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

Percentage Accurate: 73.6% → 83.1%

Time: 16.6s

Alternatives: 17

Speedup: 0.5×

• 58.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around 0 16.1%

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

   5. Simplified 29.7%

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

   6. Taylor expanded in c around inf 38.6%

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

      1. associate-+r+ 38.6%

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

      2. +-commutative 38.6%

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

      3. mul-1-neg 38.6%

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

      4. unsub-neg 38.6%

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

      5. associate-/l* 38.6%

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

      6. associate-/l* 45.4%

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

      7. *-commutative 45.4%

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

      8. associate-/l* 54.5%

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

      9. *-commutative 54.5%

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

   8. Simplified 54.5%

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

4. Final simplification 85.3%

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

Alternative 2: 70.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.009 \lor \neg \left(z \leq 9 \cdot 10^{+88}\right):\\ \;\;\;\;i \cdot \left(t \cdot b + \left(\frac{z \cdot \left(x \cdot y - b \cdot c\right)}{i} - y \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(b \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -0.009) (not (<= z 9e+88)))
   (* i (+ (* t b) (- (/ (* z (- (* x y) (* b c))) i) (* y j))))
   (+ (* j (- (* a c) (* y i))) (+ (* x (- (* y z) (* t a))) (* t (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -0.009) || !(z <= 9e+88)) {
		tmp = i * ((t * b) + (((z * ((x * y) - (b * c))) / i) - (y * j)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (t * (b * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-0.009d0)) .or. (.not. (z <= 9d+88))) then
        tmp = i * ((t * b) + (((z * ((x * y) - (b * c))) / i) - (y * j)))
    else
        tmp = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (t * (b * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -0.009) || !(z <= 9e+88)) {
		tmp = i * ((t * b) + (((z * ((x * y) - (b * c))) / i) - (y * j)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (t * (b * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -0.009) or not (z <= 9e+88):
		tmp = i * ((t * b) + (((z * ((x * y) - (b * c))) / i) - (y * j)))
	else:
		tmp = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (t * (b * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -0.009) || !(z <= 9e+88))
		tmp = Float64(i * Float64(Float64(t * b) + Float64(Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) / i) - Float64(y * j))));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(t * Float64(b * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -0.009) || ~((z <= 9e+88)))
		tmp = i * ((t * b) + (((z * ((x * y) - (b * c))) / i) - (y * j)));
	else
		tmp = (j * ((a * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (t * (b * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -0.009], N[Not[LessEqual[z, 9e+88]], $MachinePrecision]], N[(i * N[(N[(t * b), $MachinePrecision] + N[(N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.00899999999999999932 or 9e88 < z

   1. Initial program 63.8%

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

   3. Taylor expanded in a around 0 61.1%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in i around -inf 64.8%

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

      1. mul-1-neg 64.8%

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

      2. *-commutative 64.8%

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

      3. distribute-rgt-neg-in 64.8%

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

   8. Simplified 72.4%

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

   if -0.00899999999999999932 < z < 9e88

   1. Initial program 84.2%

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

   3. Taylor expanded in c around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. *-commutative 79.1%

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

      3. *-commutative 79.1%

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

      4. distribute-lft-neg-in 79.1%

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

      5. distribute-rgt-neg-out 79.1%

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

      6. associate-*l* 81.9%

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

      7. distribute-lft-neg-in 81.9%

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

      8. distribute-rgt-neg-in 81.9%

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

   5. Simplified 81.9%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.009 \lor \neg \left(z \leq 9 \cdot 10^{+88}\right):\\ \;\;\;\;i \cdot \left(t \cdot b + \left(\frac{z \cdot \left(x \cdot y - b \cdot c\right)}{i} - y \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(b \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -4 \cdot 10^{+75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{-279}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-93}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -4e+75)
     t_2
     (if (<= i 1.55e-279)
       t_1
       (if (<= i 3.2e-93)
         (* x (- (* y z) (* t a)))
         (if (<= i 1.85e-14)
           (* z (- (* x y) (* b c)))
           (if (<= i 4.8e+70) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4e+75) {
		tmp = t_2;
	} else if (i <= 1.55e-279) {
		tmp = t_1;
	} else if (i <= 3.2e-93) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 1.85e-14) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 4.8e+70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-4d+75)) then
        tmp = t_2
    else if (i <= 1.55d-279) then
        tmp = t_1
    else if (i <= 3.2d-93) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= 1.85d-14) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 4.8d+70) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4e+75) {
		tmp = t_2;
	} else if (i <= 1.55e-279) {
		tmp = t_1;
	} else if (i <= 3.2e-93) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 1.85e-14) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 4.8e+70) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -4e+75:
		tmp = t_2
	elif i <= 1.55e-279:
		tmp = t_1
	elif i <= 3.2e-93:
		tmp = x * ((y * z) - (t * a))
	elif i <= 1.85e-14:
		tmp = z * ((x * y) - (b * c))
	elif i <= 4.8e+70:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -4e+75)
		tmp = t_2;
	elseif (i <= 1.55e-279)
		tmp = t_1;
	elseif (i <= 3.2e-93)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= 1.85e-14)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 4.8e+70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -4e+75)
		tmp = t_2;
	elseif (i <= 1.55e-279)
		tmp = t_1;
	elseif (i <= 3.2e-93)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= 1.85e-14)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 4.8e+70)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4e+75], t$95$2, If[LessEqual[i, 1.55e-279], t$95$1, If[LessEqual[i, 3.2e-93], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.85e-14], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.8e+70], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -3.99999999999999971e75 or 4.79999999999999974e70 < i

