Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, E

Percentage Accurate: 85.7% → 92.3%

Time: 25.8s

Alternatives: 23

Speedup: 0.5×

• 49.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
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 k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
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 k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

Alternative 1: 92.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x \cdot 18\right) \cdot y\right) \cdot z\\ \mathbf{if}\;\left(\left(\left(t\_1 \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;t \cdot \left(t\_1 + a \cdot -4\right) + \left(\left(b \cdot c + x \cdot \left(i \cdot -4\right)\right) + -27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* (* x 18.0) y) z)))
   (if (<=
        (-
         (- (+ (- (* t_1 t) (* t (* a 4.0))) (* b c)) (* (* x 4.0) i))
         (* (* j 27.0) k))
        INFINITY)
     (+
      (* t (+ t_1 (* a -4.0)))
      (+ (+ (* b c) (* x (* i -4.0))) (* -27.0 (* j k))))
     (* x (+ (* i -4.0) (* z (* y (* 18.0 t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((x * 18.0) * y) * z;
	double tmp;
	if ((((((t_1 * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= ((double) INFINITY)) {
		tmp = (t * (t_1 + (a * -4.0))) + (((b * c) + (x * (i * -4.0))) + (-27.0 * (j * k)));
	} else {
		tmp = x * ((i * -4.0) + (z * (y * (18.0 * t))));
	}
	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 k) {
	double t_1 = ((x * 18.0) * y) * z;
	double tmp;
	if ((((((t_1 * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= Double.POSITIVE_INFINITY) {
		tmp = (t * (t_1 + (a * -4.0))) + (((b * c) + (x * (i * -4.0))) + (-27.0 * (j * k)));
	} else {
		tmp = x * ((i * -4.0) + (z * (y * (18.0 * t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((x * 18.0) * y) * z
	tmp = 0
	if (((((t_1 * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= math.inf:
		tmp = (t * (t_1 + (a * -4.0))) + (((b * c) + (x * (i * -4.0))) + (-27.0 * (j * k)))
	else:
		tmp = x * ((i * -4.0) + (z * (y * (18.0 * t))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(x * 18.0) * y) * z)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(t_1 * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k)) <= Inf)
		tmp = Float64(Float64(t * Float64(t_1 + Float64(a * -4.0))) + Float64(Float64(Float64(b * c) + Float64(x * Float64(i * -4.0))) + Float64(-27.0 * Float64(j * k))));
	else
		tmp = Float64(x * Float64(Float64(i * -4.0) + Float64(z * Float64(y * Float64(18.0 * t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((x * 18.0) * y) * z;
	tmp = 0.0;
	if ((((((t_1 * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k)) <= Inf)
		tmp = (t * (t_1 + (a * -4.0))) + (((b * c) + (x * (i * -4.0))) + (-27.0 * (j * k)));
	else
		tmp = x * ((i * -4.0) + (z * (y * (18.0 * t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(t$95$1 * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(z * N[(y * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   1. Initial program 97.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 97.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k))

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 24.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(\left(18 \cdot t\right) \cdot y\right) \cdot \color{blue}{z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\left(\left(18 \cdot t\right) \cdot y\right), \color{blue}{z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(18 \cdot t\right), y\right), z\right)\right)\right) \]

      8. *-lowering-*.f64 69.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), y\right), z\right)\right)\right) \]

   7. Simplified 69.0%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + \left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(\left(b \cdot c + x \cdot \left(i \cdot -4\right)\right) + -27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 33.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{-34}:\\ \;\;\;\;\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -3.95 \cdot 10^{-199}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-42}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(x \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= z -2e-34)
     (* (* 18.0 t) (* y (* x z)))
     (if (<= z -3.95e-199)
       (* b c)
       (if (<= z -9.5e-275)
         t_1
         (if (<= z 1.95e-42)
           (* -27.0 (* j k))
           (if (<= z 1.1e+114) t_1 (* 18.0 (* z (* x (* y t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (z <= -2e-34) {
		tmp = (18.0 * t) * (y * (x * z));
	} else if (z <= -3.95e-199) {
		tmp = b * c;
	} else if (z <= -9.5e-275) {
		tmp = t_1;
	} else if (z <= 1.95e-42) {
		tmp = -27.0 * (j * k);
	} else if (z <= 1.1e+114) {
		tmp = t_1;
	} else {
		tmp = 18.0 * (z * (x * (y * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (x * i)
    if (z <= (-2d-34)) then
        tmp = (18.0d0 * t) * (y * (x * z))
    else if (z <= (-3.95d-199)) then
        tmp = b * c
    else if (z <= (-9.5d-275)) then
        tmp = t_1
    else if (z <= 1.95d-42) then
        tmp = (-27.0d0) * (j * k)
    else if (z <= 1.1d+114) then
        tmp = t_1
    else
        tmp = 18.0d0 * (z * (x * (y * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (z <= -2e-34) {
		tmp = (18.0 * t) * (y * (x * z));
	} else if (z <= -3.95e-199) {
		tmp = b * c;
	} else if (z <= -9.5e-275) {
		tmp = t_1;
	} else if (z <= 1.95e-42) {
		tmp = -27.0 * (j * k);
	} else if (z <= 1.1e+114) {
		tmp = t_1;
	} else {
		tmp = 18.0 * (z * (x * (y * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	tmp = 0
	if z <= -2e-34:
		tmp = (18.0 * t) * (y * (x * z))
	elif z <= -3.95e-199:
		tmp = b * c
	elif z <= -9.5e-275:
		tmp = t_1
	elif z <= 1.95e-42:
		tmp = -27.0 * (j * k)
	elif z <= 1.1e+114:
		tmp = t_1
	else:
		tmp = 18.0 * (z * (x * (y * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (z <= -2e-34)
		tmp = Float64(Float64(18.0 * t) * Float64(y * Float64(x * z)));
	elseif (z <= -3.95e-199)
		tmp = Float64(b * c);
	elseif (z <= -9.5e-275)
		tmp = t_1;
	elseif (z <= 1.95e-42)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (z <= 1.1e+114)
		tmp = t_1;
	else
		tmp = Float64(18.0 * Float64(z * Float64(x * Float64(y * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	tmp = 0.0;
	if (z <= -2e-34)
		tmp = (18.0 * t) * (y * (x * z));
	elseif (z <= -3.95e-199)
		tmp = b * c;
	elseif (z <= -9.5e-275)
		tmp = t_1;
	elseif (z <= 1.95e-42)
		tmp = -27.0 * (j * k);
	elseif (z <= 1.1e+114)
		tmp = t_1;
	else
		tmp = 18.0 * (z * (x * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e-34], N[(N[(18.0 * t), $MachinePrecision] * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.95e-199], N[(b * c), $MachinePrecision], If[LessEqual[z, -9.5e-275], t$95$1, If[LessEqual[z, 1.95e-42], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+114], t$95$1, N[(18.0 * N[(z * N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.99999999999999986e-34

   1. Initial program 86.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{x}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right) \]

      6. *-lowering-*.f64 48.2%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right) \]

   7. Simplified 48.2%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(18 \cdot t\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(18 \cdot t\right), \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(\color{blue}{\left(y \cdot z\right)} \cdot x\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(y \cdot \color{blue}{\left(z \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(y \cdot \left(x \cdot \color{blue}{z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      8. *-lowering-*.f64 50.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   9. Applied egg-rr 50.9%

      \[\leadsto \color{blue}{\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)} \]

   if -1.99999999999999986e-34 < z < -3.9499999999999998e-199

   1. Initial program 81.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 81.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 31.4%

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

   7. Simplified 31.4%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -3.9499999999999998e-199 < z < -9.49999999999999961e-275 or 1.9500000000000001e-42 < z < 1.1e114

   1. Initial program 82.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 43.3%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 43.3%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

   if -9.49999999999999961e-275 < z < 1.9500000000000001e-42

   1. Initial program 90.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 90.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   6. Applied egg-rr 92.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(-4 \cdot i\right) + \left(b \cdot c + t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\right)\right) - j \cdot \left(k \cdot 27\right)} \]

   7. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(j \cdot k\right) \cdot \color{blue}{-27} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(j \cdot k\right), \color{blue}{-27}\right) \]

