {
		tmp = t_1;
	} else if (b <= -1.55e-143) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 4.1e+50) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-7.2d+52)) then
        tmp = t_1
    else if (b <= (-1.55d-143)) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 4.1d+50) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7.2e+52) {
		tmp = t_1;
	} else if (b <= -1.55e-143) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 4.1e+50) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -7.2e+52:
		tmp = t_1
	elif b <= -1.55e-143:
		tmp = j * ((t * c) - (y * i))
	elif b <= 4.1e+50:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -7.2e+52)
		tmp = t_1;
	elseif (b <= -1.55e-143)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 4.1e+50)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -7.2e+52)
		tmp = t_1;
	elseif (b <= -1.55e-143)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 4.1e+50)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+52], t$95$1, If[LessEqual[b, -1.55e-143], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.1e+50], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.2e52 or 4.1000000000000001e50 < b

   1. Initial program 70.0%

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

   3. Taylor expanded in b around inf 66.0%

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

   if -7.2e52 < b < -1.55000000000000004e-143

   1. Initial program 70.5%

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

   3. Taylor expanded in j around inf 56.5%

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

   if -1.55000000000000004e-143 < b < 4.1000000000000001e50

   1. Initial program 69.0%

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

   3. Taylor expanded in b around 0 64.9%

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

   4. Taylor expanded in t around inf 53.5%

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

      1. +-commutative 53.5%

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

      2. mul-1-neg 53.5%

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

      3. unsub-neg 53.5%

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

   6. Simplified 53.5%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+52}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-143}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -7.2 \cdot 10^{+147}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -1.42 \cdot 10^{-288}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 1450:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -7.2e+147)
   (* c (* t j))
   (if (<= j -1.42e-288)
     (* z (* x y))
     (if (<= j 1450.0) (* a (* b i)) (* t (* c 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 (j <= -7.2e+147) {
		tmp = c * (t * j);
	} else if (j <= -1.42e-288) {
		tmp = z * (x * y);
	} else if (j <= 1450.0) {
		tmp = a * (b * i);
	} else {
		tmp = t * (c * 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 (j <= (-7.2d+147)) then
        tmp = c * (t * j)
    else if (j <= (-1.42d-288)) then
        tmp = z * (x * y)
    else if (j <= 1450.0d0) then
        tmp = a * (b * i)
    else
        tmp = t * (c * 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 (j <= -7.2e+147) {
		tmp = c * (t * j);
	} else if (j <= -1.42e-288) {
		tmp = z * (x * y);
	} else if (j <= 1450.0) {
		tmp = a * (b * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -7.2e+147:
		tmp = c * (t * j)
	elif j <= -1.42e-288:
		tmp = z * (x * y)
	elif j <= 1450.0:
		tmp = a * (b * i)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -7.2e+147)
		tmp = Float64(c * Float64(t * j));
	elseif (j <= -1.42e-288)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 1450.0)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -7.2e+147)
		tmp = c * (t * j);
	elseif (j <= -1.42e-288)
		tmp = z * (x * y);
	elseif (j <= 1450.0)
		tmp = a * (b * i);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -7.2e+147], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.42e-288], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1450.0], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -7.20000000000000041e147