   1. Initial program 63.6%

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

   3. Taylor expanded in a around 0 66.0%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in i around inf 70.6%

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

      1. +-commutative 70.6%

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

      2. mul-1-neg 70.6%

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

      3. unsub-neg 70.6%

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

      4. *-commutative 70.6%

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

   8. Simplified 70.6%

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

   if -3.99999999999999971e75 < i < 1.55e-279 or 1.85000000000000001e-14 < i < 4.79999999999999974e70

   1. Initial program 82.1%

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

   3. Taylor expanded in a around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. unsub-neg 62.6%

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

   5. Simplified 62.6%

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

   if 1.55e-279 < i < 3.1999999999999999e-93

   1. Initial program 85.6%

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

      1. *-commutative 85.6%

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

      2. prod-diff 85.6%

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

      3. *-commutative 85.6%

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

      4. fmm-def 85.6%

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

      5. distribute-rgt-in 85.6%

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

      6. *-commutative 85.6%

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

      7. *-commutative 85.6%

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

      8. *-commutative 85.6%

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

      9. *-commutative 85.6%

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

   4. Applied egg-rr 85.6%

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

   5. Taylor expanded in x around inf 86.1%

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

   if 3.1999999999999999e-93 < i < 1.85000000000000001e-14

   1. Initial program 81.5%

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

   3. Taylor expanded in z around inf 62.6%

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

      1. *-commutative 62.6%

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

   5. Simplified 62.6%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4 \cdot 10^{+75}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{-279}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-93}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+70}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+177}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+172}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -1.6e+177)
     t_2
     (if (<= y -2.6e+60)
       (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))
       (if (<= y 7.5e+172) (+ (* a (- (* c j) (* x t))) t_1) (+ t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.6e+177) {
		tmp = t_2;
	} else if (y <= -2.6e+60) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else if (y <= 7.5e+172) {
		tmp = (a * ((c * j) - (x * t))) + t_1;
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-1.6d+177)) then
        tmp = t_2
    else if (y <= (-2.6d+60)) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    else if (y <= 7.5d+172) then
        tmp = (a * ((c * j) - (x * t))) + t_1
    else
        tmp = t_2 + 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 * ((t * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.6e+177) {
		tmp = t_2;
	} else if (y <= -2.6e+60) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else if (y <= 7.5e+172) {
		tmp = (a * ((c * j) - (x * t))) + t_1;
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.6e+177:
		tmp = t_2
	elif y <= -2.6e+60:
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	elif y <= 7.5e+172:
		tmp = (a * ((c * j) - (x * t))) + t_1
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.6e+177)
		tmp = t_2;
	elseif (y <= -2.6e+60)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	elseif (y <= 7.5e+172)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + t_1);
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.6e+177)
		tmp = t_2;
	elseif (y <= -2.6e+60)
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	elseif (y <= 7.5e+172)
		tmp = (a * ((c * j) - (x * t))) + t_1;
	else
		tmp = t_2 + 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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+177], t$95$2, If[LessEqual[y, -2.6e+60], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+172], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6e177