      3. *-lowering-*.f64 35.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, k\right), -27\right) \]

   9. Simplified 35.6%

      \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} \]

   if 1.1e114 < z

   1. Initial program 84.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{x}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right) \]

      6. *-lowering-*.f64 47.9%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right) \]

   7. Simplified 47.9%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(x \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(x \cdot \left(\left(t \cdot y\right) \cdot \color{blue}{z}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(x \cdot \left(t \cdot y\right)\right) \cdot \color{blue}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(x \cdot \left(t \cdot y\right)\right), \color{blue}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(t \cdot y\right)\right), z\right)\right) \]

      6. *-lowering-*.f64 49.6%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, y\right)\right), z\right)\right) \]

   9. Applied egg-rr 49.6%

      \[\leadsto 18 \cdot \color{blue}{\left(\left(x \cdot \left(t \cdot y\right)\right) \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-34}:\\ \;\;\;\;\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -3.95 \cdot 10^{-199}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-275}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-42}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+114}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(x \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 32.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{-34}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-42}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(x \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= z -5.4e-34)
     (* 18.0 (* x (* t (* y z))))
     (if (<= z -1.32e-198)
       (* b c)
       (if (<= z -7.6e-275)
         t_1
         (if (<= z 2.6e-42)
           (* -27.0 (* j k))
           (if (<= z 6.6e+112) t_1 (* 18.0 (* z (* x (* y t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (z <= -5.4e-34) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (z <= -1.32e-198) {
		tmp = b * c;
	} else if (z <= -7.6e-275) {
		tmp = t_1;
	} else if (z <= 2.6e-42) {
		tmp = -27.0 * (j * k);
	} else if (z <= 6.6e+112) {
		tmp = t_1;
	} else {
		tmp = 18.0 * (z * (x * (y * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (x * i)
    if (z <= (-5.4d-34)) then
        tmp = 18.0d0 * (x * (t * (y * z)))
    else if (z <= (-1.32d-198)) then
        tmp = b * c
    else if (z <= (-7.6d-275)) then
        tmp = t_1
    else if (z <= 2.6d-42) then
        tmp = (-27.0d0) * (j * k)
    else if (z <= 6.6d+112) then
        tmp = t_1
    else
        tmp = 18.0d0 * (z * (x * (y * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (z <= -5.4e-34) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (z <= -1.32e-198) {
		tmp = b * c;
	} else if (z <= -7.6e-275) {
		tmp = t_1;
	} else if (z <= 2.6e-42) {
		tmp = -27.0 * (j * k);
	} else if (z <= 6.6e+112) {
		tmp = t_1;
	} else {
		tmp = 18.0 * (z * (x * (y * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	tmp = 0
	if z <= -5.4e-34:
		tmp = 18.0 * (x * (t * (y * z)))
	elif z <= -1.32e-198:
		tmp = b * c
	elif z <= -7.6e-275:
		tmp = t_1
	elif z <= 2.6e-42:
		tmp = -27.0 * (j * k)
	elif z <= 6.6e+112:
		tmp = t_1
	else:
		tmp = 18.0 * (z * (x * (y * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (z <= -5.4e-34)
		tmp = Float64(18.0 * Float64(x * Float64(t * Float64(y * z))));
	elseif (z <= -1.32e-198)
		tmp = Float64(b * c);
	elseif (z <= -7.6e-275)
		tmp = t_1;
	elseif (z <= 2.6e-42)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (z <= 6.6e+112)
		tmp = t_1;
	else
		tmp = Float64(18.0 * Float64(z * Float64(x * Float64(y * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	tmp = 0.0;
	if (z <= -5.4e-34)
		tmp = 18.0 * (x * (t * (y * z)));
	elseif (z <= -1.32e-198)
		tmp = b * c;
	elseif (z <= -7.6e-275)
		tmp = t_1;
	elseif (z <= 2.6e-42)
		tmp = -27.0 * (j * k);
	elseif (z <= 6.6e+112)
		tmp = t_1;
	else
		tmp = 18.0 * (z * (x * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e-34], N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.32e-198], N[(b * c), $MachinePrecision], If[LessEqual[z, -7.6e-275], t$95$1, If[LessEqual[z, 2.6e-42], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+112], t$95$1, N[(18.0 * N[(z * N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.40000000000000034e-34

   1. Initial program 86.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{x}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right) \]

      6. *-lowering-*.f64 48.2%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right) \]

   7. Simplified 48.2%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]

   if -5.40000000000000034e-34 < z < -1.3200000000000001e-198

   1. Initial program 81.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 81.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 31.4%

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

   7. Simplified 31.4%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -1.3200000000000001e-198 < z < -7.59999999999999943e-275 or 2.6e-42 < z < 6.5999999999999998e112

   1. Initial program 82.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 43.3%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 43.3%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

   if -7.59999999999999943e-275 < z < 2.6e-42

   1. Initial program 90.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 90.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   6. Applied egg-rr 92.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(-4 \cdot i\right) + \left(b \cdot c + t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\right)\right) - j \cdot \left(k \cdot 27\right)} \]

   7. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(j \cdot k\right) \cdot \color{blue}{-27} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(j \cdot k\right), \color{blue}{-27}\right) \]

      3. *-lowering-*.f64 35.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, k\right), -27\right) \]

   9. Simplified 35.6%

      \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} \]

   if 6.5999999999999998e112 < z

   1. Initial program 84.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{x}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right) \]

      6. *-lowering-*.f64 47.9%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right) \]

   7. Simplified 47.9%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(x \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(x \cdot \left(\left(t \cdot y\right) \cdot \color{blue}{z}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(x \cdot \left(t \cdot y\right)\right) \cdot \color{blue}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(x \cdot \left(t \cdot y\right)\right), \color{blue}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(t \cdot y\right)\right), z\right)\right) \]

      6. *-lowering-*.f64 49.6%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, y\right)\right), z\right)\right) \]

   9. Applied egg-rr 49.6%

      \[\leadsto 18 \cdot \color{blue}{\left(\left(x \cdot \left(t \cdot y\right)\right) \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-34}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-275}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-42}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+112}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(x \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 32.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-200}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-275}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-42}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+118}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* t (* y z))))) (t_2 (* -4.0 (* x i))))
   (if (<= z -3.6e-32)
     t_1
     (if (<= z -2e-200)
       (* b c)
       (if (<= z -8.5e-275)
         t_2
         (if (<= z 2.4e-42)
           (* -27.0 (* j k))
           (if (<= z 4.2e+118) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (x * (t * (y * z)));
	double t_2 = -4.0 * (x * i);
	double tmp;
	if (z <= -3.6e-32) {
		tmp = t_1;
	} else if (z <= -2e-200) {
		tmp = b * c;
	} else if (z <= -8.5e-275) {
		tmp = t_2;
	} else if (z <= 2.4e-42) {
		tmp = -27.0 * (j * k);
	} else if (z <= 4.2e+118) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 18.0d0 * (x * (t * (y * z)))
    t_2 = (-4.0d0) * (x * i)
    if (z <= (-3.6d-32)) then
        tmp = t_1
    else if (z <= (-2d-200)) then
        tmp = b * c
    else if (z <= (-8.5d-275)) then
        tmp = t_2
    else if (z <= 2.4d-42) then
        tmp = (-27.0d0) * (j * k)
    else if (z <= 4.2d+118) then
        tmp = t_2
    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 k) {
	double t_1 = 18.0 * (x * (t * (y * z)));
	double t_2 = -4.0 * (x * i);
	double tmp;
	if (z <= -3.6e-32) {
		tmp = t_1;
	} else if (z <= -2e-200) {
		tmp = b * c;
	} else if (z <= -8.5e-275) {
		tmp = t_2;
	} else if (z <= 2.4e-42) {
		tmp = -27.0 * (j * k);
	} else if (z <= 4.2e+118) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (t * (y * z)))
	t_2 = -4.0 * (x * i)
	tmp = 0
	if z <= -3.6e-32:
		tmp = t_1
	elif z <= -2e-200:
		tmp = b * c
	elif z <= -8.5e-275:
		tmp = t_2
	elif z <= 2.4e-42:
		tmp = -27.0 * (j * k)
	elif z <= 4.2e+118:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(t * Float64(y * z))))
	t_2 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (z <= -3.6e-32)
		tmp = t_1;
	elseif (z <= -2e-200)
		tmp = Float64(b * c);
	elseif (z <= -8.5e-275)
		tmp = t_2;
	elseif (z <= 2.4e-42)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (z <= 4.2e+118)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (t * (y * z)));
	t_2 = -4.0 * (x * i);
	tmp = 0.0;
	if (z <= -3.6e-32)
		tmp = t_1;
	elseif (z <= -2e-200)
		tmp = b * c;
	elseif (z <= -8.5e-275)
		tmp = t_2;
	elseif (z <= 2.4e-42)
		tmp = -27.0 * (j * k);
	elseif (z <= 4.2e+118)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e-32], t$95$1, If[LessEqual[z, -2e-200], N[(b * c), $MachinePrecision], If[LessEqual[z, -8.5e-275], t$95$2, If[LessEqual[z, 2.4e-42], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+118], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.59999999999999993e-32 or 4.2e118 < z

