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

Percentage Accurate: 74.3% → 84.2%

Time: 23.8s

Alternatives: 22

Speedup: 0.5×

• 58.4% 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: 74.3% 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: 84.2% accurate, 0.5× speedup

Math

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

FPCore

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

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = c * ((a * j) + (((y * ((x * z) - (i * j))) / c) - (z * b)))
	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(t * i) - Float64(z * c)))) + 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(a * j) + Float64(Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) / c) - Float64(z * b))));
	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 * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = c * ((a * j) + (((y * ((x * z) - (i * j))) / c) - (z * b)));
	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[(t * i), $MachinePrecision] - N[(z * c), $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[(a * j), $MachinePrecision] + N[(N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] - N[(z * b), $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 93.7%

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

   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 z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 34.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 34.8%

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

   6. Taylor expanded in c around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(-1 \cdot \left(-1 \cdot \left(a \cdot j\right) + \left(-1 \cdot \frac{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)}{c} + b \cdot z\right)\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(-1, \color{blue}{\left(-1 \cdot \left(a \cdot j\right) + \left(-1 \cdot \frac{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)}{c} + b \cdot z\right)\right)}\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(-1, \left(\left(-1 \cdot \frac{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)}{c} + b \cdot z\right) + \color{blue}{-1 \cdot \left(a \cdot j\right)}\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(-1, \left(\left(-1 \cdot \frac{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)}{c} + b \cdot z\right) + \left(\mathsf{neg}\left(a \cdot j\right)\right)\right)\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(-1, \left(\left(-1 \cdot \frac{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)}{c} + b \cdot z\right) - \color{blue}{a \cdot j}\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(-1 \cdot \frac{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)}{c} + b \cdot z\right), \color{blue}{\left(a \cdot j\right)}\right)\right)\right) \]

   8. Simplified 54.8%

      \[\leadsto \color{blue}{c \cdot \left(-1 \cdot \left(\left(b \cdot z - \frac{y \cdot \left(z \cdot x - i \cdot j\right)}{c}\right) - j \cdot a\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.3%

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

Alternative 2: 49.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot i - z \cdot c\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+111}:\\ \;\;\;\;\left(y \cdot b\right) \cdot \frac{t\_1}{y}\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-227}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-101}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+183}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t i) (* z c))))
   (if (<= b -5.5e+111)
     (* (* y b) (/ t_1 y))
     (if (<= b -2.1e-45)
       (* t (- (* b i) (* x a)))
       (if (<= b 1.65e-227)
         (* y (* z (- x (* i (/ j z)))))
         (if (<= b 1.9e-101)
           (* a (* x (- (/ (* c j) x) t)))
           (if (<= b 4.5e+74)
             (* y (* x (- z (/ (* t a) y))))
             (if (<= b 1.95e+183) (* i (- (* t b) (* y j))) (* b 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 * i) - (z * c);
	double tmp;
	if (b <= -5.5e+111) {
		tmp = (y * b) * (t_1 / y);
	} else if (b <= -2.1e-45) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= 1.65e-227) {
		tmp = y * (z * (x - (i * (j / z))));
	} else if (b <= 1.9e-101) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (b <= 4.5e+74) {
		tmp = y * (x * (z - ((t * a) / y)));
	} else if (b <= 1.95e+183) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = b * 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 * i) - (z * c)
    if (b <= (-5.5d+111)) then
        tmp = (y * b) * (t_1 / y)
    else if (b <= (-2.1d-45)) then
        tmp = t * ((b * i) - (x * a))
    else if (b <= 1.65d-227) then
        tmp = y * (z * (x - (i * (j / z))))
    else if (b <= 1.9d-101) then
        tmp = a * (x * (((c * j) / x) - t))
    else if (b <= 4.5d+74) then
        tmp = y * (x * (z - ((t * a) / y)))
    else if (b <= 1.95d+183) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = b * 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 * i) - (z * c);
	double tmp;
	if (b <= -5.5e+111) {
		tmp = (y * b) * (t_1 / y);
	} else if (b <= -2.1e-45) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= 1.65e-227) {
		tmp = y * (z * (x - (i * (j / z))));
	} else if (b <= 1.9e-101) {
		tmp = a * (x * (((c * j) / x) - t));
	} else if (b <= 4.5e+74) {
		tmp = y * (x * (z - ((t * a) / y)));
	} else if (b <= 1.95e+183) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = b * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * i) - (z * c)
	tmp = 0
	if b <= -5.5e+111:
		tmp = (y * b) * (t_1 / y)
	elif b <= -2.1e-45:
		tmp = t * ((b * i) - (x * a))
	elif b <= 1.65e-227:
		tmp = y * (z * (x - (i * (j / z))))
	elif b <= 1.9e-101:
		tmp = a * (x * (((c * j) / x) - t))
	elif b <= 4.5e+74:
		tmp = y * (x * (z - ((t * a) / y)))
	elif b <= 1.95e+183:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = b * t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * i) - Float64(z * c))
	tmp = 0.0
	if (b <= -5.5e+111)
		tmp = Float64(Float64(y * b) * Float64(t_1 / y));
	elseif (b <= -2.1e-45)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (b <= 1.65e-227)
		tmp = Float64(y * Float64(z * Float64(x - Float64(i * Float64(j / z)))));
	elseif (b <= 1.9e-101)
		tmp = Float64(a * Float64(x * Float64(Float64(Float64(c * j) / x) - t)));
	elseif (b <= 4.5e+74)
		tmp = Float64(y * Float64(x * Float64(z - Float64(Float64(t * a) / y))));
	elseif (b <= 1.95e+183)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = Float64(b * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * i) - (z * c);
	tmp = 0.0;
	if (b <= -5.5e+111)
		tmp = (y * b) * (t_1 / y);
	elseif (b <= -2.1e-45)
		tmp = t * ((b * i) - (x * a));
	elseif (b <= 1.65e-227)
		tmp = y * (z * (x - (i * (j / z))));
	elseif (b <= 1.9e-101)
		tmp = a * (x * (((c * j) / x) - t));
	elseif (b <= 4.5e+74)
		tmp = y * (x * (z - ((t * a) / y)));
	elseif (b <= 1.95e+183)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = b * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e+111], N[(N[(y * b), $MachinePrecision] * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.1e-45], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.65e-227], N[(y * N[(z * N[(x - N[(i * N[(j / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e-101], N[(a * N[(x * N[(N[(N[(c * j), $MachinePrecision] / x), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+74], N[(y * N[(x * N[(z - N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.95e+183], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * t$95$1), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -5.4999999999999998e111

   1. Initial program 70.1%

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

   3. Taylor expanded in y around -inf

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

   5. Simplified 64.0%

      \[\leadsto \color{blue}{\left(\left(j \cdot i - z \cdot x\right) + \frac{a \cdot \left(t \cdot x - j \cdot c\right) + b \cdot \left(c \cdot z - i \cdot t\right)}{y}\right) \cdot \left(0 - y\right)} \]

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \left(y \cdot \left(\frac{c \cdot z}{y} - \frac{i \cdot t}{y}\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{neg}\left(\left(b \cdot y\right) \cdot \left(\frac{c \cdot z}{y} - \frac{i \cdot t}{y}\right)\right) \]

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. div-sub N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot y\right), \color{blue}{\left(-1 \cdot \frac{c \cdot z - i \cdot t}{y}\right)}\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot b\right), \left(\color{blue}{-1} \cdot \frac{c \cdot z - i \cdot t}{y}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(\color{blue}{-1} \cdot \frac{c \cdot z - i \cdot t}{y}\right)\right) \]

      9. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(-1 \cdot \left(\frac{c \cdot z}{y} - \color{blue}{\frac{i \cdot t}{y}}\right)\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(\mathsf{neg}\left(\left(\frac{c \cdot z}{y} - \frac{i \cdot t}{y}\right)\right)\right)\right) \]

      11. div-sub N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(\mathsf{neg}\left(\frac{c \cdot z - i \cdot t}{y}\right)\right)\right) \]

      12. distribute-neg-frac2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(\frac{c \cdot z - i \cdot t}{\color{blue}{\mathsf{neg}\left(y\right)}}\right)\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(\frac{c \cdot z - i \cdot t}{-1 \cdot \color{blue}{y}}\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{/.f64}\left(\left(c \cdot z - i \cdot t\right), \color{blue}{\left(-1 \cdot y\right)}\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(c \cdot z\right), \left(i \cdot t\right)\right), \left(\color{blue}{-1} \cdot y\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \left(i \cdot t\right)\right), \left(-1 \cdot y\right)\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \left(t \cdot i\right)\right), \left(-1 \cdot y\right)\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right), \left(-1 \cdot y\right)\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right), \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      20. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right), \left(0 - \color{blue}{y}\right)\right)\right) \]

      21. --lowering--.f64 73.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, z\right), \mathsf{*.f64}\left(t, i\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 73.9%

      \[\leadsto \color{blue}{\left(y \cdot b\right) \cdot \frac{c \cdot z - t \cdot i}{0 - y}} \]

   if -5.4999999999999998e111 < b < -2.09999999999999995e-45

   1. Initial program 81.6%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + 1 \cdot \left(\color{blue}{b} \cdot i\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + b \cdot \color{blue}{i}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \color{blue}{-1 \cdot \left(a \cdot x\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i - \color{blue}{a \cdot x}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot i\right), \color{blue}{\left(a \cdot x\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      11. *-lowering-*.f64 60.7%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \mathsf{*.f64}\left(a, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 60.7%

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

   if -2.09999999999999995e-45 < b < 1.65e-227

   1. Initial program 74.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 75.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 75.9%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\left(x \cdot y - b \cdot c\right) + \frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} + \color{blue}{\left(x \cdot y - b \cdot c\right)}\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} + x \cdot y\right) - \color{blue}{b \cdot c}\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(x \cdot y + \frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right) - \color{blue}{b} \cdot c\right)\right) \]

      8. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot y + \color{blue}{\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} - b \cdot c\right)}\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} - b \cdot c\right)}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot x\right), \left(\color{blue}{\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}} - b \cdot c\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}} - b \cdot c\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{\_.f64}\left(\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right), \color{blue}{\left(b \cdot c\right)}\right)\right)\right) \]

   8. Simplified 71.6%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(z \cdot \left(x + -1 \cdot \frac{i \cdot j}{z}\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(x + -1 \cdot \frac{i \cdot j}{z}\right)}\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(x + \left(\mathsf{neg}\left(\frac{i \cdot j}{z}\right)\right)\right)\right)\right) \]

       4. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \left(x - \color{blue}{\frac{i \cdot j}{z}}\right)\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{i \cdot j}{z}\right)}\right)\right)\right) \]

       6. associate-/l* N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \left(i \cdot \color{blue}{\frac{j}{z}}\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(i, \color{blue}{\left(\frac{j}{z}\right)}\right)\right)\right)\right) \]

       8. /-lowering-/.f64 69.8%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(i, \mathsf{/.f64}\left(j, \color{blue}{z}\right)\right)\right)\right)\right) \]

   11. Simplified 69.8%

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

   if 1.65e-227 < b < 1.90000000000000005e-101

   1. Initial program 64.1%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 68.6%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 68.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{c \cdot j}{x} - t\right)}\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{c \cdot j}{x}\right), \color{blue}{t}\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(c \cdot j\right), x\right), t\right)\right)\right) \]