   1. Initial program 53.7%

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

   3. Taylor expanded in y around inf 80.0%

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

      1. +-commutative 80.0%

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

      2. mul-1-neg 80.0%

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

      3. unsub-neg 80.0%

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

      4. *-commutative 80.0%

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

   5. Simplified 80.0%

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

   if -1.6e177 < y < -2.60000000000000008e60

   1. Initial program 80.9%

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

   3. Taylor expanded in b around 0 90.4%

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

   if -2.60000000000000008e60 < y < 7.4999999999999994e172

   1. Initial program 80.5%

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

   3. Taylor expanded in y around 0 76.6%

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

      1. sub-neg 76.6%

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

      2. *-commutative 76.6%

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

      3. *-commutative 76.6%

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

      4. mul-1-neg 76.6%

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

      5. *-commutative 76.6%

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

      6. distribute-lft-neg-in 76.6%

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

      7. mul-1-neg 76.6%

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

      8. *-commutative 76.6%

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

      9. distribute-rgt-in 77.7%

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

      10. +-commutative 77.7%

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

      11. mul-1-neg 77.7%

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

      12. unsub-neg 77.7%

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

      13. distribute-rgt-neg-in 77.7%

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

      14. sub-neg 77.7%

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

      15. distribute-rgt-neg-out 77.7%

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

      16. +-commutative 77.7%

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

   5. Simplified 77.7%

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

   if 7.4999999999999994e172 < y

   1. Initial program 63.5%

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

   3. Taylor expanded in a around 0 68.2%

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

   5. Simplified 82.9%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+177}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+172}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+178}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -1.4e+176)
     t_1
     (if (<= y -1.2e+60)
       (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))
       (if (<= y 1.1e+178)
         (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.4e+176) {
		tmp = t_1;
	} else if (y <= -1.2e+60) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else if (y <= 1.1e+178) {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (y <= (-1.4d+176)) then
        tmp = t_1
    else if (y <= (-1.2d+60)) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    else if (y <= 1.1d+178) then
        tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.4e+176) {
		tmp = t_1;
	} else if (y <= -1.2e+60) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else if (y <= 1.1e+178) {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.4e+176:
		tmp = t_1
	elif y <= -1.2e+60:
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	elif y <= 1.1e+178:
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.4e+176)
		tmp = t_1;
	elseif (y <= -1.2e+60)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	elseif (y <= 1.1e+178)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.4e+176)
		tmp = t_1;
	elseif (y <= -1.2e+60)
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	elseif (y <= 1.1e+178)
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+176], t$95$1, If[LessEqual[y, -1.2e+60], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+178], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4000000000000001e176 or 1.09999999999999999e178 < y