   1. Initial program 85.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{x}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right) \]

      6. *-lowering-*.f64 48.1%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right) \]

   7. Simplified 48.1%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]

   if -3.59999999999999993e-32 < z < -2e-200

   1. Initial program 82.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 82.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 30.3%

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

   7. Simplified 30.3%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -2e-200 < z < -8.49999999999999952e-275 or 2.40000000000000003e-42 < z < 4.2e118

   1. Initial program 81.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 81.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 44.2%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 44.2%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

   if -8.49999999999999952e-275 < z < 2.40000000000000003e-42

   1. Initial program 90.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 90.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   6. Applied egg-rr 92.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(-4 \cdot i\right) + \left(b \cdot c + t \cdot \left(x \cdot \left(18 \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\right)\right) - j \cdot \left(k \cdot 27\right)} \]

   7. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(j \cdot k\right) \cdot \color{blue}{-27} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(j \cdot k\right), \color{blue}{-27}\right) \]

      3. *-lowering-*.f64 35.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, k\right), -27\right) \]

   9. Simplified 35.6%

      \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-32}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-200}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-275}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-42}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+118}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \left(x \cdot \left(18 \cdot \left(y \cdot t\right)\right)\right) - t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-181}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{-63}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (* t (+ (* a -4.0) (* x (* 18.0 (* y z)))))))
   (if (<= t -1.7e+81)
     t_2
     (if (<= t -2e-150)
       (- (* z (* x (* 18.0 (* y t)))) t_1)
       (if (<= t 8.5e-181)
         (+ (* b c) (* x (* i -4.0)))
         (if (<= t 1.72e-63) (- (* -4.0 (* x i)) 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 k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	double tmp;
	if (t <= -1.7e+81) {
		tmp = t_2;
	} else if (t <= -2e-150) {
		tmp = (z * (x * (18.0 * (y * t)))) - t_1;
	} else if (t <= 8.5e-181) {
		tmp = (b * c) + (x * (i * -4.0));
	} else if (t <= 1.72e-63) {
		tmp = (-4.0 * (x * i)) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = t * ((a * (-4.0d0)) + (x * (18.0d0 * (y * z))))
    if (t <= (-1.7d+81)) then
        tmp = t_2
    else if (t <= (-2d-150)) then
        tmp = (z * (x * (18.0d0 * (y * t)))) - t_1
    else if (t <= 8.5d-181) then
        tmp = (b * c) + (x * (i * (-4.0d0)))
    else if (t <= 1.72d-63) then
        tmp = ((-4.0d0) * (x * i)) - 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 k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	double tmp;
	if (t <= -1.7e+81) {
		tmp = t_2;
	} else if (t <= -2e-150) {
		tmp = (z * (x * (18.0 * (y * t)))) - t_1;
	} else if (t <= 8.5e-181) {
		tmp = (b * c) + (x * (i * -4.0));
	} else if (t <= 1.72e-63) {
		tmp = (-4.0 * (x * i)) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))))
	tmp = 0
	if t <= -1.7e+81:
		tmp = t_2
	elif t <= -2e-150:
		tmp = (z * (x * (18.0 * (y * t)))) - t_1
	elif t <= 8.5e-181:
		tmp = (b * c) + (x * (i * -4.0))
	elif t <= 1.72e-63:
		tmp = (-4.0 * (x * i)) - t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(t * Float64(Float64(a * -4.0) + Float64(x * Float64(18.0 * Float64(y * z)))))
	tmp = 0.0
	if (t <= -1.7e+81)
		tmp = t_2;
	elseif (t <= -2e-150)
		tmp = Float64(Float64(z * Float64(x * Float64(18.0 * Float64(y * t)))) - t_1);
	elseif (t <= 8.5e-181)
		tmp = Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)));
	elseif (t <= 1.72e-63)
		tmp = Float64(Float64(-4.0 * Float64(x * i)) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	tmp = 0.0;
	if (t <= -1.7e+81)
		tmp = t_2;
	elseif (t <= -2e-150)
		tmp = (z * (x * (18.0 * (y * t)))) - t_1;
	elseif (t <= 8.5e-181)
		tmp = (b * c) + (x * (i * -4.0));
	elseif (t <= 1.72e-63)
		tmp = (-4.0 * (x * i)) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+81], t$95$2, If[LessEqual[t, -2e-150], N[(N[(z * N[(x * N[(18.0 * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 8.5e-181], N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.72e-63], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.70000000000000001e81 or 1.71999999999999989e-63 < t

   1. Initial program 87.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot a\right), \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\color{blue}{18} \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 71.5%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 71.5%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)} \]

   if -1.70000000000000001e81 < t < -2.00000000000000001e-150

   1. Initial program 81.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-lowering-*.f64 61.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 61.4%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right) \cdot x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot \left(\left(18 \cdot t\right) \cdot y\right)\right) \cdot z\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(x \cdot \left(\left(18 \cdot t\right) \cdot y\right)\right), z\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(\left(18 \cdot t\right) \cdot y\right)\right), z\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(18 \cdot \left(t \cdot y\right)\right)\right), z\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \left(t \cdot y\right)\right)\right), z\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. *-lowering-*.f64 63.4%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, y\right)\right)\right), z\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   7. Applied egg-rr 63.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(18 \cdot \left(t \cdot y\right)\right)\right) \cdot z} - \left(j \cdot 27\right) \cdot k \]

   if -2.00000000000000001e-150 < t < 8.49999999999999953e-181

   1. Initial program 89.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 95.2%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(-4 \cdot i + \left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{x} \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 76.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 76.4%

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

   9. Taylor expanded in t around 0

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

       1. +-commutative N/A

          \[\leadsto b \cdot c + \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

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

          \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot i\right) \cdot \color{blue}{x}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

       7. *-lowering-*.f64 73.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, \color{blue}{i}\right)\right)\right) \]

   11. Simplified 73.3%

       \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i\right)} \]