      4. *-lowering-*.f64 72.4%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(c, j\right), x\right), t\right)\right)\right) \]

   8. Simplified 72.4%

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

   if 1.90000000000000005e-101 < b < 4.5e74

   1. Initial program 80.2%

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

   3. Taylor expanded in y around -inf

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

   5. Simplified 73.6%

      \[\leadsto \color{blue}{\left(\left(j \cdot i - z \cdot x\right) + \frac{a \cdot \left(t \cdot x - j \cdot c\right) + b \cdot \left(c \cdot z - i \cdot t\right)}{y}\right) \cdot \left(0 - y\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(x \cdot \left(\frac{a \cdot t}{y} - z\right)\right)}, \mathsf{\_.f64}\left(0, y\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{a \cdot t}{y} - z\right)\right), \mathsf{\_.f64}\left(\color{blue}{0}, y\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{a \cdot t}{y}\right), z\right)\right), \mathsf{\_.f64}\left(0, y\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(a \cdot t\right), y\right), z\right)\right), \mathsf{\_.f64}\left(0, y\right)\right) \]

      4. *-lowering-*.f64 67.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), y\right), z\right)\right), \mathsf{\_.f64}\left(0, y\right)\right) \]

   8. Simplified 67.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(\frac{a \cdot t}{y} - z\right)\right)} \cdot \left(0 - y\right) \]

   if 4.5e74 < b < 1.9499999999999999e183

   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 i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot t\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(-1 \cdot \left(j \cdot y\right) + 1 \cdot \left(\color{blue}{b} \cdot t\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(-1 \cdot \left(j \cdot y\right) + b \cdot \color{blue}{t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t + \left(\mathsf{neg}\left(j \cdot y\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t - \color{blue}{j \cdot y}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(b \cdot t\right), \color{blue}{\left(j \cdot y\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, t\right), \left(\color{blue}{j} \cdot y\right)\right)\right) \]

      10. *-lowering-*.f64 68.7%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, t\right), \mathsf{*.f64}\left(j, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 68.7%

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

   if 1.9499999999999999e183 < b

   1. Initial program 67.9%

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

   3. Taylor expanded in b around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

         \[\leadsto b \cdot \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(c \cdot z + \left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(\mathsf{neg}\left(\left(c \cdot z - i \cdot t\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(\mathsf{neg}\left(\left(c \cdot z + \left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)}\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + i \cdot \color{blue}{t}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(i \cdot t + \color{blue}{\left(\mathsf{neg}\left(c \cdot z\right)\right)}\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(i \cdot t - \color{blue}{c \cdot z}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(i \cdot t\right), \color{blue}{\left(c \cdot z\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, t\right), \left(\color{blue}{c} \cdot z\right)\right)\right) \]

      16. *-lowering-*.f64 68.1%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, t\right), \mathsf{*.f64}\left(c, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 68.1%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+111}:\\ \;\;\;\;\left(y \cdot b\right) \cdot \frac{t \cdot i - z \cdot c}{y}\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-227}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-101}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{c \cdot j}{x} - t\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+183}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6000000000000:\\ \;\;\;\;c \cdot \left(a \cdot j + \left(\frac{y \cdot \left(x \cdot z - i \cdot j\right)}{c} - z \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-69}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(t \cdot b - y \cdot j\right)\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -6000000000000.0)
   (* c (+ (* a j) (- (/ (* y (- (* x z) (* i j))) c) (* z b))))
   (if (<= y 1.85e-69)
     (+
      (+ (* x (- (* y z) (* t a))) (* i (- (* t b) (* y j))))
      (* c (- (* a j) (* z b))))
     (+ (* j (- (* a c) (* y i))) (* z (- (* x y) (* b c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -6000000000000.0) {
		tmp = c * ((a * j) + (((y * ((x * z) - (i * j))) / c) - (z * b)));
	} else if (y <= 1.85e-69) {
		tmp = ((x * ((y * z) - (t * a))) + (i * ((t * b) - (y * j)))) + (c * ((a * j) - (z * b)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-6000000000000.0d0)) then
        tmp = c * ((a * j) + (((y * ((x * z) - (i * j))) / c) - (z * b)))
    else if (y <= 1.85d-69) then
        tmp = ((x * ((y * z) - (t * a))) + (i * ((t * b) - (y * j)))) + (c * ((a * j) - (z * b)))
    else
        tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -6000000000000.0) {
		tmp = c * ((a * j) + (((y * ((x * z) - (i * j))) / c) - (z * b)));
	} else if (y <= 1.85e-69) {
		tmp = ((x * ((y * z) - (t * a))) + (i * ((t * b) - (y * j)))) + (c * ((a * j) - (z * b)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -6000000000000.0:
		tmp = c * ((a * j) + (((y * ((x * z) - (i * j))) / c) - (z * b)))
	elif y <= 1.85e-69:
		tmp = ((x * ((y * z) - (t * a))) + (i * ((t * b) - (y * j)))) + (c * ((a * j) - (z * b)))
	else:
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -6000000000000.0)
		tmp = Float64(c * Float64(Float64(a * j) + Float64(Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) / c) - Float64(z * b))));
	elseif (y <= 1.85e-69)
		tmp = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(i * Float64(Float64(t * b) - Float64(y * j)))) + Float64(c * Float64(Float64(a * j) - Float64(z * b))));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -6000000000000.0)
		tmp = c * ((a * j) + (((y * ((x * z) - (i * j))) / c) - (z * b)));
	elseif (y <= 1.85e-69)
		tmp = ((x * ((y * z) - (t * a))) + (i * ((t * b) - (y * j)))) + (c * ((a * j) - (z * b)));
	else
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -6000000000000.0], N[(c * N[(N[(a * j), $MachinePrecision] + N[(N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e-69], N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6e12

   1. Initial program 62.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 59.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 59.8%

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

   6. Taylor expanded in c around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(-1 \cdot \left(-1 \cdot \left(a \cdot j\right) + \left(-1 \cdot \frac{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)}{c} + b \cdot z\right)\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(-1, \color{blue}{\left(-1 \cdot \left(a \cdot j\right) + \left(-1 \cdot \frac{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)}{c} + b \cdot z\right)\right)}\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(-1, \left(\left(-1 \cdot \frac{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)}{c} + b \cdot z\right) + \color{blue}{-1 \cdot \left(a \cdot j\right)}\right)\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(-1, \left(\left(-1 \cdot \frac{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)}{c} + b \cdot z\right) + \left(\mathsf{neg}\left(a \cdot j\right)\right)\right)\right)\right) \]

      8. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(-1, \left(\left(-1 \cdot \frac{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)}{c} + b \cdot z\right) - \color{blue}{a \cdot j}\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(-1 \cdot \frac{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)}{c} + b \cdot z\right), \color{blue}{\left(a \cdot j\right)}\right)\right)\right) \]

   8. Simplified 77.8%

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

   if -6e12 < y < 1.8500000000000001e-69

   1. Initial program 85.3%

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

   3. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*r* N/A

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

      11. distribute-rgt-in N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

   5. Simplified 85.9%

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

   if 1.8500000000000001e-69 < y

   1. Initial program 66.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 73.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 73.2%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6000000000000:\\ \;\;\;\;c \cdot \left(a \cdot j + \left(\frac{y \cdot \left(x \cdot z - i \cdot j\right)}{c} - z \cdot b\right)\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-69}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(t \cdot b - y \cdot j\right)\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-73}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z - \frac{b \cdot \left(z \cdot c\right)}{y}\right) - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.6e+121)
   (* y (- (* x z) (* i j)))
   (if (<= y -9.6e-73)
     (- (* z (- (* x y) (* b c))) (* i (* y j)))
     (if (<= y 7e-71)
       (* t (- (* b i) (* x a)))
       (if (<= y 1.65e+17)
         (- (* j (- (* a c) (* y i))) (* a (* x t)))
         (* y (- (- (* x z) (/ (* b (* z c)) y)) (* i j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.6e+121) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -9.6e-73) {
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j));
	} else if (y <= 7e-71) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 1.65e+17) {
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t));
	} else {
		tmp = y * (((x * z) - ((b * (z * c)) / y)) - (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.6d+121)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= (-9.6d-73)) then
        tmp = (z * ((x * y) - (b * c))) - (i * (y * j))
    else if (y <= 7d-71) then
        tmp = t * ((b * i) - (x * a))
    else if (y <= 1.65d+17) then
        tmp = (j * ((a * c) - (y * i))) - (a * (x * t))
    else
        tmp = y * (((x * z) - ((b * (z * c)) / y)) - (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.6e+121) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -9.6e-73) {
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j));
	} else if (y <= 7e-71) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 1.65e+17) {
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t));
	} else {
		tmp = y * (((x * z) - ((b * (z * c)) / y)) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.6e+121:
		tmp = y * ((x * z) - (i * j))
	elif y <= -9.6e-73:
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j))
	elif y <= 7e-71:
		tmp = t * ((b * i) - (x * a))
	elif y <= 1.65e+17:
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t))
	else:
		tmp = y * (((x * z) - ((b * (z * c)) / y)) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.6e+121)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= -9.6e-73)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(i * Float64(y * j)));
	elseif (y <= 7e-71)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (y <= 1.65e+17)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(a * Float64(x * t)));
	else
		tmp = Float64(y * Float64(Float64(Float64(x * z) - Float64(Float64(b * Float64(z * c)) / y)) - Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.6e+121)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= -9.6e-73)
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j));
	elseif (y <= 7e-71)
		tmp = t * ((b * i) - (x * a));
	elseif (y <= 1.65e+17)
		tmp = (j * ((a * c) - (y * i))) - (a * (x * t));
	else
		tmp = y * (((x * z) - ((b * (z * c)) / y)) - (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.6e+121], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.6e-73], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-71], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+17], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(N[(x * z), $MachinePrecision] - N[(N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.6e121

   1. Initial program 57.7%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot z + \color{blue}{-1 \cdot \left(i \cdot j\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot z + \left(\mathsf{neg}\left(i \cdot j\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot z - \color{blue}{i \cdot j}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(x \cdot z\right), \color{blue}{\left(i \cdot j\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(z \cdot x\right), \left(\color{blue}{i} \cdot j\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(\color{blue}{i} \cdot j\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(j \cdot \color{blue}{i}\right)\right)\right) \]

      9. *-lowering-*.f64 85.5%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, x\right), \mathsf{*.f64}\left(j, \color{blue}{i}\right)\right)\right) \]

   5. Simplified 85.5%

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

   if -1.6e121 < y < -9.60000000000000022e-73

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 69.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 69.8%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(z \cdot \left(x \cdot y - b \cdot c\right)\right), \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \left(\color{blue}{i} \cdot \left(j \cdot y\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \mathsf{*.f64}\left(i, \color{blue}{\left(j \cdot y\right)}\right)\right) \]

      11. *-lowering-*.f64 65.4%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 65.4%

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

   if -9.60000000000000022e-73 < y < 6.9999999999999998e-71

   1. Initial program 85.8%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + 1 \cdot \left(\color{blue}{b} \cdot i\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + b \cdot \color{blue}{i}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \color{blue}{-1 \cdot \left(a \cdot x\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i - \color{blue}{a \cdot x}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot i\right), \color{blue}{\left(a \cdot x\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      11. *-lowering-*.f64 58.3%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \mathsf{*.f64}\left(a, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 58.3%