   1. Initial program 56.3%

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

   3. Taylor expanded in y around inf 78.6%

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

      1. +-commutative 78.6%

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

      2. mul-1-neg 78.6%

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

      3. unsub-neg 78.6%

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

      4. *-commutative 78.6%

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

   5. Simplified 78.6%

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

   if -1.4000000000000001e176 < y < -1.2e60

   1. Initial program 80.9%

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

   3. Taylor expanded in b around 0 90.4%

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

   if -1.2e60 < y < 1.09999999999999999e178

   1. Initial program 80.7%

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

   3. Taylor expanded in y around 0 76.3%

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

      1. sub-neg 76.3%

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

      2. *-commutative 76.3%

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

      3. *-commutative 76.3%

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

      4. mul-1-neg 76.3%

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

      5. *-commutative 76.3%

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

      6. distribute-lft-neg-in 76.3%

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

      7. mul-1-neg 76.3%

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

      8. *-commutative 76.3%

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

      9. distribute-rgt-in 77.4%

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

      10. +-commutative 77.4%

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

      11. mul-1-neg 77.4%

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

      12. unsub-neg 77.4%

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

      13. distribute-rgt-neg-in 77.4%

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

      14. sub-neg 77.4%

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

      15. distribute-rgt-neg-out 77.4%

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

      16. +-commutative 77.4%

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

   5. Simplified 77.4%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+176}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+178}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.1 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.16 \cdot 10^{-279}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.38 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(t \cdot \left(c \cdot \frac{j}{t} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -1.1e+76)
     t_1
     (if (<= i 1.16e-279)
       (* a (- (* c j) (* x t)))
       (if (<= i 1.38e-104)
         (* x (- (* y z) (* t a)))
         (if (<= i 1.3e+71) (* a (* t (- (* c (/ j t)) x))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.1e+76) {
		tmp = t_1;
	} else if (i <= 1.16e-279) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.38e-104) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 1.3e+71) {
		tmp = a * (t * ((c * (j / t)) - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-1.1d+76)) then
        tmp = t_1
    else if (i <= 1.16d-279) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 1.38d-104) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= 1.3d+71) then
        tmp = a * (t * ((c * (j / t)) - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.1e+76) {
		tmp = t_1;
	} else if (i <= 1.16e-279) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.38e-104) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 1.3e+71) {
		tmp = a * (t * ((c * (j / t)) - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.1e+76:
		tmp = t_1
	elif i <= 1.16e-279:
		tmp = a * ((c * j) - (x * t))
	elif i <= 1.38e-104:
		tmp = x * ((y * z) - (t * a))
	elif i <= 1.3e+71:
		tmp = a * (t * ((c * (j / t)) - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.1e+76)
		tmp = t_1;
	elseif (i <= 1.16e-279)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 1.38e-104)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= 1.3e+71)
		tmp = Float64(a * Float64(t * Float64(Float64(c * Float64(j / t)) - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.1e+76)
		tmp = t_1;
	elseif (i <= 1.16e-279)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 1.38e-104)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= 1.3e+71)
		tmp = a * (t * ((c * (j / t)) - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.1e+76], t$95$1, If[LessEqual[i, 1.16e-279], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.38e-104], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e+71], N[(a * N[(t * N[(N[(c * N[(j / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.1e76 or 1.29999999999999996e71 < i

   1. Initial program 63.6%

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

   3. Taylor expanded in a around 0 66.0%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in i around inf 70.6%

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

      1. +-commutative 70.6%

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

      2. mul-1-neg 70.6%

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

      3. unsub-neg 70.6%

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

      4. *-commutative 70.6%

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

   8. Simplified 70.6%

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

   if -1.1e76 < i < 1.16e-279

   1. Initial program 85.6%

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

   3. Taylor expanded in a around inf 62.0%

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

      1. +-commutative 62.0%

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

      2. mul-1-neg 62.0%

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

      3. unsub-neg 62.0%

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

   5. Simplified 62.0%

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

   if 1.16e-279 < i < 1.38000000000000006e-104

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

      2. prod-diff 85.0%

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

      3. *-commutative 85.0%

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

      4. fmm-def 85.0%

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

      5. distribute-rgt-in 85.0%

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

      6. *-commutative 85.0%

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

      7. *-commutative 85.0%

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

      8. *-commutative 85.0%

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

      9. *-commutative 85.0%

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

   4. Applied egg-rr 85.0%

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

   5. Taylor expanded in x around inf 85.5%

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

   if 1.38000000000000006e-104 < i < 1.29999999999999996e71

   1. Initial program 75.1%

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

   3. Taylor expanded in a around inf 54.5%

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

      1. +-commutative 54.5%

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

      2. mul-1-neg 54.5%

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

      3. unsub-neg 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in t around inf 54.5%

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

      1. associate-/l* 56.5%

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

   8. Simplified 56.5%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.1 \cdot 10^{+76}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 1.16 \cdot 10^{-279}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.38 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(t \cdot \left(c \cdot \frac{j}{t} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+60} \lor \neg \left(y \leq 1.06 \cdot 10^{+178}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -4.5e+60) (not (<= y 1.06e+178)))
   (* y (- (* x z) (* i j)))
   (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -4.5e+60) || !(y <= 1.06e+178)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-4.5d+60)) .or. (.not. (y <= 1.06d+178))) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -4.5e+60) || !(y <= 1.06e+178)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -4.5e+60) or not (y <= 1.06e+178):
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -4.5e+60) || !(y <= 1.06e+178))
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -4.5e+60) || ~((y <= 1.06e+178)))
		tmp = y * ((x * z) - (i * j));
	else
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -4.5e+60], N[Not[LessEqual[y, 1.06e+178]], $MachinePrecision]], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.50000000000000013e60 or 1.05999999999999994e178 < y