   if 8.49999999999999953e-181 < t < 1.71999999999999989e-63

   1. Initial program 82.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-lowering-*.f64 72.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 72.3%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \left(x \cdot \left(18 \cdot \left(y \cdot t\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-181}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{-63}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-150}:\\ \;\;\;\;\left(18 \cdot \left(y \cdot t\right)\right) \cdot \left(x \cdot z\right) - t\_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-181}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{-63}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (* t (+ (* a -4.0) (* x (* 18.0 (* y z)))))))
   (if (<= t -3.7e+87)
     t_2
     (if (<= t -4e-150)
       (- (* (* 18.0 (* y t)) (* x z)) t_1)
       (if (<= t 4.8e-181)
         (+ (* b c) (* x (* i -4.0)))
         (if (<= t 1.72e-63) (- (* -4.0 (* x i)) 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 k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	double tmp;
	if (t <= -3.7e+87) {
		tmp = t_2;
	} else if (t <= -4e-150) {
		tmp = ((18.0 * (y * t)) * (x * z)) - t_1;
	} else if (t <= 4.8e-181) {
		tmp = (b * c) + (x * (i * -4.0));
	} else if (t <= 1.72e-63) {
		tmp = (-4.0 * (x * i)) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = t * ((a * (-4.0d0)) + (x * (18.0d0 * (y * z))))
    if (t <= (-3.7d+87)) then
        tmp = t_2
    else if (t <= (-4d-150)) then
        tmp = ((18.0d0 * (y * t)) * (x * z)) - t_1
    else if (t <= 4.8d-181) then
        tmp = (b * c) + (x * (i * (-4.0d0)))
    else if (t <= 1.72d-63) then
        tmp = ((-4.0d0) * (x * i)) - 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 k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	double tmp;
	if (t <= -3.7e+87) {
		tmp = t_2;
	} else if (t <= -4e-150) {
		tmp = ((18.0 * (y * t)) * (x * z)) - t_1;
	} else if (t <= 4.8e-181) {
		tmp = (b * c) + (x * (i * -4.0));
	} else if (t <= 1.72e-63) {
		tmp = (-4.0 * (x * i)) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))))
	tmp = 0
	if t <= -3.7e+87:
		tmp = t_2
	elif t <= -4e-150:
		tmp = ((18.0 * (y * t)) * (x * z)) - t_1
	elif t <= 4.8e-181:
		tmp = (b * c) + (x * (i * -4.0))
	elif t <= 1.72e-63:
		tmp = (-4.0 * (x * i)) - t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(t * Float64(Float64(a * -4.0) + Float64(x * Float64(18.0 * Float64(y * z)))))
	tmp = 0.0
	if (t <= -3.7e+87)
		tmp = t_2;
	elseif (t <= -4e-150)
		tmp = Float64(Float64(Float64(18.0 * Float64(y * t)) * Float64(x * z)) - t_1);
	elseif (t <= 4.8e-181)
		tmp = Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)));
	elseif (t <= 1.72e-63)
		tmp = Float64(Float64(-4.0 * Float64(x * i)) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	tmp = 0.0;
	if (t <= -3.7e+87)
		tmp = t_2;
	elseif (t <= -4e-150)
		tmp = ((18.0 * (y * t)) * (x * z)) - t_1;
	elseif (t <= 4.8e-181)
		tmp = (b * c) + (x * (i * -4.0));
	elseif (t <= 1.72e-63)
		tmp = (-4.0 * (x * i)) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+87], t$95$2, If[LessEqual[t, -4e-150], N[(N[(N[(18.0 * N[(y * t), $MachinePrecision]), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 4.8e-181], N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.72e-63], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.70000000000000003e87 or 1.71999999999999989e-63 < t

   1. Initial program 87.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot a\right), \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\color{blue}{18} \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 71.5%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 71.5%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)} \]

   if -3.70000000000000003e87 < t < -4.00000000000000003e-150

   1. Initial program 81.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-lowering-*.f64 61.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 61.4%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right) \cdot x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(\left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot \left(z \cdot \left(\left(18 \cdot t\right) \cdot y\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(x \cdot z\right) \cdot \left(\left(18 \cdot t\right) \cdot y\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(x \cdot z\right), \left(\left(18 \cdot t\right) \cdot y\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, z\right), \left(\left(18 \cdot t\right) \cdot y\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, z\right), \left(18 \cdot \left(t \cdot y\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{*.f64}\left(18, \left(t \cdot y\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. *-lowering-*.f64 63.6%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, y\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   7. Applied egg-rr 63.6%

      \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot \left(18 \cdot \left(t \cdot y\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if -4.00000000000000003e-150 < t < 4.8000000000000002e-181

   1. Initial program 89.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 95.2%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(-4 \cdot i + \left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{x} \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 76.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 76.4%

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

   9. Taylor expanded in t around 0

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

       1. +-commutative N/A

          \[\leadsto b \cdot c + \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

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

          \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot i\right) \cdot \color{blue}{x}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

       7. *-lowering-*.f64 73.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, \color{blue}{i}\right)\right)\right) \]

   11. Simplified 73.3%

       \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i\right)} \]

   if 4.8000000000000002e-181 < t < 1.71999999999999989e-63

   1. Initial program 82.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-lowering-*.f64 72.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 72.3%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-150}:\\ \;\;\;\;\left(18 \cdot \left(y \cdot t\right)\right) \cdot \left(x \cdot z\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-181}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{-63}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-150}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) - t\_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-181}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-66}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (* t (+ (* a -4.0) (* x (* 18.0 (* y z)))))))
   (if (<= t -2.4e+81)
     t_2
     (if (<= t -1.4e-150)
       (- (* 18.0 (* x (* t (* y z)))) t_1)
       (if (<= t 9.5e-181)
         (+ (* b c) (* x (* i -4.0)))
         (if (<= t 4.2e-66) (- (* -4.0 (* x i)) 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 k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	double tmp;
	if (t <= -2.4e+81) {
		tmp = t_2;
	} else if (t <= -1.4e-150) {
		tmp = (18.0 * (x * (t * (y * z)))) - t_1;
	} else if (t <= 9.5e-181) {
		tmp = (b * c) + (x * (i * -4.0));
	} else if (t <= 4.2e-66) {
		tmp = (-4.0 * (x * i)) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = t * ((a * (-4.0d0)) + (x * (18.0d0 * (y * z))))
    if (t <= (-2.4d+81)) then
        tmp = t_2
    else if (t <= (-1.4d-150)) then
        tmp = (18.0d0 * (x * (t * (y * z)))) - t_1
    else if (t <= 9.5d-181) then
        tmp = (b * c) + (x * (i * (-4.0d0)))
    else if (t <= 4.2d-66) then
        tmp = ((-4.0d0) * (x * i)) - 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 k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	double tmp;
	if (t <= -2.4e+81) {
		tmp = t_2;
	} else if (t <= -1.4e-150) {
		tmp = (18.0 * (x * (t * (y * z)))) - t_1;
	} else if (t <= 9.5e-181) {
		tmp = (b * c) + (x * (i * -4.0));
	} else if (t <= 4.2e-66) {
		tmp = (-4.0 * (x * i)) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))))
	tmp = 0
	if t <= -2.4e+81:
		tmp = t_2
	elif t <= -1.4e-150:
		tmp = (18.0 * (x * (t * (y * z)))) - t_1
	elif t <= 9.5e-181:
		tmp = (b * c) + (x * (i * -4.0))
	elif t <= 4.2e-66:
		tmp = (-4.0 * (x * i)) - t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(t * Float64(Float64(a * -4.0) + Float64(x * Float64(18.0 * Float64(y * z)))))
	tmp = 0.0
	if (t <= -2.4e+81)
		tmp = t_2;
	elseif (t <= -1.4e-150)
		tmp = Float64(Float64(18.0 * Float64(x * Float64(t * Float64(y * z)))) - t_1);
	elseif (t <= 9.5e-181)
		tmp = Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)));
	elseif (t <= 4.2e-66)
		tmp = Float64(Float64(-4.0 * Float64(x * i)) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	tmp = 0.0;
	if (t <= -2.4e+81)
		tmp = t_2;
	elseif (t <= -1.4e-150)
		tmp = (18.0 * (x * (t * (y * z)))) - t_1;
	elseif (t <= 9.5e-181)
		tmp = (b * c) + (x * (i * -4.0));
	elseif (t <= 4.2e-66)
		tmp = (-4.0 * (x * i)) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e+81], t$95$2, If[LessEqual[t, -1.4e-150], N[(N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 9.5e-181], N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-66], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.3999999999999999e81 or 4.2000000000000001e-66 < t

   1. Initial program 87.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot a\right), \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\color{blue}{18} \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 71.5%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 71.5%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)} \]

   if -2.3999999999999999e81 < t < -1.39999999999999998e-150

   1. Initial program 81.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-lowering-*.f64 61.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 61.4%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

   if -1.39999999999999998e-150 < t < 9.49999999999999998e-181

   1. Initial program 89.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 95.2%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(-4 \cdot i + \left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{x} \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 76.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 76.4%

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

   9. Taylor expanded in t around 0

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

       1. +-commutative N/A

          \[\leadsto b \cdot c + \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

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

          \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot i\right) \cdot \color{blue}{x}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

       7. *-lowering-*.f64 73.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, \color{blue}{i}\right)\right)\right) \]