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

   if 6.9999999999999998e-71 < y < 1.65e17

   1. Initial program 85.7%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(a \cdot \left(t \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(0 - a \cdot \left(t \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot \left(t \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, \left(t \cdot x\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(t, x\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0 - a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   if 1.65e17 < y

   1. Initial program 63.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 70.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 70.7%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(z \cdot \left(x \cdot y - b \cdot c\right)\right), \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \left(\color{blue}{i} \cdot \left(j \cdot y\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \mathsf{*.f64}\left(i, \color{blue}{\left(j \cdot y\right)}\right)\right) \]

      11. *-lowering-*.f64 58.6%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 58.6%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\left(-1 \cdot \frac{b \cdot \left(c \cdot z\right)}{y} + x \cdot z\right) - i \cdot j\right)}\right) \]

       2. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \frac{b \cdot \left(c \cdot z\right)}{y} + x \cdot z\right), \color{blue}{\left(i \cdot j\right)}\right)\right) \]

       3. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(x \cdot z + -1 \cdot \frac{b \cdot \left(c \cdot z\right)}{y}\right), \left(\color{blue}{i} \cdot j\right)\right)\right) \]

       4. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(x \cdot z + \left(\mathsf{neg}\left(\frac{b \cdot \left(c \cdot z\right)}{y}\right)\right)\right), \left(i \cdot j\right)\right)\right) \]

       5. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(x \cdot z - \frac{b \cdot \left(c \cdot z\right)}{y}\right), \left(\color{blue}{i} \cdot j\right)\right)\right) \]

       6. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot z\right), \left(\frac{b \cdot \left(c \cdot z\right)}{y}\right)\right), \left(\color{blue}{i} \cdot j\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, z\right), \left(\frac{b \cdot \left(c \cdot z\right)}{y}\right)\right), \left(i \cdot j\right)\right)\right) \]

       8. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{/.f64}\left(\left(b \cdot \left(c \cdot z\right)\right), y\right)\right), \left(i \cdot j\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \left(c \cdot z\right)\right), y\right)\right), \left(i \cdot j\right)\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(c, z\right)\right), y\right)\right), \left(i \cdot j\right)\right)\right) \]

       11. *-lowering-*.f64 68.0%

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(c, z\right)\right), y\right)\right), \mathsf{*.f64}\left(i, \color{blue}{j}\right)\right)\right) \]

   11. Simplified 68.0%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-73}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z - \frac{b \cdot \left(z \cdot c\right)}{y}\right) - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z - \frac{b \cdot \left(z \cdot c\right)}{y}\right) - i \cdot j\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-84}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -2.8e+94)
   (* y (* x (- z (/ (* t a) y))))
   (if (<= x -5.4e-18)
     (* y (- (- (* x z) (/ (* b (* z c)) y)) (* i j)))
     (if (<= x 2.4e-84)
       (+ (* j (- (* a c) (* y i))) (* t (* b i)))
       (if (<= x 2.25e+52)
         (- (* z (- (* x y) (* b c))) (* y (* i j)))
         (* x (- (* y z) (* t a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -2.8e+94) {
		tmp = y * (x * (z - ((t * a) / y)));
	} else if (x <= -5.4e-18) {
		tmp = y * (((x * z) - ((b * (z * c)) / y)) - (i * j));
	} else if (x <= 2.4e-84) {
		tmp = (j * ((a * c) - (y * i))) + (t * (b * i));
	} else if (x <= 2.25e+52) {
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-2.8d+94)) then
        tmp = y * (x * (z - ((t * a) / y)))
    else if (x <= (-5.4d-18)) then
        tmp = y * (((x * z) - ((b * (z * c)) / y)) - (i * j))
    else if (x <= 2.4d-84) then
        tmp = (j * ((a * c) - (y * i))) + (t * (b * i))
    else if (x <= 2.25d+52) then
        tmp = (z * ((x * y) - (b * c))) - (y * (i * j))
    else
        tmp = x * ((y * z) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -2.8e+94) {
		tmp = y * (x * (z - ((t * a) / y)));
	} else if (x <= -5.4e-18) {
		tmp = y * (((x * z) - ((b * (z * c)) / y)) - (i * j));
	} else if (x <= 2.4e-84) {
		tmp = (j * ((a * c) - (y * i))) + (t * (b * i));
	} else if (x <= 2.25e+52) {
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -2.8e+94:
		tmp = y * (x * (z - ((t * a) / y)))
	elif x <= -5.4e-18:
		tmp = y * (((x * z) - ((b * (z * c)) / y)) - (i * j))
	elif x <= 2.4e-84:
		tmp = (j * ((a * c) - (y * i))) + (t * (b * i))
	elif x <= 2.25e+52:
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j))
	else:
		tmp = x * ((y * z) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -2.8e+94)
		tmp = Float64(y * Float64(x * Float64(z - Float64(Float64(t * a) / y))));
	elseif (x <= -5.4e-18)
		tmp = Float64(y * Float64(Float64(Float64(x * z) - Float64(Float64(b * Float64(z * c)) / y)) - Float64(i * j)));
	elseif (x <= 2.4e-84)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(t * Float64(b * i)));
	elseif (x <= 2.25e+52)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(y * Float64(i * j)));
	else
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -2.8e+94)
		tmp = y * (x * (z - ((t * a) / y)));
	elseif (x <= -5.4e-18)
		tmp = y * (((x * z) - ((b * (z * c)) / y)) - (i * j));
	elseif (x <= 2.4e-84)
		tmp = (j * ((a * c) - (y * i))) + (t * (b * i));
	elseif (x <= 2.25e+52)
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j));
	else
		tmp = x * ((y * z) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -2.8e+94], N[(y * N[(x * N[(z - N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.4e-18], N[(y * N[(N[(N[(x * z), $MachinePrecision] - N[(N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e-84], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.25e+52], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.79999999999999998e94

   1. Initial program 67.3%

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

   3. Taylor expanded in y around -inf

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

   5. Simplified 63.8%

      \[\leadsto \color{blue}{\left(\left(j \cdot i - z \cdot x\right) + \frac{a \cdot \left(t \cdot x - j \cdot c\right) + b \cdot \left(c \cdot z - i \cdot t\right)}{y}\right) \cdot \left(0 - y\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(x \cdot \left(\frac{a \cdot t}{y} - z\right)\right)}, \mathsf{\_.f64}\left(0, y\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{a \cdot t}{y} - z\right)\right), \mathsf{\_.f64}\left(\color{blue}{0}, y\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{a \cdot t}{y}\right), z\right)\right), \mathsf{\_.f64}\left(0, y\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(a \cdot t\right), y\right), z\right)\right), \mathsf{\_.f64}\left(0, y\right)\right) \]

      4. *-lowering-*.f64 70.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), y\right), z\right)\right), \mathsf{\_.f64}\left(0, y\right)\right) \]

   8. Simplified 70.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(\frac{a \cdot t}{y} - z\right)\right)} \cdot \left(0 - y\right) \]

   if -2.79999999999999998e94 < x < -5.39999999999999977e-18

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 64.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 64.5%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(z \cdot \left(x \cdot y - b \cdot c\right)\right), \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \left(\color{blue}{i} \cdot \left(j \cdot y\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \mathsf{*.f64}\left(i, \color{blue}{\left(j \cdot y\right)}\right)\right) \]

      11. *-lowering-*.f64 53.2%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 53.2%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\left(-1 \cdot \frac{b \cdot \left(c \cdot z\right)}{y} + x \cdot z\right) - i \cdot j\right)}\right) \]

       2. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \frac{b \cdot \left(c \cdot z\right)}{y} + x \cdot z\right), \color{blue}{\left(i \cdot j\right)}\right)\right) \]

       3. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(x \cdot z + -1 \cdot \frac{b \cdot \left(c \cdot z\right)}{y}\right), \left(\color{blue}{i} \cdot j\right)\right)\right) \]

       4. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(x \cdot z + \left(\mathsf{neg}\left(\frac{b \cdot \left(c \cdot z\right)}{y}\right)\right)\right), \left(i \cdot j\right)\right)\right) \]

       5. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(x \cdot z - \frac{b \cdot \left(c \cdot z\right)}{y}\right), \left(\color{blue}{i} \cdot j\right)\right)\right) \]

       6. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot z\right), \left(\frac{b \cdot \left(c \cdot z\right)}{y}\right)\right), \left(\color{blue}{i} \cdot j\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, z\right), \left(\frac{b \cdot \left(c \cdot z\right)}{y}\right)\right), \left(i \cdot j\right)\right)\right) \]

       8. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{/.f64}\left(\left(b \cdot \left(c \cdot z\right)\right), y\right)\right), \left(i \cdot j\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \left(c \cdot z\right)\right), y\right)\right), \left(i \cdot j\right)\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(c, z\right)\right), y\right)\right), \left(i \cdot j\right)\right)\right) \]

       11. *-lowering-*.f64 60.8%

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(c, z\right)\right), y\right)\right), \mathsf{*.f64}\left(i, \color{blue}{j}\right)\right)\right) \]

   11. Simplified 60.8%

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

   if -5.39999999999999977e-18 < x < 2.40000000000000017e-84

   1. Initial program 67.1%

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

   3. Taylor expanded in i around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(b \cdot \left(i \cdot t\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(b \cdot i\right) \cdot t\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(b \cdot i\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot i\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(i \cdot b\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-lowering-*.f64 70.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, b\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 70.9%

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

   if 2.40000000000000017e-84 < x < 2.25e52

   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 z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 73.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 73.0%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(z \cdot \left(x \cdot y - b \cdot c\right)\right), \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \left(\color{blue}{i} \cdot \left(j \cdot y\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \mathsf{*.f64}\left(i, \color{blue}{\left(j \cdot y\right)}\right)\right) \]

      11. *-lowering-*.f64 70.0%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 70.0%

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

      1. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \left(\left(i \cdot j\right) \cdot \color{blue}{y}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \left(\left(j \cdot i\right) \cdot y\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \mathsf{*.f64}\left(\left(j \cdot i\right), \color{blue}{y}\right)\right) \]

      4. *-lowering-*.f64 70.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, i\right), y\right)\right) \]