   1. Initial program 63.5%

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

   3. Taylor expanded in y around inf 72.6%

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

      1. +-commutative 72.6%

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

      2. mul-1-neg 72.6%

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

      3. unsub-neg 72.6%

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

      4. *-commutative 72.6%

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

   5. Simplified 72.6%

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

   if -4.50000000000000013e60 < y < 1.05999999999999994e178

   1. Initial program 80.7%

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

   3. Taylor expanded in y around 0 76.3%

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

      1. sub-neg 76.3%

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

      2. *-commutative 76.3%

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

      3. *-commutative 76.3%

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

      4. mul-1-neg 76.3%

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

      5. *-commutative 76.3%

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

      6. distribute-lft-neg-in 76.3%

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

      7. mul-1-neg 76.3%

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

      8. *-commutative 76.3%

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

      9. distribute-rgt-in 77.4%

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

      10. +-commutative 77.4%

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

      11. mul-1-neg 77.4%

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

      12. unsub-neg 77.4%

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

      13. distribute-rgt-neg-in 77.4%

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

      14. sub-neg 77.4%

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

      15. distribute-rgt-neg-out 77.4%

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

      16. +-commutative 77.4%

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

   5. Simplified 77.4%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+60} \lor \neg \left(y \leq 1.06 \cdot 10^{+178}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 30.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -3.9 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.05e+76)
   (* y (* i (- j)))
   (if (<= i -3.9e-85)
     (* a (* c j))
     (if (<= i 2.6e+72) (* t (* x (- a))) (* t (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.05e+76) {
		tmp = y * (i * -j);
	} else if (i <= -3.9e-85) {
		tmp = a * (c * j);
	} else if (i <= 2.6e+72) {
		tmp = t * (x * -a);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-1.05d+76)) then
        tmp = y * (i * -j)
    else if (i <= (-3.9d-85)) then
        tmp = a * (c * j)
    else if (i <= 2.6d+72) then
        tmp = t * (x * -a)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.05e+76) {
		tmp = y * (i * -j);
	} else if (i <= -3.9e-85) {
		tmp = a * (c * j);
	} else if (i <= 2.6e+72) {
		tmp = t * (x * -a);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.05e+76:
		tmp = y * (i * -j)
	elif i <= -3.9e-85:
		tmp = a * (c * j)
	elif i <= 2.6e+72:
		tmp = t * (x * -a)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.05e+76)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (i <= -3.9e-85)
		tmp = Float64(a * Float64(c * j));
	elseif (i <= 2.6e+72)
		tmp = Float64(t * Float64(x * Float64(-a)));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -1.05e+76)
		tmp = y * (i * -j);
	elseif (i <= -3.9e-85)
		tmp = a * (c * j);
	elseif (i <= 2.6e+72)
		tmp = t * (x * -a);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.05e+76], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.9e-85], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.6e+72], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.05000000000000003e76

   1. Initial program 62.8%

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

   3. Taylor expanded in y around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

      4. *-commutative 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in z around 0 47.9%

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

      1. mul-1-neg 47.9%

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

      2. distribute-lft-neg-out 47.9%

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

      3. *-commutative 47.9%

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

   8. Simplified 47.9%

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

   if -1.05000000000000003e76 < i < -3.89999999999999988e-85

   1. Initial program 86.9%

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

   3. Taylor expanded in a around inf 72.8%

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

      1. +-commutative 72.8%

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

      2. mul-1-neg 72.8%

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

      3. unsub-neg 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in c around inf 47.3%

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

      1. *-commutative 47.3%

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

   8. Simplified 47.3%

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

   if -3.89999999999999988e-85 < i < 2.59999999999999981e72

   1. Initial program 81.2%

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

   3. Taylor expanded in t around inf 47.6%

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

      1. distribute-lft-out-- 47.6%

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

   5. Simplified 47.6%

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

   6. Taylor expanded in a around inf 41.4%

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

      1. associate-*r* 41.4%

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

      2. neg-mul-1 41.4%

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

   8. Simplified 41.4%

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

   if 2.59999999999999981e72 < i

   1. Initial program 64.4%

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

   3. Taylor expanded in t around inf 56.6%

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

      1. distribute-lft-out-- 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in a around 0 45.9%

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

      1. *-commutative 45.9%

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

   8. Simplified 45.9%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -3.9 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -4 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.22 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* b i))))
   (if (<= i -4e+162)
     t_1
     (if (<= i -1.22e-85)
       (* a (* c j))
       (if (<= i 7.5e+70) (* t (* 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 = t * (b * i);
	double tmp;
	if (i <= -4e+162) {
		tmp = t_1;
	} else if (i <= -1.22e-85) {
		tmp = a * (c * j);
	} else if (i <= 7.5e+70) {
		tmp = t * (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 = t * (b * i)
    if (i <= (-4d+162)) then
        tmp = t_1
    else if (i <= (-1.22d-85)) then
        tmp = a * (c * j)
    else if (i <= 7.5d+70) then
        tmp = t * (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 = t * (b * i);
	double tmp;
	if (i <= -4e+162) {
		tmp = t_1;
	} else if (i <= -1.22e-85) {
		tmp = a * (c * j);
	} else if (i <= 7.5e+70) {
		tmp = t * (x * -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (b * i)
	tmp = 0
	if i <= -4e+162:
		tmp = t_1
	elif i <= -1.22e-85:
		tmp = a * (c * j)
	elif i <= 7.5e+70:
		tmp = t * (x * -a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (i <= -4e+162)
		tmp = t_1;
	elseif (i <= -1.22e-85)
		tmp = Float64(a * Float64(c * j));
	elseif (i <= 7.5e+70)
		tmp = Float64(t * Float64(x * Float64(-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 = t * (b * i);
	tmp = 0.0;
	if (i <= -4e+162)
		tmp = t_1;
	elseif (i <= -1.22e-85)
		tmp = a * (c * j);
	elseif (i <= 7.5e+70)
		tmp = t * (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[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4e+162], t$95$1, If[LessEqual[i, -1.22e-85], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.5e+70], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.9999999999999998e162 or 7.50000000000000031e70 < i