   11. Simplified 73.3%

       \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i\right)} \]

   if 9.49999999999999998e-181 < t < 4.2000000000000001e-66

   1. Initial program 82.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-lowering-*.f64 72.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 72.3%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-150}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-181}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-66}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ t_2 := t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-181}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* -4.0 (* x i)) (* (* j 27.0) k)))
        (t_2 (* t (+ (* a -4.0) (* x (* 18.0 (* y z)))))))
   (if (<= t -1.75e-29)
     t_2
     (if (<= t -1.9e-150)
       t_1
       (if (<= t 7e-181)
         (+ (* b c) (* x (* i -4.0)))
         (if (<= t 8e-65) 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 k) {
	double t_1 = (-4.0 * (x * i)) - ((j * 27.0) * k);
	double t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	double tmp;
	if (t <= -1.75e-29) {
		tmp = t_2;
	} else if (t <= -1.9e-150) {
		tmp = t_1;
	} else if (t <= 7e-181) {
		tmp = (b * c) + (x * (i * -4.0));
	} else if (t <= 8e-65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((-4.0d0) * (x * i)) - ((j * 27.0d0) * k)
    t_2 = t * ((a * (-4.0d0)) + (x * (18.0d0 * (y * z))))
    if (t <= (-1.75d-29)) then
        tmp = t_2
    else if (t <= (-1.9d-150)) then
        tmp = t_1
    else if (t <= 7d-181) then
        tmp = (b * c) + (x * (i * (-4.0d0)))
    else if (t <= 8d-65) 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 k) {
	double t_1 = (-4.0 * (x * i)) - ((j * 27.0) * k);
	double t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	double tmp;
	if (t <= -1.75e-29) {
		tmp = t_2;
	} else if (t <= -1.9e-150) {
		tmp = t_1;
	} else if (t <= 7e-181) {
		tmp = (b * c) + (x * (i * -4.0));
	} else if (t <= 8e-65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (-4.0 * (x * i)) - ((j * 27.0) * k)
	t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))))
	tmp = 0
	if t <= -1.75e-29:
		tmp = t_2
	elif t <= -1.9e-150:
		tmp = t_1
	elif t <= 7e-181:
		tmp = (b * c) + (x * (i * -4.0))
	elif t <= 8e-65:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(-4.0 * Float64(x * i)) - Float64(Float64(j * 27.0) * k))
	t_2 = Float64(t * Float64(Float64(a * -4.0) + Float64(x * Float64(18.0 * Float64(y * z)))))
	tmp = 0.0
	if (t <= -1.75e-29)
		tmp = t_2;
	elseif (t <= -1.9e-150)
		tmp = t_1;
	elseif (t <= 7e-181)
		tmp = Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)));
	elseif (t <= 8e-65)
		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, k)
	t_1 = (-4.0 * (x * i)) - ((j * 27.0) * k);
	t_2 = t * ((a * -4.0) + (x * (18.0 * (y * z))));
	tmp = 0.0;
	if (t <= -1.75e-29)
		tmp = t_2;
	elseif (t <= -1.9e-150)
		tmp = t_1;
	elseif (t <= 7e-181)
		tmp = (b * c) + (x * (i * -4.0));
	elseif (t <= 8e-65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(a * -4.0), $MachinePrecision] + N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.75e-29], t$95$2, If[LessEqual[t, -1.9e-150], t$95$1, If[LessEqual[t, 7e-181], N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-65], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7499999999999999e-29 or 7.99999999999999939e-65 < t

   1. Initial program 85.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(-4 \cdot a\right), \color{blue}{\left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\color{blue}{18} \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{18}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot 18\right)}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \left(x \cdot \left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 67.5%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, a\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 67.5%

      \[\leadsto \color{blue}{t \cdot \left(-4 \cdot a + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)} \]

   if -1.7499999999999999e-29 < t < -1.8999999999999999e-150 or 6.99999999999999993e-181 < t < 7.99999999999999939e-65

   1. Initial program 83.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-lowering-*.f64 69.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 69.7%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

   if -1.8999999999999999e-150 < t < 6.99999999999999993e-181

   1. Initial program 89.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 95.2%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(-4 \cdot i + \left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{x} \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 76.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 76.4%

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

   9. Taylor expanded in t around 0

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

       1. +-commutative N/A

          \[\leadsto b \cdot c + \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

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

          \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot i\right) \cdot \color{blue}{x}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

       7. *-lowering-*.f64 73.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, \color{blue}{i}\right)\right)\right) \]

   11. Simplified 73.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-29}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-150}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-181}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-65}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-87}:\\ \;\;\;\;b \cdot c + t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+111}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(i \cdot -4\right)\right) + -27 \cdot \left(j \cdot k\right)\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(i \cdot -4 + z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z -1.8e-87)
   (+ (* b c) (* t (+ (* (* (* x 18.0) y) z) (* a -4.0))))
   (if (<= z 1.85e+111)
     (+ (+ (+ (* b c) (* x (* i -4.0))) (* -27.0 (* j k))) (* t (* a -4.0)))
     (-
      (+ (* b c) (* x (+ (* i -4.0) (* z (* y (* 18.0 t))))))
      (* (* j 27.0) k)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= -1.8e-87) {
		tmp = (b * c) + (t * ((((x * 18.0) * y) * z) + (a * -4.0)));
	} else if (z <= 1.85e+111) {
		tmp = (((b * c) + (x * (i * -4.0))) + (-27.0 * (j * k))) + (t * (a * -4.0));
	} else {
		tmp = ((b * c) + (x * ((i * -4.0) + (z * (y * (18.0 * t)))))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: tmp
    if (z <= (-1.8d-87)) then
        tmp = (b * c) + (t * ((((x * 18.0d0) * y) * z) + (a * (-4.0d0))))
    else if (z <= 1.85d+111) then
        tmp = (((b * c) + (x * (i * (-4.0d0)))) + ((-27.0d0) * (j * k))) + (t * (a * (-4.0d0)))
    else
        tmp = ((b * c) + (x * ((i * (-4.0d0)) + (z * (y * (18.0d0 * t)))))) - ((j * 27.0d0) * k)
    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 k) {
	double tmp;
	if (z <= -1.8e-87) {
		tmp = (b * c) + (t * ((((x * 18.0) * y) * z) + (a * -4.0)));
	} else if (z <= 1.85e+111) {
		tmp = (((b * c) + (x * (i * -4.0))) + (-27.0 * (j * k))) + (t * (a * -4.0));
	} else {
		tmp = ((b * c) + (x * ((i * -4.0) + (z * (y * (18.0 * t)))))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if z <= -1.8e-87:
		tmp = (b * c) + (t * ((((x * 18.0) * y) * z) + (a * -4.0)))
	elif z <= 1.85e+111:
		tmp = (((b * c) + (x * (i * -4.0))) + (-27.0 * (j * k))) + (t * (a * -4.0))
	else:
		tmp = ((b * c) + (x * ((i * -4.0) + (z * (y * (18.0 * t)))))) - ((j * 27.0) * k)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= -1.8e-87)
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(Float64(x * 18.0) * y) * z) + Float64(a * -4.0))));
	elseif (z <= 1.85e+111)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(x * Float64(i * -4.0))) + Float64(-27.0 * Float64(j * k))) + Float64(t * Float64(a * -4.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(i * -4.0) + Float64(z * Float64(y * Float64(18.0 * t)))))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (z <= -1.8e-87)
		tmp = (b * c) + (t * ((((x * 18.0) * y) * z) + (a * -4.0)));
	elseif (z <= 1.85e+111)
		tmp = (((b * c) + (x * (i * -4.0))) + (-27.0 * (j * k))) + (t * (a * -4.0));
	else
		tmp = ((b * c) + (x * ((i * -4.0) + (z * (y * (18.0 * t)))))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, -1.8e-87], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+111], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(z * N[(y * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999996e-87

   1. Initial program 85.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \color{blue}{\left(b \cdot c\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 78.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right) \]

   7. Simplified 78.2%

      \[\leadsto t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \color{blue}{b \cdot c} \]

   if -1.79999999999999996e-87 < z < 1.8500000000000001e111

   1. Initial program 86.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 86.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 84.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 84.1%