   1. Initial program 79.9%

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

   3. Taylor expanded in b around 0 76.8%

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

   4. Taylor expanded in c around inf 41.5%

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

   if -7.20000000000000041e147 < j < -1.42e-288

   1. Initial program 64.9%

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

   3. Taylor expanded in z around inf 51.6%

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

   4. Taylor expanded in x around inf 38.3%

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

   if -1.42e-288 < j < 1450

   1. Initial program 64.0%

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

   3. Taylor expanded in b around inf 51.4%

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

   4. Taylor expanded in a around inf 38.8%

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

   if 1450 < j

   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 i around inf 62.2%

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

   5. Simplified 59.6%

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

   6. Taylor expanded in t around inf 39.7%

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

      1. associate-*r* 41.9%

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

      2. *-commutative 41.9%

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

      3. +-commutative 41.9%

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

      4. mul-1-neg 41.9%

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

      5. unsub-neg 41.9%

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

      6. associate-/l* 38.1%

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

   8. Simplified 38.1%

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

   9. Taylor expanded in c around inf 27.6%

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

       1. *-commutative 27.6%

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

       2. *-commutative 27.6%

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

       3. associate-*l* 31.6%

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

   11. Simplified 31.6%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.2 \cdot 10^{+147}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -1.42 \cdot 10^{-288}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 1450:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{+76} \lor \neg \left(a \leq 1.65 \cdot 10^{+25}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.85e+76) (not (<= a 1.65e+25))) (* 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 ((a <= -1.85e+76) || !(a <= 1.65e+25)) {
		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 ((a <= (-1.85d+76)) .or. (.not. (a <= 1.65d+25))) 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 ((a <= -1.85e+76) || !(a <= 1.65e+25)) {
		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 (a <= -1.85e+76) or not (a <= 1.65e+25):
		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 ((a <= -1.85e+76) || !(a <= 1.65e+25))
		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 ((a <= -1.85e+76) || ~((a <= 1.65e+25)))
		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[a, -1.85e+76], N[Not[LessEqual[a, 1.65e+25]], $MachinePrecision]], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.85e76 or 1.6500000000000001e25 < a

   1. Initial program 57.6%

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

   3. Taylor expanded in b around inf 48.8%

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

   4. Taylor expanded in a around inf 45.9%

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

   if -1.85e76 < a < 1.6500000000000001e25

   1. Initial program 78.8%

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

   3. Taylor expanded in b around 0 64.0%

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

   4. Taylor expanded in c around inf 27.0%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{+76} \lor \neg \left(a \leq 1.65 \cdot 10^{+25}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.35 \cdot 10^{+76} \lor \neg \left(a \leq 1.76 \cdot 10^{+25}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -2.35e+76) (not (<= a 1.76e+25))) (* b (* a i)) (* t (* c 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 ((a <= -2.35e+76) || !(a <= 1.76e+25)) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * 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 ((a <= (-2.35d+76)) .or. (.not. (a <= 1.76d+25))) then
        tmp = b * (a * i)
    else
        tmp = t * (c * 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 ((a <= -2.35e+76) || !(a <= 1.76e+25)) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -2.35e+76) or not (a <= 1.76e+25):
		tmp = b * (a * i)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -2.35e+76) || !(a <= 1.76e+25))
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -2.35e+76) || ~((a <= 1.76e+25)))
		tmp = b * (a * i);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -2.35e+76], N[Not[LessEqual[a, 1.76e+25]], $MachinePrecision]], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.3500000000000002e76 or 1.76000000000000001e25 < a

   1. Initial program 57.6%

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

   3. Taylor expanded in b around inf 48.8%

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

   4. Taylor expanded in a around inf 45.9%

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

   if -2.3500000000000002e76 < a < 1.76000000000000001e25

   1. Initial program 78.8%

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

   3. Taylor expanded in i around inf 70.4%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in t around inf 35.5%

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

      1. associate-*r* 33.4%

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

      2. *-commutative 33.4%

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

      3. +-commutative 33.4%

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

      4. mul-1-neg 33.4%

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

      5. unsub-neg 33.4%

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

      6. associate-/l* 30.8%

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

   8. Simplified 30.8%

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

   9. Taylor expanded in c around inf 27.0%

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

       1. *-commutative 27.0%

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

       2. *-commutative 27.0%

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

       3. associate-*l* 29.0%

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

   11. Simplified 29.0%

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

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.35 \cdot 10^{+76} \lor \neg \left(a \leq 1.76 \cdot 10^{+25}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 23.0% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.7%

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

3. Taylor expanded in b around inf 40.9%

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

4. Taylor expanded in a around inf 25.1%

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

5. Final simplification 25.1%

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

Alternative 24: 22.8% 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 69.7%

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

3. Taylor expanded in b around inf 40.9%

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

4. Taylor expanded in a around inf 26.5%

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

5. Final simplification 26.5%

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

Developer target: 68.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024130 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

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