   1. Initial program 63.9%

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

   3. Taylor expanded in t around inf 51.8%

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

      1. distribute-lft-out-- 51.8%

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

   5. Simplified 51.8%

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

   6. Taylor expanded in a around 0 45.5%

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

      1. *-commutative 45.5%

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

   8. Simplified 45.5%

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

   if -3.9999999999999998e162 < i < -1.22000000000000006e-85

   1. Initial program 80.5%

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

   3. Taylor expanded in a around inf 60.5%

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

      1. +-commutative 60.5%

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

      2. mul-1-neg 60.5%

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

      3. unsub-neg 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in c around inf 39.7%

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

      1. *-commutative 39.7%

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

   8. Simplified 39.7%

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

   if -1.22000000000000006e-85 < i < 7.50000000000000031e70

   1. Initial program 81.2%

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

   3. Taylor expanded in t around inf 47.6%

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

      1. distribute-lft-out-- 47.6%

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

   5. Simplified 47.6%

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

   6. Taylor expanded in a around inf 41.4%

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

      1. associate-*r* 41.4%

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

      2. neg-mul-1 41.4%

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

   8. Simplified 41.4%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4 \cdot 10^{+162}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -1.22 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.3 \cdot 10^{+75} \lor \neg \left(i \leq 6 \cdot 10^{+69}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -3.3e+75) (not (<= i 6e+69)))
   (* i (- (* t b) (* y j)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -3.3e+75) || !(i <= 6e+69)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-3.3d+75)) .or. (.not. (i <= 6d+69))) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -3.3e+75) || !(i <= 6e+69)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -3.3e+75) or not (i <= 6e+69):
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -3.3e+75) || !(i <= 6e+69))
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -3.3e+75) || ~((i <= 6e+69)))
		tmp = i * ((t * b) - (y * j));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -3.3e+75], N[Not[LessEqual[i, 6e+69]], $MachinePrecision]], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -3.29999999999999998e75 or 5.99999999999999967e69 < i

   1. Initial program 63.6%

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

   3. Taylor expanded in a around 0 66.0%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in i around inf 70.6%

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

      1. +-commutative 70.6%

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

      2. mul-1-neg 70.6%

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

      3. unsub-neg 70.6%

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

      4. *-commutative 70.6%

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

   8. Simplified 70.6%

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

   if -3.29999999999999998e75 < i < 5.99999999999999967e69

   1. Initial program 82.5%

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

   3. Taylor expanded in a around inf 58.7%

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

      1. +-commutative 58.7%

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

      2. mul-1-neg 58.7%

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

      3. unsub-neg 58.7%

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

   5. Simplified 58.7%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.3 \cdot 10^{+75} \lor \neg \left(i \leq 6 \cdot 10^{+69}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{-43} \lor \neg \left(b \leq 1.05 \cdot 10^{+123}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -2.4e-43) (not (<= b 1.05e+123)))
   (* b (- (* t i) (* z c)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2.4e-43) || !(b <= 1.05e+123)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-2.4d-43)) .or. (.not. (b <= 1.05d+123))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2.4e-43) || !(b <= 1.05e+123)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -2.4e-43) or not (b <= 1.05e+123):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -2.4e-43) || !(b <= 1.05e+123))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -2.4e-43) || ~((b <= 1.05e+123)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -2.4e-43], N[Not[LessEqual[b, 1.05e+123]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.4000000000000002e-43 or 1.04999999999999997e123 < b