      \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a\right)} + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right) \]

   if 1.8500000000000001e111 < z

   1. Initial program 84.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 84.7%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(-4 \cdot i + \left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-87}:\\ \;\;\;\;b \cdot c + t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+111}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(i \cdot -4\right)\right) + -27 \cdot \left(j \cdot k\right)\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(i \cdot -4 + z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+45}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(i \cdot -4\right)\right) + -27 \cdot \left(j \cdot k\right)\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* x (+ (* i -4.0) (* 18.0 (* t (* y z))))))))
   (if (<= x -3.4e+62)
     t_1
     (if (<= x 2.15e+45)
       (+ (+ (+ (* b c) (* x (* i -4.0))) (* -27.0 (* j k))) (* t (* a -4.0)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (x * ((i * -4.0) + (18.0 * (t * (y * z)))));
	double tmp;
	if (x <= -3.4e+62) {
		tmp = t_1;
	} else if (x <= 2.15e+45) {
		tmp = (((b * c) + (x * (i * -4.0))) + (-27.0 * (j * k))) + (t * (a * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + (x * ((i * (-4.0d0)) + (18.0d0 * (t * (y * z)))))
    if (x <= (-3.4d+62)) then
        tmp = t_1
    else if (x <= 2.15d+45) then
        tmp = (((b * c) + (x * (i * (-4.0d0)))) + ((-27.0d0) * (j * k))) + (t * (a * (-4.0d0)))
    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 k) {
	double t_1 = (b * c) + (x * ((i * -4.0) + (18.0 * (t * (y * z)))));
	double tmp;
	if (x <= -3.4e+62) {
		tmp = t_1;
	} else if (x <= 2.15e+45) {
		tmp = (((b * c) + (x * (i * -4.0))) + (-27.0 * (j * k))) + (t * (a * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (x * ((i * -4.0) + (18.0 * (t * (y * z)))))
	tmp = 0
	if x <= -3.4e+62:
		tmp = t_1
	elif x <= 2.15e+45:
		tmp = (((b * c) + (x * (i * -4.0))) + (-27.0 * (j * k))) + (t * (a * -4.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(t * Float64(y * z))))))
	tmp = 0.0
	if (x <= -3.4e+62)
		tmp = t_1;
	elseif (x <= 2.15e+45)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(x * Float64(i * -4.0))) + Float64(-27.0 * Float64(j * k))) + Float64(t * Float64(a * -4.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (x * ((i * -4.0) + (18.0 * (t * (y * z)))));
	tmp = 0.0;
	if (x <= -3.4e+62)
		tmp = t_1;
	elseif (x <= 2.15e+45)
		tmp = (((b * c) + (x * (i * -4.0))) + (-27.0 * (j * k))) + (t * (a * -4.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e+62], t$95$1, If[LessEqual[x, 2.15e+45], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.40000000000000014e62 or 2.1500000000000002e45 < x

   1. Initial program 77.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 91.7%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(-4 \cdot i + \left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{x} \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 88.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 88.9%

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

   if -3.40000000000000014e62 < x < 2.1500000000000002e45

   1. Initial program 92.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \color{blue}{\left(-4 \cdot a\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \mathsf{*.f64}\left(j, k\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 81.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(-4, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(-27, \color{blue}{\mathsf{*.f64}\left(j, k\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(i, -4\right)\right)\right)\right)\right) \]

   7. Simplified 81.9%

      \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a\right)} + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+62}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+45}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(i \cdot -4\right)\right) + -27 \cdot \left(j \cdot k\right)\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 46.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+41}:\\ \;\;\;\;\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-260}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+15}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+130}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(x \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z -5.9e+41)
   (* (* 18.0 t) (* y (* x z)))
   (if (<= z -3.1e-260)
     (+ (* b c) (* -4.0 (* t a)))
     (if (<= z 1.9e+15)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= z 5.5e+130)
         (+ (* b c) (* x (* i -4.0)))
         (* 18.0 (* z (* x (* y t)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= -5.9e+41) {
		tmp = (18.0 * t) * (y * (x * z));
	} else if (z <= -3.1e-260) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (z <= 1.9e+15) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (z <= 5.5e+130) {
		tmp = (b * c) + (x * (i * -4.0));
	} else {
		tmp = 18.0 * (z * (x * (y * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: tmp
    if (z <= (-5.9d+41)) then
        tmp = (18.0d0 * t) * (y * (x * z))
    else if (z <= (-3.1d-260)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (z <= 1.9d+15) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (z <= 5.5d+130) then
        tmp = (b * c) + (x * (i * (-4.0d0)))
    else
        tmp = 18.0d0 * (z * (x * (y * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= -5.9e+41) {
		tmp = (18.0 * t) * (y * (x * z));
	} else if (z <= -3.1e-260) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (z <= 1.9e+15) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (z <= 5.5e+130) {
		tmp = (b * c) + (x * (i * -4.0));
	} else {
		tmp = 18.0 * (z * (x * (y * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if z <= -5.9e+41:
		tmp = (18.0 * t) * (y * (x * z))
	elif z <= -3.1e-260:
		tmp = (b * c) + (-4.0 * (t * a))
	elif z <= 1.9e+15:
		tmp = (b * c) - (27.0 * (j * k))
	elif z <= 5.5e+130:
		tmp = (b * c) + (x * (i * -4.0))
	else:
		tmp = 18.0 * (z * (x * (y * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= -5.9e+41)
		tmp = Float64(Float64(18.0 * t) * Float64(y * Float64(x * z)));
	elseif (z <= -3.1e-260)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (z <= 1.9e+15)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (z <= 5.5e+130)
		tmp = Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)));
	else
		tmp = Float64(18.0 * Float64(z * Float64(x * Float64(y * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (z <= -5.9e+41)
		tmp = (18.0 * t) * (y * (x * z));
	elseif (z <= -3.1e-260)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (z <= 1.9e+15)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (z <= 5.5e+130)
		tmp = (b * c) + (x * (i * -4.0));
	else
		tmp = 18.0 * (z * (x * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, -5.9e+41], N[(N[(18.0 * t), $MachinePrecision] * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e-260], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+15], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+130], N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(18.0 * N[(z * N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.9000000000000001e41

   1. Initial program 86.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 89.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{x}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right) \]

      6. *-lowering-*.f64 51.1%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right) \]

   7. Simplified 51.1%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(18 \cdot t\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(18 \cdot t\right), \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(\color{blue}{\left(y \cdot z\right)} \cdot x\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(y \cdot \color{blue}{\left(z \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(y \cdot \left(x \cdot \color{blue}{z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      8. *-lowering-*.f64 54.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   9. Applied egg-rr 54.2%

      \[\leadsto \color{blue}{\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)} \]

   if -5.9000000000000001e41 < z < -3.09999999999999983e-260

   1. Initial program 82.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot a\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(a \cdot -4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(a \cdot \left(-4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      9. *-lowering-*.f64 59.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(-4, t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 59.1%

      \[\leadsto \color{blue}{\left(b \cdot c + a \cdot \left(-4 \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

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

      1. +-commutative N/A

         \[\leadsto b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(a \cdot t\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot \color{blue}{a}\right)\right)\right) \]

      6. *-lowering-*.f64 41.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   8. Simplified 41.3%

      \[\leadsto \color{blue}{b \cdot c + -4 \cdot \left(t \cdot a\right)} \]

   if -3.09999999999999983e-260 < z < 1.9e15

   1. Initial program 89.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 49.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 49.8%

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(j \cdot \color{blue}{\left(27 \cdot k\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(j \cdot \left(k \cdot \color{blue}{27}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(j \cdot k\right) \cdot \color{blue}{27}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(j \cdot k\right), \color{blue}{27}\right)\right) \]

      5. *-lowering-*.f64 49.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, k\right), 27\right)\right) \]

   7. Applied egg-rr 49.9%

      \[\leadsto b \cdot c - \color{blue}{\left(j \cdot k\right) \cdot 27} \]

   if 1.9e15 < z < 5.4999999999999997e130

   1. Initial program 89.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 94.5%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(-4 \cdot i + \left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{x} \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 73.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 73.2%