   10. Applied egg-rr 70.1%

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

   if 2.25e52 < x

   1. Initial program 74.1%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z - a \cdot t\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(y \cdot z\right), \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 63.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 63.3%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z - \frac{b \cdot \left(z \cdot c\right)}{y}\right) - i \cdot j\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-84}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -5.5 \cdot 10^{+132}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -6.6 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-251}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 520000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -5.5e+132)
     t_2
     (if (<= i -6.6e+44)
       (* j (- (* a c) (* y i)))
       (if (<= i -2.6e-71)
         t_1
         (if (<= i 2.7e-251)
           (* c (- (* a j) (* z b)))
           (if (<= i 520000000000.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -5.5e+132) {
		tmp = t_2;
	} else if (i <= -6.6e+44) {
		tmp = j * ((a * c) - (y * i));
	} else if (i <= -2.6e-71) {
		tmp = t_1;
	} else if (i <= 2.7e-251) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 520000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-5.5d+132)) then
        tmp = t_2
    else if (i <= (-6.6d+44)) then
        tmp = j * ((a * c) - (y * i))
    else if (i <= (-2.6d-71)) then
        tmp = t_1
    else if (i <= 2.7d-251) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 520000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -5.5e+132) {
		tmp = t_2;
	} else if (i <= -6.6e+44) {
		tmp = j * ((a * c) - (y * i));
	} else if (i <= -2.6e-71) {
		tmp = t_1;
	} else if (i <= 2.7e-251) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 520000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -5.5e+132:
		tmp = t_2
	elif i <= -6.6e+44:
		tmp = j * ((a * c) - (y * i))
	elif i <= -2.6e-71:
		tmp = t_1
	elif i <= 2.7e-251:
		tmp = c * ((a * j) - (z * b))
	elif i <= 520000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -5.5e+132)
		tmp = t_2;
	elseif (i <= -6.6e+44)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (i <= -2.6e-71)
		tmp = t_1;
	elseif (i <= 2.7e-251)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 520000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -5.5e+132)
		tmp = t_2;
	elseif (i <= -6.6e+44)
		tmp = j * ((a * c) - (y * i));
	elseif (i <= -2.6e-71)
		tmp = t_1;
	elseif (i <= 2.7e-251)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 520000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.5e+132], t$95$2, If[LessEqual[i, -6.6e+44], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.6e-71], t$95$1, If[LessEqual[i, 2.7e-251], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 520000000000.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -5.5e132 or 5.2e11 < i

   1. Initial program 67.0%

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

   3. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot t\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(-1 \cdot \left(j \cdot y\right) + 1 \cdot \left(\color{blue}{b} \cdot t\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(-1 \cdot \left(j \cdot y\right) + b \cdot \color{blue}{t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t + \left(\mathsf{neg}\left(j \cdot y\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t - \color{blue}{j \cdot y}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(b \cdot t\right), \color{blue}{\left(j \cdot y\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, t\right), \left(\color{blue}{j} \cdot y\right)\right)\right) \]

      10. *-lowering-*.f64 69.0%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, t\right), \mathsf{*.f64}\left(j, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 69.0%

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

   if -5.5e132 < i < -6.60000000000000027e44

   1. Initial program 71.8%

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

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 69.0%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 69.0%

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

   if -6.60000000000000027e44 < i < -2.5999999999999999e-71 or 2.7000000000000001e-251 < i < 5.2e11

   1. Initial program 84.7%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z - a \cdot t\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(y \cdot z\right), \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 59.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 59.8%

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

   if -2.5999999999999999e-71 < i < 2.7000000000000001e-251

   1. Initial program 71.8%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(a \cdot j - b \cdot z\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(a \cdot j\right), \color{blue}{\left(b \cdot z\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(j \cdot a\right), \left(\color{blue}{b} \cdot z\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \left(\color{blue}{b} \cdot z\right)\right)\right) \]

      5. *-lowering-*.f64 60.7%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 60.7%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.5 \cdot 10^{+132}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -6.6 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-251}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 520000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-86}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -5.2e-18)
   (* y (* x (- z (/ (* t a) y))))
   (if (<= x 2e-86)
     (+ (* j (- (* a c) (* y i))) (* t (* b i)))
     (if (<= x 1.4e+54)
       (- (* z (- (* x y) (* b c))) (* y (* i j)))
       (* x (- (* y z) (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -5.2e-18) {
		tmp = y * (x * (z - ((t * a) / y)));
	} else if (x <= 2e-86) {
		tmp = (j * ((a * c) - (y * i))) + (t * (b * i));
	} else if (x <= 1.4e+54) {
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-5.2d-18)) then
        tmp = y * (x * (z - ((t * a) / y)))
    else if (x <= 2d-86) then
        tmp = (j * ((a * c) - (y * i))) + (t * (b * i))
    else if (x <= 1.4d+54) then
        tmp = (z * ((x * y) - (b * c))) - (y * (i * j))
    else
        tmp = x * ((y * z) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -5.2e-18) {
		tmp = y * (x * (z - ((t * a) / y)));
	} else if (x <= 2e-86) {
		tmp = (j * ((a * c) - (y * i))) + (t * (b * i));
	} else if (x <= 1.4e+54) {
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -5.2e-18:
		tmp = y * (x * (z - ((t * a) / y)))
	elif x <= 2e-86:
		tmp = (j * ((a * c) - (y * i))) + (t * (b * i))
	elif x <= 1.4e+54:
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j))
	else:
		tmp = x * ((y * z) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -5.2e-18)
		tmp = Float64(y * Float64(x * Float64(z - Float64(Float64(t * a) / y))));
	elseif (x <= 2e-86)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(t * Float64(b * i)));
	elseif (x <= 1.4e+54)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(y * Float64(i * j)));
	else
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -5.2e-18)
		tmp = y * (x * (z - ((t * a) / y)));
	elseif (x <= 2e-86)
		tmp = (j * ((a * c) - (y * i))) + (t * (b * i));
	elseif (x <= 1.4e+54)
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j));
	else
		tmp = x * ((y * z) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -5.2e-18], N[(y * N[(x * N[(z - N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e-86], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e+54], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.2000000000000001e-18

   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 y around -inf

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

   5. Simplified 68.6%

      \[\leadsto \color{blue}{\left(\left(j \cdot i - z \cdot x\right) + \frac{a \cdot \left(t \cdot x - j \cdot c\right) + b \cdot \left(c \cdot z - i \cdot t\right)}{y}\right) \cdot \left(0 - y\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(x \cdot \left(\frac{a \cdot t}{y} - z\right)\right)}, \mathsf{\_.f64}\left(0, y\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{a \cdot t}{y} - z\right)\right), \mathsf{\_.f64}\left(\color{blue}{0}, y\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{a \cdot t}{y}\right), z\right)\right), \mathsf{\_.f64}\left(0, y\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(a \cdot t\right), y\right), z\right)\right), \mathsf{\_.f64}\left(0, y\right)\right) \]

      4. *-lowering-*.f64 61.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), y\right), z\right)\right), \mathsf{\_.f64}\left(0, y\right)\right) \]

   8. Simplified 61.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(\frac{a \cdot t}{y} - z\right)\right)} \cdot \left(0 - y\right) \]

   if -5.2000000000000001e-18 < x < 2.00000000000000017e-86

   1. Initial program 67.1%

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

   3. Taylor expanded in i around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(b \cdot \left(i \cdot t\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(b \cdot i\right) \cdot t\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(b \cdot i\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot i\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(i \cdot b\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-lowering-*.f64 70.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, b\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 70.9%

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

   if 2.00000000000000017e-86 < x < 1.40000000000000008e54

   1. Initial program 87.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 70.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 70.9%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(z \cdot \left(x \cdot y - b \cdot c\right)\right), \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \left(\color{blue}{i} \cdot \left(j \cdot y\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \mathsf{*.f64}\left(i, \color{blue}{\left(j \cdot y\right)}\right)\right) \]

      11. *-lowering-*.f64 68.0%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 68.0%

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

      1. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \left(\left(i \cdot j\right) \cdot \color{blue}{y}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \left(\left(j \cdot i\right) \cdot y\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \mathsf{*.f64}\left(\left(j \cdot i\right), \color{blue}{y}\right)\right) \]

      4. *-lowering-*.f64 68.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, i\right), y\right)\right) \]

   10. Applied egg-rr 68.0%

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

   if 1.40000000000000008e54 < x

   1. Initial program 73.7%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z - a \cdot t\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(y \cdot z\right), \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 64.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 64.4%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-86}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-84}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -3.1e-19)
   (* y (* x (- z (/ (* t a) y))))
   (if (<= x 3.6e-84)
     (+ (* j (- (* a c) (* y i))) (* t (* b i)))
     (if (<= x 2.5e+55)
       (- (* z (- (* x y) (* b c))) (* i (* y j)))
       (* x (- (* y z) (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -3.1e-19) {
		tmp = y * (x * (z - ((t * a) / y)));
	} else if (x <= 3.6e-84) {
		tmp = (j * ((a * c) - (y * i))) + (t * (b * i));
	} else if (x <= 2.5e+55) {
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-3.1d-19)) then
        tmp = y * (x * (z - ((t * a) / y)))
    else if (x <= 3.6d-84) then
        tmp = (j * ((a * c) - (y * i))) + (t * (b * i))
    else if (x <= 2.5d+55) then
        tmp = (z * ((x * y) - (b * c))) - (i * (y * j))
    else
        tmp = x * ((y * z) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -3.1e-19) {
		tmp = y * (x * (z - ((t * a) / y)));
	} else if (x <= 3.6e-84) {
		tmp = (j * ((a * c) - (y * i))) + (t * (b * i));
	} else if (x <= 2.5e+55) {
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -3.1e-19:
		tmp = y * (x * (z - ((t * a) / y)))
	elif x <= 3.6e-84:
		tmp = (j * ((a * c) - (y * i))) + (t * (b * i))
	elif x <= 2.5e+55:
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j))
	else:
		tmp = x * ((y * z) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -3.1e-19)
		tmp = Float64(y * Float64(x * Float64(z - Float64(Float64(t * a) / y))));
	elseif (x <= 3.6e-84)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(t * Float64(b * i)));
	elseif (x <= 2.5e+55)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(i * Float64(y * j)));
	else
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -3.1e-19)
		tmp = y * (x * (z - ((t * a) / y)));
	elseif (x <= 3.6e-84)
		tmp = (j * ((a * c) - (y * i))) + (t * (b * i));
	elseif (x <= 2.5e+55)
		tmp = (z * ((x * y) - (b * c))) - (i * (y * j));
	else
		tmp = x * ((y * z) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -3.1e-19], N[(y * N[(x * N[(z - N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e-84], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e+55], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.0999999999999999e-19

   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 y around -inf

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

   5. Simplified 68.6%

      \[\leadsto \color{blue}{\left(\left(j \cdot i - z \cdot x\right) + \frac{a \cdot \left(t \cdot x - j \cdot c\right) + b \cdot \left(c \cdot z - i \cdot t\right)}{y}\right) \cdot \left(0 - y\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(x \cdot \left(\frac{a \cdot t}{y} - z\right)\right)}, \mathsf{\_.f64}\left(0, y\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{a \cdot t}{y} - z\right)\right), \mathsf{\_.f64}\left(\color{blue}{0}, y\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{a \cdot t}{y}\right), z\right)\right), \mathsf{\_.f64}\left(0, y\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(a \cdot t\right), y\right), z\right)\right), \mathsf{\_.f64}\left(0, y\right)\right) \]

      4. *-lowering-*.f64 61.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), y\right), z\right)\right), \mathsf{\_.f64}\left(0, y\right)\right) \]

   8. Simplified 61.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(\frac{a \cdot t}{y} - z\right)\right)} \cdot \left(0 - y\right) \]

   if -3.0999999999999999e-19 < x < 3.60000000000000003e-84

   1. Initial program 67.1%

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

   3. Taylor expanded in i around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(b \cdot \left(i \cdot t\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(b \cdot i\right) \cdot t\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(b \cdot i\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot i\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(i \cdot b\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-lowering-*.f64 70.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, b\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 70.9%

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

   if 3.60000000000000003e-84 < x < 2.50000000000000023e55

   1. Initial program 87.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 70.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 70.9%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(z \cdot \left(x \cdot y - b \cdot c\right)\right), \color{blue}{\left(i \cdot \left(j \cdot y\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \left(\color{blue}{i} \cdot \left(j \cdot y\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \left(i \cdot \left(j \cdot y\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \mathsf{*.f64}\left(i, \color{blue}{\left(j \cdot y\right)}\right)\right) \]