   1. Initial program 71.6%

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

   3. Taylor expanded in b around inf 61.3%

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

      1. *-commutative 61.3%

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

   5. Simplified 61.3%

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

   if -2.4000000000000002e-43 < b < 1.04999999999999997e123

   1. Initial program 79.1%

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

   3. Taylor expanded in a around inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

   5. Simplified 56.2%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{-43} \lor \neg \left(b \leq 1.05 \cdot 10^{+123}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 41.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.85 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -2.85e+76)
   (* y (* i (- j)))
   (if (<= i 7.8e+71) (* a (- (* c j) (* x t))) (* t (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -2.85e+76) {
		tmp = y * (i * -j);
	} else if (i <= 7.8e+71) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-2.85d+76)) then
        tmp = y * (i * -j)
    else if (i <= 7.8d+71) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -2.85e+76) {
		tmp = y * (i * -j);
	} else if (i <= 7.8e+71) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -2.85e+76:
		tmp = y * (i * -j)
	elif i <= 7.8e+71:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -2.85e+76)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (i <= 7.8e+71)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -2.85e+76)
		tmp = y * (i * -j);
	elseif (i <= 7.8e+71)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -2.85e+76], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.8e+71], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.85000000000000002e76

   1. Initial program 62.8%

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

   3. Taylor expanded in y around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

      4. *-commutative 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in z around 0 47.9%

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

      1. mul-1-neg 47.9%

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

      2. distribute-lft-neg-out 47.9%

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

      3. *-commutative 47.9%

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

   8. Simplified 47.9%

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

   if -2.85000000000000002e76 < i < 7.8000000000000002e71

   1. Initial program 82.5%

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

   3. Taylor expanded in a around inf 58.7%

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

      1. +-commutative 58.7%

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

      2. mul-1-neg 58.7%

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

      3. unsub-neg 58.7%

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

   5. Simplified 58.7%

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

   if 7.8000000000000002e71 < i

   1. Initial program 64.4%

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

   3. Taylor expanded in t around inf 56.6%

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

      1. distribute-lft-out-- 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in a around 0 45.9%

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

      1. *-commutative 45.9%

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

   8. Simplified 45.9%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.85 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+68} \lor \neg \left(c \leq 2.1 \cdot 10^{-48}\right):\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -3.8e+68) (not (<= c 2.1e-48)))
   (* b (* z (- c)))
   (* t (* x (- a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.8e+68) || !(c <= 2.1e-48)) {
		tmp = b * (z * -c);
	} else {
		tmp = t * (x * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-3.8d+68)) .or. (.not. (c <= 2.1d-48))) then
        tmp = b * (z * -c)
    else
        tmp = t * (x * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.8e+68) || !(c <= 2.1e-48)) {
		tmp = b * (z * -c);
	} else {
		tmp = t * (x * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -3.8e+68) or not (c <= 2.1e-48):
		tmp = b * (z * -c)
	else:
		tmp = t * (x * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -3.8e+68) || !(c <= 2.1e-48))
		tmp = Float64(b * Float64(z * Float64(-c)));
	else
		tmp = Float64(t * Float64(x * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -3.8e+68) || ~((c <= 2.1e-48)))
		tmp = b * (z * -c);
	else
		tmp = t * (x * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -3.8e+68], N[Not[LessEqual[c, 2.1e-48]], $MachinePrecision]], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.8000000000000001e68 or 2.09999999999999989e-48 < c

   1. Initial program 72.3%

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

   3. Taylor expanded in a around 0 55.9%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in c around inf 38.6%

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

      1. mul-1-neg 38.6%

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

      2. *-commutative 38.6%

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

      3. distribute-rgt-neg-in 38.6%

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

   8. Simplified 38.6%

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

   if -3.8000000000000001e68 < c < 2.09999999999999989e-48

   1. Initial program 79.6%

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

   3. Taylor expanded in t around inf 63.2%

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

      1. distribute-lft-out-- 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in a around inf 46.8%

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

      1. associate-*r* 46.8%

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

      2. neg-mul-1 46.8%

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

   8. Simplified 46.8%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+68} \lor \neg \left(c \leq 2.1 \cdot 10^{-48}\right):\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-10} \lor \neg \left(x \leq 3.4 \cdot 10^{+120}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -1.02e-10) (not (<= x 3.4e+120))) (* y (* x z)) (* a (* 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 ((x <= -1.02e-10) || !(x <= 3.4e+120)) {
		tmp = y * (x * z);
	} else {
		tmp = a * (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 ((x <= (-1.02d-10)) .or. (.not. (x <= 3.4d+120))) then
        tmp = y * (x * z)
    else
        tmp = a * (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 ((x <= -1.02e-10) || !(x <= 3.4e+120)) {
		tmp = y * (x * z);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -1.02e-10) or not (x <= 3.4e+120):
		tmp = y * (x * z)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -1.02e-10) || !(x <= 3.4e+120))
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(a * 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 ((x <= -1.02e-10) || ~((x <= 3.4e+120)))
		tmp = y * (x * z);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -1.02e-10], N[Not[LessEqual[x, 3.4e+120]], $MachinePrecision]], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.01999999999999997e-10 or 3.39999999999999999e120 < x