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

   9. Taylor expanded in t around 0

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

       1. +-commutative N/A

          \[\leadsto b \cdot c + \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

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

          \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot i\right) \cdot \color{blue}{x}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

       7. *-lowering-*.f64 53.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, \color{blue}{i}\right)\right)\right) \]

   11. Simplified 53.3%

       \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i\right)} \]

   if 5.4999999999999997e130 < z

   1. Initial program 83.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 91.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{x}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right) \]

      6. *-lowering-*.f64 49.1%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right) \]

   7. Simplified 49.1%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(x \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(x \cdot \left(\left(t \cdot y\right) \cdot \color{blue}{z}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(x \cdot \left(t \cdot y\right)\right) \cdot \color{blue}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(x \cdot \left(t \cdot y\right)\right), \color{blue}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(t \cdot y\right)\right), z\right)\right) \]

      6. *-lowering-*.f64 50.8%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, y\right)\right), z\right)\right) \]

   9. Applied egg-rr 50.8%

      \[\leadsto 18 \cdot \color{blue}{\left(\left(x \cdot \left(t \cdot y\right)\right) \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+41}:\\ \;\;\;\;\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-260}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+15}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+130}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(x \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 45.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+40}:\\ \;\;\;\;\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-259}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+15}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+130}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(x \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z -4.4e+40)
   (* (* 18.0 t) (* y (* x z)))
   (if (<= z -3.8e-259)
     (+ (* b c) (* -4.0 (* t a)))
     (if (<= z 1.7e+15)
       (- (* b c) (* (* j 27.0) k))
       (if (<= z 3.8e+130)
         (+ (* b c) (* x (* i -4.0)))
         (* 18.0 (* z (* x (* y t)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= -4.4e+40) {
		tmp = (18.0 * t) * (y * (x * z));
	} else if (z <= -3.8e-259) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (z <= 1.7e+15) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (z <= 3.8e+130) {
		tmp = (b * c) + (x * (i * -4.0));
	} else {
		tmp = 18.0 * (z * (x * (y * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: tmp
    if (z <= (-4.4d+40)) then
        tmp = (18.0d0 * t) * (y * (x * z))
    else if (z <= (-3.8d-259)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (z <= 1.7d+15) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else if (z <= 3.8d+130) then
        tmp = (b * c) + (x * (i * (-4.0d0)))
    else
        tmp = 18.0d0 * (z * (x * (y * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= -4.4e+40) {
		tmp = (18.0 * t) * (y * (x * z));
	} else if (z <= -3.8e-259) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (z <= 1.7e+15) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (z <= 3.8e+130) {
		tmp = (b * c) + (x * (i * -4.0));
	} else {
		tmp = 18.0 * (z * (x * (y * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if z <= -4.4e+40:
		tmp = (18.0 * t) * (y * (x * z))
	elif z <= -3.8e-259:
		tmp = (b * c) + (-4.0 * (t * a))
	elif z <= 1.7e+15:
		tmp = (b * c) - ((j * 27.0) * k)
	elif z <= 3.8e+130:
		tmp = (b * c) + (x * (i * -4.0))
	else:
		tmp = 18.0 * (z * (x * (y * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= -4.4e+40)
		tmp = Float64(Float64(18.0 * t) * Float64(y * Float64(x * z)));
	elseif (z <= -3.8e-259)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (z <= 1.7e+15)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (z <= 3.8e+130)
		tmp = Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)));
	else
		tmp = Float64(18.0 * Float64(z * Float64(x * Float64(y * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (z <= -4.4e+40)
		tmp = (18.0 * t) * (y * (x * z));
	elseif (z <= -3.8e-259)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (z <= 1.7e+15)
		tmp = (b * c) - ((j * 27.0) * k);
	elseif (z <= 3.8e+130)
		tmp = (b * c) + (x * (i * -4.0));
	else
		tmp = 18.0 * (z * (x * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, -4.4e+40], N[(N[(18.0 * t), $MachinePrecision] * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-259], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+15], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+130], N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(18.0 * N[(z * N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.3999999999999998e40

   1. Initial program 86.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 89.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{x}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right) \]

      6. *-lowering-*.f64 51.1%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right) \]

   7. Simplified 51.1%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(18 \cdot t\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(18 \cdot t\right), \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(\color{blue}{\left(y \cdot z\right)} \cdot x\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(y \cdot \color{blue}{\left(z \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(y \cdot \left(x \cdot \color{blue}{z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      8. *-lowering-*.f64 54.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   9. Applied egg-rr 54.2%

      \[\leadsto \color{blue}{\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)} \]

   if -4.3999999999999998e40 < z < -3.8e-259

   1. Initial program 82.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot a\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(a \cdot -4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(a \cdot \left(-4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      9. *-lowering-*.f64 59.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(-4, t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 59.1%

      \[\leadsto \color{blue}{\left(b \cdot c + a \cdot \left(-4 \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

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

      1. +-commutative N/A

         \[\leadsto b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(a \cdot t\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot \color{blue}{a}\right)\right)\right) \]

      6. *-lowering-*.f64 41.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   8. Simplified 41.3%

      \[\leadsto \color{blue}{b \cdot c + -4 \cdot \left(t \cdot a\right)} \]

   if -3.8e-259 < z < 1.7e15

   1. Initial program 89.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 49.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 49.8%

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]

   if 1.7e15 < z < 3.8000000000000002e130

   1. Initial program 89.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 94.5%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(-4 \cdot i + \left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{x} \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 73.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 73.2%

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

   9. Taylor expanded in t around 0

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

       1. +-commutative N/A

          \[\leadsto b \cdot c + \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

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

          \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot i\right) \cdot \color{blue}{x}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

       7. *-lowering-*.f64 53.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, \color{blue}{i}\right)\right)\right) \]

   11. Simplified 53.3%

       \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i\right)} \]

   if 3.8000000000000002e130 < z

   1. Initial program 83.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 91.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{x}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right) \]

      6. *-lowering-*.f64 49.1%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right) \]

   7. Simplified 49.1%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(x \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(x \cdot \left(\left(t \cdot y\right) \cdot \color{blue}{z}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(x \cdot \left(t \cdot y\right)\right) \cdot \color{blue}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(x \cdot \left(t \cdot y\right)\right), \color{blue}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(t \cdot y\right)\right), z\right)\right) \]

      6. *-lowering-*.f64 50.8%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, y\right)\right), z\right)\right) \]

   9. Applied egg-rr 50.8%

      \[\leadsto 18 \cdot \color{blue}{\left(\left(x \cdot \left(t \cdot y\right)\right) \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+40}:\\ \;\;\;\;\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-259}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+15}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+130}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(x \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 46.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+45}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+164}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+239}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -5.2e+113)
   (* x (* 18.0 (* z (* y t))))
   (if (<= x 1.7e+45)
     (+ (* b c) (* -4.0 (* t a)))
     (if (<= x 4e+164)
       (* 18.0 (* x (* t (* y z))))
       (if (<= x 1.6e+239) (* -4.0 (* x i)) (* (* 18.0 t) (* y (* x z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -5.2e+113) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if (x <= 1.7e+45) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 4e+164) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (x <= 1.6e+239) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = (18.0 * t) * (y * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: tmp
    if (x <= (-5.2d+113)) then
        tmp = x * (18.0d0 * (z * (y * t)))
    else if (x <= 1.7d+45) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (x <= 4d+164) then
        tmp = 18.0d0 * (x * (t * (y * z)))
    else if (x <= 1.6d+239) then
        tmp = (-4.0d0) * (x * i)
    else
        tmp = (18.0d0 * t) * (y * (x * 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 k) {
	double tmp;
	if (x <= -5.2e+113) {
		tmp = x * (18.0 * (z * (y * t)));
	} else if (x <= 1.7e+45) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (x <= 4e+164) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (x <= 1.6e+239) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = (18.0 * t) * (y * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -5.2e+113:
		tmp = x * (18.0 * (z * (y * t)))
	elif x <= 1.7e+45:
		tmp = (b * c) + (-4.0 * (t * a))
	elif x <= 4e+164:
		tmp = 18.0 * (x * (t * (y * z)))
	elif x <= 1.6e+239:
		tmp = -4.0 * (x * i)
	else:
		tmp = (18.0 * t) * (y * (x * z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -5.2e+113)
		tmp = Float64(x * Float64(18.0 * Float64(z * Float64(y * t))));
	elseif (x <= 1.7e+45)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 4e+164)
		tmp = Float64(18.0 * Float64(x * Float64(t * Float64(y * z))));
	elseif (x <= 1.6e+239)
		tmp = Float64(-4.0 * Float64(x * i));
	else
		tmp = Float64(Float64(18.0 * t) * Float64(y * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -5.2e+113)
		tmp = x * (18.0 * (z * (y * t)));
	elseif (x <= 1.7e+45)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (x <= 4e+164)
		tmp = 18.0 * (x * (t * (y * z)));
	elseif (x <= 1.6e+239)
		tmp = -4.0 * (x * i);
	else
		tmp = (18.0 * t) * (y * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -5.2e+113], N[(x * N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+45], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e+164], N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+239], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], N[(N[(18.0 * t), $MachinePrecision] * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -5.1999999999999998e113