      11. *-lowering-*.f64 68.0%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(b, c\right)\right)\right), \mathsf{*.f64}\left(i, \mathsf{*.f64}\left(j, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 68.0%

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

   if 2.50000000000000023e55 < x

   1. Initial program 73.7%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z - a \cdot t\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(y \cdot z\right), \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 64.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 64.4%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-84}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -8.5 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -4.3 \cdot 10^{+36}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq -4.3 \cdot 10^{-61}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+18}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -8.5e+132)
     t_1
     (if (<= i -4.3e+36)
       (* j (- (* a c) (* y i)))
       (if (<= i -4.3e-61)
         (* z (* x y))
         (if (<= i 4.2e+18) (* c (- (* a j) (* z b))) 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 <= -8.5e+132) {
		tmp = t_1;
	} else if (i <= -4.3e+36) {
		tmp = j * ((a * c) - (y * i));
	} else if (i <= -4.3e-61) {
		tmp = z * (x * y);
	} else if (i <= 4.2e+18) {
		tmp = c * ((a * j) - (z * b));
	} 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 <= (-8.5d+132)) then
        tmp = t_1
    else if (i <= (-4.3d+36)) then
        tmp = j * ((a * c) - (y * i))
    else if (i <= (-4.3d-61)) then
        tmp = z * (x * y)
    else if (i <= 4.2d+18) then
        tmp = c * ((a * j) - (z * b))
    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 <= -8.5e+132) {
		tmp = t_1;
	} else if (i <= -4.3e+36) {
		tmp = j * ((a * c) - (y * i));
	} else if (i <= -4.3e-61) {
		tmp = z * (x * y);
	} else if (i <= 4.2e+18) {
		tmp = c * ((a * j) - (z * b));
	} 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 <= -8.5e+132:
		tmp = t_1
	elif i <= -4.3e+36:
		tmp = j * ((a * c) - (y * i))
	elif i <= -4.3e-61:
		tmp = z * (x * y)
	elif i <= 4.2e+18:
		tmp = c * ((a * j) - (z * b))
	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 <= -8.5e+132)
		tmp = t_1;
	elseif (i <= -4.3e+36)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (i <= -4.3e-61)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 4.2e+18)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	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 <= -8.5e+132)
		tmp = t_1;
	elseif (i <= -4.3e+36)
		tmp = j * ((a * c) - (y * i));
	elseif (i <= -4.3e-61)
		tmp = z * (x * y);
	elseif (i <= 4.2e+18)
		tmp = c * ((a * j) - (z * b));
	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, -8.5e+132], t$95$1, If[LessEqual[i, -4.3e+36], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -4.3e-61], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.2e+18], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -8.49999999999999969e132 or 4.2e18 < i

   1. Initial program 67.0%

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

   3. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot t\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(-1 \cdot \left(j \cdot y\right) + 1 \cdot \left(\color{blue}{b} \cdot t\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(-1 \cdot \left(j \cdot y\right) + b \cdot \color{blue}{t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t + \left(\mathsf{neg}\left(j \cdot y\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t - \color{blue}{j \cdot y}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(b \cdot t\right), \color{blue}{\left(j \cdot y\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, t\right), \left(\color{blue}{j} \cdot y\right)\right)\right) \]

      10. *-lowering-*.f64 70.8%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, t\right), \mathsf{*.f64}\left(j, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 70.8%

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

   if -8.49999999999999969e132 < i < -4.30000000000000005e36

   1. Initial program 71.8%

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

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 69.0%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 69.0%

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

   if -4.30000000000000005e36 < i < -4.3000000000000003e-61

   1. Initial program 78.9%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y - b \cdot c\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 53.0%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 53.0%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(y \cdot \color{blue}{x}\right)\right) \]

      7. *-lowering-*.f64 43.6%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right) \]

   8. Simplified 43.6%

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

   if -4.3000000000000003e-61 < i < 4.2e18

   1. Initial program 78.9%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(a \cdot j - b \cdot z\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(a \cdot j\right), \color{blue}{\left(b \cdot z\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(j \cdot a\right), \left(\color{blue}{b} \cdot z\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \left(\color{blue}{b} \cdot z\right)\right)\right) \]

      5. *-lowering-*.f64 48.7%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 48.7%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.5 \cdot 10^{+132}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -4.3 \cdot 10^{+36}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq -4.3 \cdot 10^{-61}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+18}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.25 \cdot 10^{+168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.35 \cdot 10^{+21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -1.25e+168)
     t_1
     (if (<= i 2.35e+21)
       (+ (* j (- (* a c) (* y i))) (* z (- (* x y) (* b c))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.25e+168) {
		tmp = t_1;
	} else if (i <= 2.35e+21) {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-1.25d+168)) then
        tmp = t_1
    else if (i <= 2.35d+21) then
        tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.25e+168) {
		tmp = t_1;
	} else if (i <= 2.35e+21) {
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} 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 <= -1.25e+168:
		tmp = t_1
	elif i <= 2.35e+21:
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)))
	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 <= -1.25e+168)
		tmp = t_1;
	elseif (i <= 2.35e+21)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * 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 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.25e+168)
		tmp = t_1;
	elseif (i <= 2.35e+21)
		tmp = (j * ((a * c) - (y * i))) + (z * ((x * y) - (b * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.25e+168], t$95$1, If[LessEqual[i, 2.35e+21], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -1.24999999999999992e168 or 2.35e21 < i

   1. Initial program 65.3%

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

   3. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot t\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(-1 \cdot \left(j \cdot y\right) + 1 \cdot \left(\color{blue}{b} \cdot t\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(-1 \cdot \left(j \cdot y\right) + b \cdot \color{blue}{t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t + \left(\mathsf{neg}\left(j \cdot y\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t - \color{blue}{j \cdot y}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(b \cdot t\right), \color{blue}{\left(j \cdot y\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, t\right), \left(\color{blue}{j} \cdot y\right)\right)\right) \]

      10. *-lowering-*.f64 71.4%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, t\right), \mathsf{*.f64}\left(j, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 71.4%

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

   if -1.24999999999999992e168 < i < 2.35e21

   1. Initial program 78.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 70.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 70.3%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.25 \cdot 10^{+168}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 2.35 \cdot 10^{+21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-56}:\\ \;\;\;\;j \cdot \left(0 - y \cdot i\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-70}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 1550:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -7.4e+99)
   (* y (* x z))
   (if (<= y -7.2e-56)
     (* j (- 0.0 (* y i)))
     (if (<= y 8.8e-70)
       (* b (* t i))
       (if (<= y 1550.0) (* j (* a c)) (* z (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -7.4e+99) {
		tmp = y * (x * z);
	} else if (y <= -7.2e-56) {
		tmp = j * (0.0 - (y * i));
	} else if (y <= 8.8e-70) {
		tmp = b * (t * i);
	} else if (y <= 1550.0) {
		tmp = j * (a * c);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-7.4d+99)) then
        tmp = y * (x * z)
    else if (y <= (-7.2d-56)) then
        tmp = j * (0.0d0 - (y * i))
    else if (y <= 8.8d-70) then
        tmp = b * (t * i)
    else if (y <= 1550.0d0) then
        tmp = j * (a * c)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -7.4e+99) {
		tmp = y * (x * z);
	} else if (y <= -7.2e-56) {
		tmp = j * (0.0 - (y * i));
	} else if (y <= 8.8e-70) {
		tmp = b * (t * i);
	} else if (y <= 1550.0) {
		tmp = j * (a * c);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -7.4e+99:
		tmp = y * (x * z)
	elif y <= -7.2e-56:
		tmp = j * (0.0 - (y * i))
	elif y <= 8.8e-70:
		tmp = b * (t * i)
	elif y <= 1550.0:
		tmp = j * (a * c)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -7.4e+99)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= -7.2e-56)
		tmp = Float64(j * Float64(0.0 - Float64(y * i)));
	elseif (y <= 8.8e-70)
		tmp = Float64(b * Float64(t * i));
	elseif (y <= 1550.0)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -7.4e+99)
		tmp = y * (x * z);
	elseif (y <= -7.2e-56)
		tmp = j * (0.0 - (y * i));
	elseif (y <= 8.8e-70)
		tmp = b * (t * i);
	elseif (y <= 1550.0)
		tmp = j * (a * c);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -7.4e+99], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.2e-56], N[(j * N[(0.0 - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e-70], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1550.0], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.4000000000000002e99

   1. Initial program 57.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 51.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 51.0%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\left(x \cdot y - b \cdot c\right) + \frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} + \color{blue}{\left(x \cdot y - b \cdot c\right)}\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} + x \cdot y\right) - \color{blue}{b \cdot c}\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(x \cdot y + \frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right) - \color{blue}{b} \cdot c\right)\right) \]

      8. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot y + \color{blue}{\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} - b \cdot c\right)}\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} - b \cdot c\right)}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot x\right), \left(\color{blue}{\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}} - b \cdot c\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}} - b \cdot c\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{\_.f64}\left(\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right), \color{blue}{\left(b \cdot c\right)}\right)\right)\right) \]

   8. Simplified 52.9%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. associate-*r* N/A

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(z \cdot \color{blue}{x}\right)\right) \]

       6. *-lowering-*.f64 62.9%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{x}\right)\right) \]

   11. Simplified 62.9%

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

   if -7.4000000000000002e99 < y < -7.19999999999999956e-56

   1. Initial program 76.0%

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

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 56.2%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 56.2%

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

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(-1 \cdot \left(i \cdot y\right)\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(\mathsf{neg}\left(i \cdot y\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(i \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(i \cdot \left(-1 \cdot \color{blue}{y}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, \color{blue}{\left(-1 \cdot y\right)}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, \left(0 - \color{blue}{y}\right)\right)\right) \]

      7. --lowering--.f64 40.9%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(0, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 40.9%

      \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(0 - y\right)\right)} \]

   if -7.19999999999999956e-56 < y < 8.7999999999999996e-70

   1. Initial program 86.2%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + 1 \cdot \left(\color{blue}{b} \cdot i\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + b \cdot \color{blue}{i}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \color{blue}{-1 \cdot \left(a \cdot x\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i - \color{blue}{a \cdot x}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot i\right), \color{blue}{\left(a \cdot x\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      11. *-lowering-*.f64 57.6%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \mathsf{*.f64}\left(a, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 57.6%

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

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t \cdot \color{blue}{i}\right)\right) \]

      3. *-lowering-*.f64 36.4%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(t, \color{blue}{i}\right)\right) \]

   8. Simplified 36.4%

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

   if 8.7999999999999996e-70 < y < 1550

   1. Initial program 80.0%

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

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 80.5%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 80.5%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(c \cdot \color{blue}{a}\right)\right) \]

      2. *-lowering-*.f64 70.5%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(c, \color{blue}{a}\right)\right) \]

   8. Simplified 70.5%

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

   if 1550 < y

   1. Initial program 65.1%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y - b \cdot c\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 47.4%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 47.4%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(y \cdot \color{blue}{x}\right)\right) \]

      7. *-lowering-*.f64 41.6%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right) \]