   1. Initial program 73.4%

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

   3. Taylor expanded in y around inf 43.7%

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

      1. +-commutative 43.7%

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

      2. mul-1-neg 43.7%

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

      3. unsub-neg 43.7%

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

      4. *-commutative 43.7%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in z around inf 36.6%

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

      1. *-commutative 36.6%

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

   8. Simplified 36.6%

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

   if -1.01999999999999997e-10 < x < 3.39999999999999999e120

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf 42.0%

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

      1. +-commutative 42.0%

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

      2. mul-1-neg 42.0%

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

      3. unsub-neg 42.0%

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

   5. Simplified 42.0%

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

   6. Taylor expanded in c around inf 30.0%

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

      1. *-commutative 30.0%

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

   8. Simplified 30.0%

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

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-10} \lor \neg \left(x \leq 3.4 \cdot 10^{+120}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+14} \lor \neg \left(b \leq 1.28\right):\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -3.8e+14) (not (<= b 1.28))) (* t (* b i)) (* a (* 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 ((b <= -3.8e+14) || !(b <= 1.28)) {
		tmp = t * (b * i);
	} else {
		tmp = a * (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 ((b <= (-3.8d+14)) .or. (.not. (b <= 1.28d0))) then
        tmp = t * (b * i)
    else
        tmp = a * (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 ((b <= -3.8e+14) || !(b <= 1.28)) {
		tmp = t * (b * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -3.8e+14) or not (b <= 1.28):
		tmp = t * (b * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -3.8e+14) || !(b <= 1.28))
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(a * 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 ((b <= -3.8e+14) || ~((b <= 1.28)))
		tmp = t * (b * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -3.8e+14], N[Not[LessEqual[b, 1.28]], $MachinePrecision]], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.8e14 or 1.28000000000000003 < b

   1. Initial program 70.2%

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

   3. Taylor expanded in t around inf 57.9%

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

      1. distribute-lft-out-- 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in a around 0 39.0%

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

      1. *-commutative 39.0%

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

   8. Simplified 39.0%

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

   if -3.8e14 < b < 1.28000000000000003

   1. Initial program 80.8%

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

   3. Taylor expanded in a around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. mul-1-neg 55.0%

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

      3. unsub-neg 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in c around inf 25.5%

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

      1. *-commutative 25.5%

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

   8. Simplified 25.5%

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

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+14} \lor \neg \left(b \leq 1.28\right):\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+16} \lor \neg \left(t \leq 14500000\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -2.4e+16) (not (<= t 14500000.0))) (* b (* t i)) (* a (* 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 ((t <= -2.4e+16) || !(t <= 14500000.0)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (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 ((t <= (-2.4d+16)) .or. (.not. (t <= 14500000.0d0))) then
        tmp = b * (t * i)
    else
        tmp = a * (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 ((t <= -2.4e+16) || !(t <= 14500000.0)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -2.4e+16) or not (t <= 14500000.0):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -2.4e+16) || !(t <= 14500000.0))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * 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 ((t <= -2.4e+16) || ~((t <= 14500000.0)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -2.4e+16], N[Not[LessEqual[t, 14500000.0]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4e16 or 1.45e7 < t

   1. Initial program 73.8%

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

   3. Taylor expanded in t around inf 63.8%

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

      1. distribute-lft-out-- 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in a around 0 30.6%

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

   if -2.4e16 < t < 1.45e7

   1. Initial program 78.3%

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

   3. Taylor expanded in a around inf 44.3%

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

      1. +-commutative 44.3%

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

      2. mul-1-neg 44.3%

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

      3. unsub-neg 44.3%

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

   5. Simplified 44.3%

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

   6. Taylor expanded in c around inf 30.7%

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

      1. *-commutative 30.7%

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

   8. Simplified 30.7%

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

4. Final simplification 30.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+16} \lor \neg \left(t \leq 14500000\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 22.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.9%

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

3. Taylor expanded in a around inf 48.4%

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

   1. +-commutative 48.4%

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

   2. mul-1-neg 48.4%

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

   3. unsub-neg 48.4%

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

5. Simplified 48.4%

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

6. Taylor expanded in c around inf 21.6%

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

   1. *-commutative 21.6%

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

8. Simplified 21.6%

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

9. Final simplification 21.6%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer Target 1: 59.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024177 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))