   8. Simplified 41.6%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-56}:\\ \;\;\;\;j \cdot \left(0 - y \cdot i\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-70}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 1550:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-56}:\\ \;\;\;\;i \cdot \left(0 - y \cdot j\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-73}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 0.7:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -9e+99)
   (* y (* x z))
   (if (<= y -2.8e-56)
     (* i (- 0.0 (* y j)))
     (if (<= y 6e-73)
       (* b (* t i))
       (if (<= y 0.7) (* j (* a c)) (* z (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -9e+99) {
		tmp = y * (x * z);
	} else if (y <= -2.8e-56) {
		tmp = i * (0.0 - (y * j));
	} else if (y <= 6e-73) {
		tmp = b * (t * i);
	} else if (y <= 0.7) {
		tmp = j * (a * c);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-9d+99)) then
        tmp = y * (x * z)
    else if (y <= (-2.8d-56)) then
        tmp = i * (0.0d0 - (y * j))
    else if (y <= 6d-73) then
        tmp = b * (t * i)
    else if (y <= 0.7d0) then
        tmp = j * (a * c)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -9e+99) {
		tmp = y * (x * z);
	} else if (y <= -2.8e-56) {
		tmp = i * (0.0 - (y * j));
	} else if (y <= 6e-73) {
		tmp = b * (t * i);
	} else if (y <= 0.7) {
		tmp = j * (a * c);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -9e+99:
		tmp = y * (x * z)
	elif y <= -2.8e-56:
		tmp = i * (0.0 - (y * j))
	elif y <= 6e-73:
		tmp = b * (t * i)
	elif y <= 0.7:
		tmp = j * (a * c)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -9e+99)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= -2.8e-56)
		tmp = Float64(i * Float64(0.0 - Float64(y * j)));
	elseif (y <= 6e-73)
		tmp = Float64(b * Float64(t * i));
	elseif (y <= 0.7)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -9e+99)
		tmp = y * (x * z);
	elseif (y <= -2.8e-56)
		tmp = i * (0.0 - (y * j));
	elseif (y <= 6e-73)
		tmp = b * (t * i);
	elseif (y <= 0.7)
		tmp = j * (a * c);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -9e+99], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e-56], N[(i * N[(0.0 - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-73], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.7], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.9999999999999999e99

   1. Initial program 57.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 51.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 51.0%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\left(x \cdot y - b \cdot c\right) + \frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} + \color{blue}{\left(x \cdot y - b \cdot c\right)}\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} + x \cdot y\right) - \color{blue}{b \cdot c}\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(x \cdot y + \frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right) - \color{blue}{b} \cdot c\right)\right) \]

      8. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot y + \color{blue}{\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} - b \cdot c\right)}\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} - b \cdot c\right)}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot x\right), \left(\color{blue}{\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}} - b \cdot c\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}} - b \cdot c\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{\_.f64}\left(\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right), \color{blue}{\left(b \cdot c\right)}\right)\right)\right) \]

   8. Simplified 52.9%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. associate-*r* N/A

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(z \cdot \color{blue}{x}\right)\right) \]

       6. *-lowering-*.f64 62.9%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{x}\right)\right) \]

   11. Simplified 62.9%

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

   if -8.9999999999999999e99 < y < -2.79999999999999993e-56

   1. Initial program 76.0%

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

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 56.2%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 56.2%

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

   6. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(i \cdot \left(j \cdot y\right)\right) \]

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(\mathsf{neg}\left(j \cdot y\right)\right)\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(0 - \color{blue}{j \cdot y}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(0, \color{blue}{\left(j \cdot y\right)}\right)\right) \]

      8. *-lowering-*.f64 40.8%

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(j, \color{blue}{y}\right)\right)\right) \]

   8. Simplified 40.8%

      \[\leadsto \color{blue}{i \cdot \left(0 - j \cdot y\right)} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(\mathsf{neg}\left(j \cdot y\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{neg.f64}\left(\left(j \cdot y\right)\right)\right) \]

      3. *-lowering-*.f64 40.8%

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(j, y\right)\right)\right) \]

   10. Applied egg-rr 40.8%

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

   if -2.79999999999999993e-56 < y < 6e-73

   1. Initial program 86.2%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + 1 \cdot \left(\color{blue}{b} \cdot i\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + b \cdot \color{blue}{i}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \color{blue}{-1 \cdot \left(a \cdot x\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i - \color{blue}{a \cdot x}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot i\right), \color{blue}{\left(a \cdot x\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      11. *-lowering-*.f64 57.6%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \mathsf{*.f64}\left(a, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 57.6%

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

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t \cdot \color{blue}{i}\right)\right) \]

      3. *-lowering-*.f64 36.4%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(t, \color{blue}{i}\right)\right) \]

   8. Simplified 36.4%

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

   if 6e-73 < y < 0.69999999999999996

   1. Initial program 80.0%

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

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 80.5%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 80.5%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(c \cdot \color{blue}{a}\right)\right) \]

      2. *-lowering-*.f64 70.5%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(c, \color{blue}{a}\right)\right) \]

   8. Simplified 70.5%

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

   if 0.69999999999999996 < y

   1. Initial program 65.1%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y - b \cdot c\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 47.4%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 47.4%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(y \cdot \color{blue}{x}\right)\right) \]

      7. *-lowering-*.f64 41.6%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right) \]

   8. Simplified 41.6%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-56}:\\ \;\;\;\;i \cdot \left(0 - y \cdot j\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-73}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 0.7:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -1.95e-19)
   (* y (* x (- z (/ (* t a) y))))
   (if (<= x 2.25e+53)
     (+ (* j (- (* a c) (* y i))) (* t (* b i)))
     (* x (- (* y z) (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -1.95e-19) {
		tmp = y * (x * (z - ((t * a) / y)));
	} else if (x <= 2.25e+53) {
		tmp = (j * ((a * c) - (y * i))) + (t * (b * i));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-1.95d-19)) then
        tmp = y * (x * (z - ((t * a) / y)))
    else if (x <= 2.25d+53) then
        tmp = (j * ((a * c) - (y * i))) + (t * (b * i))
    else
        tmp = x * ((y * z) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -1.95e-19) {
		tmp = y * (x * (z - ((t * a) / y)));
	} else if (x <= 2.25e+53) {
		tmp = (j * ((a * c) - (y * i))) + (t * (b * i));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -1.95e-19:
		tmp = y * (x * (z - ((t * a) / y)))
	elif x <= 2.25e+53:
		tmp = (j * ((a * c) - (y * i))) + (t * (b * i))
	else:
		tmp = x * ((y * z) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -1.95e-19)
		tmp = Float64(y * Float64(x * Float64(z - Float64(Float64(t * a) / y))));
	elseif (x <= 2.25e+53)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(t * Float64(b * i)));
	else
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -1.95e-19)
		tmp = y * (x * (z - ((t * a) / y)));
	elseif (x <= 2.25e+53)
		tmp = (j * ((a * c) - (y * i))) + (t * (b * i));
	else
		tmp = x * ((y * z) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -1.95e-19], N[(y * N[(x * N[(z - N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.25e+53], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.94999999999999998e-19

   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 y around -inf

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

   5. Simplified 68.6%

      \[\leadsto \color{blue}{\left(\left(j \cdot i - z \cdot x\right) + \frac{a \cdot \left(t \cdot x - j \cdot c\right) + b \cdot \left(c \cdot z - i \cdot t\right)}{y}\right) \cdot \left(0 - y\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(x \cdot \left(\frac{a \cdot t}{y} - z\right)\right)}, \mathsf{\_.f64}\left(0, y\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{a \cdot t}{y} - z\right)\right), \mathsf{\_.f64}\left(\color{blue}{0}, y\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{a \cdot t}{y}\right), z\right)\right), \mathsf{\_.f64}\left(0, y\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(a \cdot t\right), y\right), z\right)\right), \mathsf{\_.f64}\left(0, y\right)\right) \]

      4. *-lowering-*.f64 61.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(a, t\right), y\right), z\right)\right), \mathsf{\_.f64}\left(0, y\right)\right) \]

   8. Simplified 61.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(\frac{a \cdot t}{y} - z\right)\right)} \cdot \left(0 - y\right) \]

   if -1.94999999999999998e-19 < x < 2.2500000000000001e53

   1. Initial program 72.1%

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

   3. Taylor expanded in i around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(b \cdot \left(i \cdot t\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(b \cdot i\right) \cdot t\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(b \cdot i\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(b \cdot i\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(i \cdot b\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-lowering-*.f64 64.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(i, b\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 64.6%

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

   if 2.2500000000000001e53 < x

   1. Initial program 73.7%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z - a \cdot t\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(y \cdot z\right), \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 64.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 64.4%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.00098:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -1.06e-23)
     t_1
     (if (<= y 1.26e-74)
       (* t (- (* b i) (* x a)))
       (if (<= y 0.00098) (* a (- (* c j) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.06e-23) {
		tmp = t_1;
	} else if (y <= 1.26e-74) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 0.00098) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (y <= (-1.06d-23)) then
        tmp = t_1
    else if (y <= 1.26d-74) then
        tmp = t * ((b * i) - (x * a))
    else if (y <= 0.00098d0) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.06e-23) {
		tmp = t_1;
	} else if (y <= 1.26e-74) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 0.00098) {
		tmp = a * ((c * j) - (x * t));
	} 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 <= -1.06e-23:
		tmp = t_1
	elif y <= 1.26e-74:
		tmp = t * ((b * i) - (x * a))
	elif y <= 0.00098:
		tmp = a * ((c * j) - (x * t))
	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 <= -1.06e-23)
		tmp = t_1;
	elseif (y <= 1.26e-74)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (y <= 0.00098)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.06e-23)
		tmp = t_1;
	elseif (y <= 1.26e-74)
		tmp = t * ((b * i) - (x * a));
	elseif (y <= 0.00098)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.06e-23], t$95$1, If[LessEqual[y, 1.26e-74], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00098], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05999999999999994e-23 or 9.7999999999999997e-4 < y

   1. Initial program 65.5%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot z + \color{blue}{-1 \cdot \left(i \cdot j\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot z + \left(\mathsf{neg}\left(i \cdot j\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot z - \color{blue}{i \cdot j}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(x \cdot z\right), \color{blue}{\left(i \cdot j\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(z \cdot x\right), \left(\color{blue}{i} \cdot j\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(\color{blue}{i} \cdot j\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(j \cdot \color{blue}{i}\right)\right)\right) \]

      9. *-lowering-*.f64 66.5%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, x\right), \mathsf{*.f64}\left(j, \color{blue}{i}\right)\right)\right) \]

   5. Simplified 66.5%

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

   if -1.05999999999999994e-23 < y < 1.25999999999999997e-74

   1. Initial program 85.5%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + 1 \cdot \left(\color{blue}{b} \cdot i\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + b \cdot \color{blue}{i}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \color{blue}{-1 \cdot \left(a \cdot x\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i - \color{blue}{a \cdot x}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot i\right), \color{blue}{\left(a \cdot x\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      11. *-lowering-*.f64 57.4%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \mathsf{*.f64}\left(a, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 57.4%

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

   if 1.25999999999999997e-74 < y < 9.7999999999999997e-4

   1. Initial program 80.0%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 90.2%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 90.2%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.00098:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-74}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 57:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -8.2e+73)
   (* y (* x z))
   (if (<= y 1.2e-74)
     (* b (* t i))
     (if (<= y 57.0) (* j (* a c)) (* z (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -8.2e+73) {
		tmp = y * (x * z);
	} else if (y <= 1.2e-74) {
		tmp = b * (t * i);
	} else if (y <= 57.0) {
		tmp = j * (a * c);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-8.2d+73)) then
        tmp = y * (x * z)
    else if (y <= 1.2d-74) then
        tmp = b * (t * i)
    else if (y <= 57.0d0) then
        tmp = j * (a * c)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -8.2e+73) {
		tmp = y * (x * z);
	} else if (y <= 1.2e-74) {
		tmp = b * (t * i);
	} else if (y <= 57.0) {
		tmp = j * (a * c);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -8.2e+73:
		tmp = y * (x * z)
	elif y <= 1.2e-74:
		tmp = b * (t * i)
	elif y <= 57.0:
		tmp = j * (a * c)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -8.2e+73)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 1.2e-74)
		tmp = Float64(b * Float64(t * i));
	elseif (y <= 57.0)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -8.2e+73)
		tmp = y * (x * z);
	elseif (y <= 1.2e-74)
		tmp = b * (t * i);
	elseif (y <= 57.0)
		tmp = j * (a * c);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -8.2e+73], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-74], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 57.0], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.1999999999999996e73

   1. Initial program 58.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 54.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 54.9%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\left(x \cdot y - b \cdot c\right) + \frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} + \color{blue}{\left(x \cdot y - b \cdot c\right)}\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} + x \cdot y\right) - \color{blue}{b \cdot c}\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(x \cdot y + \frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right) - \color{blue}{b} \cdot c\right)\right) \]

      8. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot y + \color{blue}{\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} - b \cdot c\right)}\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} - b \cdot c\right)}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot x\right), \left(\color{blue}{\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}} - b \cdot c\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}} - b \cdot c\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{\_.f64}\left(\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right), \color{blue}{\left(b \cdot c\right)}\right)\right)\right) \]

   8. Simplified 56.5%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. associate-*r* N/A

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(z \cdot \color{blue}{x}\right)\right) \]

       6. *-lowering-*.f64 57.3%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{x}\right)\right) \]

   11. Simplified 57.3%

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

   if -8.1999999999999996e73 < y < 1.1999999999999999e-74

   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. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + 1 \cdot \left(\color{blue}{b} \cdot i\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + b \cdot \color{blue}{i}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \color{blue}{-1 \cdot \left(a \cdot x\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i - \color{blue}{a \cdot x}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot i\right), \color{blue}{\left(a \cdot x\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      11. *-lowering-*.f64 50.1%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \mathsf{*.f64}\left(a, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 50.1%

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

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t \cdot \color{blue}{i}\right)\right) \]

      3. *-lowering-*.f64 32.7%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(t, \color{blue}{i}\right)\right) \]

   8. Simplified 32.7%

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

   if 1.1999999999999999e-74 < y < 57

   1. Initial program 80.0%

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

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 80.5%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 80.5%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(c \cdot \color{blue}{a}\right)\right) \]

      2. *-lowering-*.f64 70.5%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(c, \color{blue}{a}\right)\right) \]

   8. Simplified 70.5%

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

   if 57 < y

   1. Initial program 65.1%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y - b \cdot c\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 47.4%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 47.4%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(y \cdot \color{blue}{x}\right)\right) \]

      7. *-lowering-*.f64 41.6%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right) \]

   8. Simplified 41.6%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-74}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 57:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-70}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 3:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -2.4e+74)
   (* y (* x z))
   (if (<= y 1.45e-70)
     (* b (* t i))
     (if (<= y 3.0) (* j (* a c)) (* x (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -2.4e+74) {
		tmp = y * (x * z);
	} else if (y <= 1.45e-70) {
		tmp = b * (t * i);
	} else if (y <= 3.0) {
		tmp = j * (a * c);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-2.4d+74)) then
        tmp = y * (x * z)
    else if (y <= 1.45d-70) then
        tmp = b * (t * i)
    else if (y <= 3.0d0) then
        tmp = j * (a * c)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -2.4e+74) {
		tmp = y * (x * z);
	} else if (y <= 1.45e-70) {
		tmp = b * (t * i);
	} else if (y <= 3.0) {
		tmp = j * (a * c);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -2.4e+74:
		tmp = y * (x * z)
	elif y <= 1.45e-70:
		tmp = b * (t * i)
	elif y <= 3.0:
		tmp = j * (a * c)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -2.4e+74)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 1.45e-70)
		tmp = Float64(b * Float64(t * i));
	elseif (y <= 3.0)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -2.4e+74)
		tmp = y * (x * z);
	elseif (y <= 1.45e-70)
		tmp = b * (t * i);
	elseif (y <= 3.0)
		tmp = j * (a * c);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -2.4e+74], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-70], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.0], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.40000000000000008e74

   1. Initial program 58.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 54.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 54.9%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\left(x \cdot y - b \cdot c\right) + \frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} + \color{blue}{\left(x \cdot y - b \cdot c\right)}\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} + x \cdot y\right) - \color{blue}{b \cdot c}\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(x \cdot y + \frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right) - \color{blue}{b} \cdot c\right)\right) \]

      8. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot y + \color{blue}{\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} - b \cdot c\right)}\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} - b \cdot c\right)}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot x\right), \left(\color{blue}{\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}} - b \cdot c\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}} - b \cdot c\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{\_.f64}\left(\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right), \color{blue}{\left(b \cdot c\right)}\right)\right)\right) \]

   8. Simplified 56.5%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. associate-*r* N/A

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(z \cdot \color{blue}{x}\right)\right) \]

       6. *-lowering-*.f64 57.3%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{x}\right)\right) \]

   11. Simplified 57.3%

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

   if -2.40000000000000008e74 < y < 1.44999999999999986e-70

   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. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + 1 \cdot \left(\color{blue}{b} \cdot i\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + b \cdot \color{blue}{i}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \color{blue}{-1 \cdot \left(a \cdot x\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i - \color{blue}{a \cdot x}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot i\right), \color{blue}{\left(a \cdot x\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      11. *-lowering-*.f64 50.1%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \mathsf{*.f64}\left(a, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 50.1%

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

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t \cdot \color{blue}{i}\right)\right) \]

      3. *-lowering-*.f64 32.7%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(t, \color{blue}{i}\right)\right) \]

   8. Simplified 32.7%

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

   if 1.44999999999999986e-70 < y < 3

   1. Initial program 80.0%

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

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 80.5%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 80.5%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(c \cdot \color{blue}{a}\right)\right) \]

      2. *-lowering-*.f64 70.5%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(c, \color{blue}{a}\right)\right) \]

   8. Simplified 70.5%

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

   if 3 < y

   1. Initial program 65.1%

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

      1. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \left(b \cdot \frac{\left(c \cdot z\right) \cdot \left(c \cdot z\right) - \left(t \cdot i\right) \cdot \left(t \cdot i\right)}{c \cdot z + t \cdot i}\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \left(b \cdot \frac{1}{\frac{c \cdot z + t \cdot i}{\left(c \cdot z\right) \cdot \left(c \cdot z\right) - \left(t \cdot i\right) \cdot \left(t \cdot i\right)}}\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \left(\frac{b}{\frac{c \cdot z + t \cdot i}{\left(c \cdot z\right) \cdot \left(c \cdot z\right) - \left(t \cdot i\right) \cdot \left(t \cdot i\right)}}\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{/.f64}\left(b, \left(\frac{c \cdot z + t \cdot i}{\left(c \cdot z\right) \cdot \left(c \cdot z\right) - \left(t \cdot i\right) \cdot \left(t \cdot i\right)}\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{/.f64}\left(b, \left(\frac{1}{\frac{\left(c \cdot z\right) \cdot \left(c \cdot z\right) - \left(t \cdot i\right) \cdot \left(t \cdot i\right)}{c \cdot z + t \cdot i}}\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{/.f64}\left(b, \left(\frac{1}{c \cdot z - t \cdot i}\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{/.f64}\left(b, \mathsf{/.f64}\left(1, \left(c \cdot z - t \cdot i\right)\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{/.f64}\left(b, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(c \cdot z\right), \left(t \cdot i\right)\right)\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{/.f64}\left(b, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(z \cdot c\right), \left(t \cdot i\right)\right)\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{/.f64}\left(b, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, c\right), \left(t \cdot i\right)\right)\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      11. *-lowering-*.f64 65.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{/.f64}\left(b, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, c\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   4. Applied egg-rr 65.1%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z - a \cdot t\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(y \cdot z\right), \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(z \cdot y\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, y\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, y\right), \left(t \cdot \color{blue}{a}\right)\right)\right) \]

      6. *-lowering-*.f64 43.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, y\right), \mathsf{*.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 43.5%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 40.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   10. Simplified 40.4%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-70}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 3:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-74}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 140:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= y -1.4e+74)
     t_1
     (if (<= y 2.45e-74) (* b (* t i)) (if (<= y 140.0) (* j (* a c)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -1.4e+74) {
		tmp = t_1;
	} else if (y <= 2.45e-74) {
		tmp = b * (t * i);
	} else if (y <= 140.0) {
		tmp = j * (a * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (y <= (-1.4d+74)) then
        tmp = t_1
    else if (y <= 2.45d-74) then
        tmp = b * (t * i)
    else if (y <= 140.0d0) then
        tmp = j * (a * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -1.4e+74) {
		tmp = t_1;
	} else if (y <= 2.45e-74) {
		tmp = b * (t * i);
	} else if (y <= 140.0) {
		tmp = j * (a * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if y <= -1.4e+74:
		tmp = t_1
	elif y <= 2.45e-74:
		tmp = b * (t * i)
	elif y <= 140.0:
		tmp = j * (a * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -1.4e+74)
		tmp = t_1;
	elseif (y <= 2.45e-74)
		tmp = Float64(b * Float64(t * i));
	elseif (y <= 140.0)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (y <= -1.4e+74)
		tmp = t_1;
	elseif (y <= 2.45e-74)
		tmp = b * (t * i);
	elseif (y <= 140.0)
		tmp = j * (a * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+74], t$95$1, If[LessEqual[y, 2.45e-74], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 140.0], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.40000000000000001e74 or 140 < y

   1. Initial program 62.3%

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

      1. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \left(b \cdot \frac{\left(c \cdot z\right) \cdot \left(c \cdot z\right) - \left(t \cdot i\right) \cdot \left(t \cdot i\right)}{c \cdot z + t \cdot i}\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \left(b \cdot \frac{1}{\frac{c \cdot z + t \cdot i}{\left(c \cdot z\right) \cdot \left(c \cdot z\right) - \left(t \cdot i\right) \cdot \left(t \cdot i\right)}}\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \left(\frac{b}{\frac{c \cdot z + t \cdot i}{\left(c \cdot z\right) \cdot \left(c \cdot z\right) - \left(t \cdot i\right) \cdot \left(t \cdot i\right)}}\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{/.f64}\left(b, \left(\frac{c \cdot z + t \cdot i}{\left(c \cdot z\right) \cdot \left(c \cdot z\right) - \left(t \cdot i\right) \cdot \left(t \cdot i\right)}\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{/.f64}\left(b, \left(\frac{1}{\frac{\left(c \cdot z\right) \cdot \left(c \cdot z\right) - \left(t \cdot i\right) \cdot \left(t \cdot i\right)}{c \cdot z + t \cdot i}}\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{/.f64}\left(b, \left(\frac{1}{c \cdot z - t \cdot i}\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{/.f64}\left(b, \mathsf{/.f64}\left(1, \left(c \cdot z - t \cdot i\right)\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{/.f64}\left(b, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(c \cdot z\right), \left(t \cdot i\right)\right)\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{/.f64}\left(b, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(z \cdot c\right), \left(t \cdot i\right)\right)\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{/.f64}\left(b, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, c\right), \left(t \cdot i\right)\right)\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      11. *-lowering-*.f64 62.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(t, a\right)\right)\right), \mathsf{/.f64}\left(b, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, c\right), \mathsf{*.f64}\left(t, i\right)\right)\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   4. Applied egg-rr 62.3%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z - a \cdot t\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(y \cdot z\right), \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(z \cdot y\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, y\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, y\right), \left(t \cdot \color{blue}{a}\right)\right)\right) \]

      6. *-lowering-*.f64 51.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, y\right), \mathsf{*.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 51.2%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 46.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   10. Simplified 46.3%

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

   if -1.40000000000000001e74 < y < 2.4500000000000001e-74

   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. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + 1 \cdot \left(\color{blue}{b} \cdot i\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + b \cdot \color{blue}{i}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \color{blue}{-1 \cdot \left(a \cdot x\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i - \color{blue}{a \cdot x}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot i\right), \color{blue}{\left(a \cdot x\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      11. *-lowering-*.f64 50.1%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \mathsf{*.f64}\left(a, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 50.1%

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

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t \cdot \color{blue}{i}\right)\right) \]

      3. *-lowering-*.f64 32.7%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(t, \color{blue}{i}\right)\right) \]

   8. Simplified 32.7%

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

   if 2.4500000000000001e-74 < y < 140

   1. Initial program 80.0%

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

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 80.5%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 80.5%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(j, \left(c \cdot \color{blue}{a}\right)\right) \]

      2. *-lowering-*.f64 70.5%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(c, \color{blue}{a}\right)\right) \]

   8. Simplified 70.5%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-74}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 140:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -5.5 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 10^{+20}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -5.5e-66) t_1 (if (<= i 1e+20) (* c (- (* a j) (* z b))) 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 <= -5.5e-66) {
		tmp = t_1;
	} else if (i <= 1e+20) {
		tmp = c * ((a * j) - (z * b));
	} 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 <= (-5.5d-66)) then
        tmp = t_1
    else if (i <= 1d+20) then
        tmp = c * ((a * j) - (z * b))
    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 <= -5.5e-66) {
		tmp = t_1;
	} else if (i <= 1e+20) {
		tmp = c * ((a * j) - (z * b));
	} 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 <= -5.5e-66:
		tmp = t_1
	elif i <= 1e+20:
		tmp = c * ((a * j) - (z * b))
	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 <= -5.5e-66)
		tmp = t_1;
	elseif (i <= 1e+20)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	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 <= -5.5e-66)
		tmp = t_1;
	elseif (i <= 1e+20)
		tmp = c * ((a * j) - (z * b));
	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, -5.5e-66], t$95$1, If[LessEqual[i, 1e+20], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -5.50000000000000053e-66 or 1e20 < i

   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 i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot t\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(-1 \cdot \left(j \cdot y\right) + 1 \cdot \left(\color{blue}{b} \cdot t\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(-1 \cdot \left(j \cdot y\right) + b \cdot \color{blue}{t}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t + \left(\mathsf{neg}\left(j \cdot y\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t - \color{blue}{j \cdot y}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(b \cdot t\right), \color{blue}{\left(j \cdot y\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, t\right), \left(\color{blue}{j} \cdot y\right)\right)\right) \]

      10. *-lowering-*.f64 59.3%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, t\right), \mathsf{*.f64}\left(j, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 59.3%

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

   if -5.50000000000000053e-66 < i < 1e20

   1. Initial program 78.5%

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

   3. Taylor expanded in c around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{\left(a \cdot j - b \cdot z\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(a \cdot j\right), \color{blue}{\left(b \cdot z\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\left(j \cdot a\right), \left(\color{blue}{b} \cdot z\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \left(\color{blue}{b} \cdot z\right)\right)\right) \]

      5. *-lowering-*.f64 49.6%

         \[\leadsto \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(b, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 49.6%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.5 \cdot 10^{-66}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 10^{+20}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 51.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 260000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -5.5e+91)
     t_1
     (if (<= b 260000.0) (* a (- (* c j) (* x t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.5e+91) {
		tmp = t_1;
	} else if (b <= 260000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-5.5d+91)) then
        tmp = t_1
    else if (b <= 260000.0d0) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.5e+91) {
		tmp = t_1;
	} else if (b <= 260000.0) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -5.5e+91:
		tmp = t_1
	elif b <= 260000.0:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = 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)))
	tmp = 0.0
	if (b <= -5.5e+91)
		tmp = t_1;
	elseif (b <= 260000.0)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.5e+91)
		tmp = t_1;
	elseif (b <= 260000.0)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e+91], t$95$1, If[LessEqual[b, 260000.0], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.4999999999999998e91 or 2.6e5 < b

   1. Initial program 72.4%

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

   3. Taylor expanded in b around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

         \[\leadsto b \cdot \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)\right) \]

      4. distribute-neg-in N/A

         \[\leadsto b \cdot \left(\mathsf{neg}\left(\left(c \cdot z + \left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(\mathsf{neg}\left(\left(c \cdot z - i \cdot t\right)\right)\right)\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(\mathsf{neg}\left(\left(c \cdot z + \left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)\right)\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(i \cdot t\right)\right)\right)\right)}\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(c \cdot z\right)\right) + i \cdot \color{blue}{t}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(i \cdot t + \color{blue}{\left(\mathsf{neg}\left(c \cdot z\right)\right)}\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(b, \left(i \cdot t - \color{blue}{c \cdot z}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(i \cdot t\right), \color{blue}{\left(c \cdot z\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, t\right), \left(\color{blue}{c} \cdot z\right)\right)\right) \]

      16. *-lowering-*.f64 61.0%

          \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, t\right), \mathsf{*.f64}\left(c, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 61.0%

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

   if -5.4999999999999998e91 < b < 2.6e5

   1. Initial program 74.6%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 44.0%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 44.0%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+91}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 260000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 41.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+97}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+160}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.35e+97)
   (* y (* x z))
   (if (<= y 2.15e+160) (* a (- (* c j) (* x t))) (* z (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.35e+97) {
		tmp = y * (x * z);
	} else if (y <= 2.15e+160) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.35d+97)) then
        tmp = y * (x * z)
    else if (y <= 2.15d+160) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.35e+97) {
		tmp = y * (x * z);
	} else if (y <= 2.15e+160) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.35e+97:
		tmp = y * (x * z)
	elif y <= 2.15e+160:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.35e+97)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 2.15e+160)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.35e+97)
		tmp = y * (x * z);
	elseif (y <= 2.15e+160)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.35e+97], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+160], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.34999999999999997e97

   1. Initial program 56.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(x \cdot y - b \cdot c\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(b \cdot c\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 52.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, b\right)\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 52.1%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\left(x \cdot y - b \cdot c\right) + \frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} + \color{blue}{\left(x \cdot y - b \cdot c\right)}\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} + x \cdot y\right) - \color{blue}{b \cdot c}\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(x \cdot y + \frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right) - \color{blue}{b} \cdot c\right)\right) \]

      8. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot y + \color{blue}{\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} - b \cdot c\right)}\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z} - b \cdot c\right)}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot x\right), \left(\color{blue}{\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}} - b \cdot c\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}} - b \cdot c\right)\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{\_.f64}\left(\left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{z}\right), \color{blue}{\left(b \cdot c\right)}\right)\right)\right) \]

   8. Simplified 54.0%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. associate-*r* N/A

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(z \cdot \color{blue}{x}\right)\right) \]

       6. *-lowering-*.f64 63.8%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{x}\right)\right) \]

   11. Simplified 63.8%

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

   if -1.34999999999999997e97 < y < 2.14999999999999994e160

   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

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 47.1%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 47.1%

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

   if 2.14999999999999994e160 < y

   1. Initial program 62.6%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y - b \cdot c\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 50.8%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 50.8%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(z \cdot y\right) \cdot x \]

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y\right)}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(y \cdot \color{blue}{x}\right)\right) \]

      7. *-lowering-*.f64 46.1%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right) \]

   8. Simplified 46.1%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+97}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+160}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;i \leq -3.5 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= i -3.5e+74) t_1 (if (<= i 3.2e+35) (* a (* c j)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (i <= -3.5e+74) {
		tmp = t_1;
	} else if (i <= 3.2e+35) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t * i)
    if (i <= (-3.5d+74)) then
        tmp = t_1
    else if (i <= 3.2d+35) then
        tmp = a * (c * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (i <= -3.5e+74) {
		tmp = t_1;
	} else if (i <= 3.2e+35) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if i <= -3.5e+74:
		tmp = t_1
	elif i <= 3.2e+35:
		tmp = a * (c * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (i <= -3.5e+74)
		tmp = t_1;
	elseif (i <= 3.2e+35)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	tmp = 0.0;
	if (i <= -3.5e+74)
		tmp = t_1;
	elseif (i <= 3.2e+35)
		tmp = a * (c * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.5e+74], t$95$1, If[LessEqual[i, 3.2e+35], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -3.50000000000000014e74 or 3.19999999999999983e35 < i

   1. Initial program 67.9%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)}\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + \color{blue}{\left(\mathsf{neg}\left(-1\right)\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + 1 \cdot \left(\color{blue}{b} \cdot i\right)\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(-1 \cdot \left(a \cdot x\right) + b \cdot \color{blue}{i}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \color{blue}{-1 \cdot \left(a \cdot x\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i + \left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(b \cdot i - \color{blue}{a \cdot x}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(b \cdot i\right), \color{blue}{\left(a \cdot x\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(i \cdot b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \left(\color{blue}{a} \cdot x\right)\right)\right) \]

      11. *-lowering-*.f64 48.5%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, b\right), \mathsf{*.f64}\left(a, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 48.5%

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

   6. Taylor expanded in i around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(t \cdot \color{blue}{i}\right)\right) \]

      3. *-lowering-*.f64 44.9%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(t, \color{blue}{i}\right)\right) \]

   8. Simplified 44.9%

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

   if -3.50000000000000014e74 < i < 3.19999999999999983e35

   1. Initial program 77.7%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 45.2%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 45.2%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 27.7%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(c, \color{blue}{j}\right)\right) \]

   8. Simplified 27.7%

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

Alternative 22: 22.4% 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 73.6%

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

3. Taylor expanded in a around inf

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

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

   2. +-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

   3. mul-1-neg N/A

      \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

   4. unsub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

   8. *-lowering-*.f64 38.2%

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

5. Simplified 38.2%

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

6. Taylor expanded in j around inf

   \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]
7. Step-by-step derivation

   1. *-lowering-*.f64 22.4%

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(c, \color{blue}{j}\right)\right) \]

8. Simplified 22.4%

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

Developer Target 1: 60.7% 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 2024191 
(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)))))