   1. Initial program 67.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 70.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{x}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right) \]

      6. *-lowering-*.f64 60.6%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right) \]

   7. Simplified 60.6%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot \color{blue}{x} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right), \color{blue}{x}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(t \cdot \left(y \cdot z\right)\right)\right), x\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(\left(t \cdot y\right) \cdot z\right)\right), x\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \left(z \cdot \left(t \cdot y\right)\right)\right), x\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(z, \left(t \cdot y\right)\right)\right), x\right) \]

      7. *-lowering-*.f64 60.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(t, y\right)\right)\right), x\right) \]

   9. Applied egg-rr 60.7%

      \[\leadsto \color{blue}{\left(18 \cdot \left(z \cdot \left(t \cdot y\right)\right)\right) \cdot x} \]

   if -5.1999999999999998e113 < x < 1.7e45

   1. Initial program 91.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot a\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(a \cdot -4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(a \cdot \left(-4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      9. *-lowering-*.f64 69.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(-4, t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 69.6%

      \[\leadsto \color{blue}{\left(b \cdot c + a \cdot \left(-4 \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

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

      1. +-commutative N/A

         \[\leadsto b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(a \cdot t\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot \color{blue}{a}\right)\right)\right) \]

      6. *-lowering-*.f64 47.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   8. Simplified 47.1%

      \[\leadsto \color{blue}{b \cdot c + -4 \cdot \left(t \cdot a\right)} \]

   if 1.7e45 < x < 4e164

   1. Initial program 86.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{x}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right) \]

      6. *-lowering-*.f64 64.3%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right) \]

   7. Simplified 64.3%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]

   if 4e164 < x < 1.6000000000000001e239

   1. Initial program 87.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 80.2%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 80.2%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

   if 1.6000000000000001e239 < x

   1. Initial program 73.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 79.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{x}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right) \]

      6. *-lowering-*.f64 51.0%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right) \]

   7. Simplified 51.0%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(18 \cdot t\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(18 \cdot t\right), \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(\color{blue}{\left(y \cdot z\right)} \cdot x\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(y \cdot \color{blue}{\left(z \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(y \cdot \left(x \cdot \color{blue}{z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      8. *-lowering-*.f64 63.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   9. Applied egg-rr 63.3%

      \[\leadsto \color{blue}{\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+45}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+164}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+239}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4 + z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{if}\;x \leq -3 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-212}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+36}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (+ (* i -4.0) (* z (* y (* 18.0 t)))))))
   (if (<= x -3e+65)
     t_1
     (if (<= x 7e-212)
       (- (* a (* t -4.0)) (* (* j 27.0) k))
       (if (<= x 4.9e+36) (- (* b c) (* j (* 27.0 k))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((i * -4.0) + (z * (y * (18.0 * t))));
	double tmp;
	if (x <= -3e+65) {
		tmp = t_1;
	} else if (x <= 7e-212) {
		tmp = (a * (t * -4.0)) - ((j * 27.0) * k);
	} else if (x <= 4.9e+36) {
		tmp = (b * c) - (j * (27.0 * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((i * (-4.0d0)) + (z * (y * (18.0d0 * t))))
    if (x <= (-3d+65)) then
        tmp = t_1
    else if (x <= 7d-212) then
        tmp = (a * (t * (-4.0d0))) - ((j * 27.0d0) * k)
    else if (x <= 4.9d+36) then
        tmp = (b * c) - (j * (27.0d0 * k))
    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 k) {
	double t_1 = x * ((i * -4.0) + (z * (y * (18.0 * t))));
	double tmp;
	if (x <= -3e+65) {
		tmp = t_1;
	} else if (x <= 7e-212) {
		tmp = (a * (t * -4.0)) - ((j * 27.0) * k);
	} else if (x <= 4.9e+36) {
		tmp = (b * c) - (j * (27.0 * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((i * -4.0) + (z * (y * (18.0 * t))))
	tmp = 0
	if x <= -3e+65:
		tmp = t_1
	elif x <= 7e-212:
		tmp = (a * (t * -4.0)) - ((j * 27.0) * k)
	elif x <= 4.9e+36:
		tmp = (b * c) - (j * (27.0 * k))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(i * -4.0) + Float64(z * Float64(y * Float64(18.0 * t)))))
	tmp = 0.0
	if (x <= -3e+65)
		tmp = t_1;
	elseif (x <= 7e-212)
		tmp = Float64(Float64(a * Float64(t * -4.0)) - Float64(Float64(j * 27.0) * k));
	elseif (x <= 4.9e+36)
		tmp = Float64(Float64(b * c) - Float64(j * Float64(27.0 * k)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((i * -4.0) + (z * (y * (18.0 * t))));
	tmp = 0.0;
	if (x <= -3e+65)
		tmp = t_1;
	elseif (x <= 7e-212)
		tmp = (a * (t * -4.0)) - ((j * 27.0) * k);
	elseif (x <= 4.9e+36)
		tmp = (b * c) - (j * (27.0 * k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(z * N[(y * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3e+65], t$95$1, If[LessEqual[x, 7e-212], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.9e+36], N[(N[(b * c), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.0000000000000002e65 or 4.89999999999999981e36 < x

   1. Initial program 78.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(\left(18 \cdot t\right) \cdot y\right) \cdot \color{blue}{z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\left(\left(18 \cdot t\right) \cdot y\right), \color{blue}{z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(18 \cdot t\right), y\right), z\right)\right)\right) \]

      8. *-lowering-*.f64 83.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), y\right), z\right)\right)\right) \]

   7. Simplified 83.3%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + \left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)} \]

   if -3.0000000000000002e65 < x < 6.9999999999999995e-212

   1. Initial program 89.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(-4 \cdot a\right) \cdot t\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(a \cdot -4\right) \cdot t\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(a \cdot \left(-4 \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. *-lowering-*.f64 55.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(-4, t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 55.4%

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]

   if 6.9999999999999995e-212 < x < 4.89999999999999981e36

   1. Initial program 95.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 62.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

   5. Simplified 62.8%

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(j \cdot \color{blue}{\left(27 \cdot k\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(j \cdot \left(k \cdot \color{blue}{27}\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(k \cdot 27\right) \cdot \color{blue}{j}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\left(k \cdot 27\right), \color{blue}{j}\right)\right) \]

      5. *-lowering-*.f64 62.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(k, 27\right), j\right)\right) \]

   7. Applied egg-rr 62.8%

      \[\leadsto b \cdot c - \color{blue}{\left(k \cdot 27\right) \cdot j} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-212}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+36}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 76.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-63}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* t (+ (* (* (* x 18.0) y) z) (* a -4.0))))))
   (if (<= t -3.4e-29)
     t_1
     (if (<= t 1.4e-63)
       (- (- (* b c) (* (* x 4.0) i)) (* (* j 27.0) k))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (t * ((((x * 18.0) * y) * z) + (a * -4.0)));
	double tmp;
	if (t <= -3.4e-29) {
		tmp = t_1;
	} else if (t <= 1.4e-63) {
		tmp = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + (t * ((((x * 18.0d0) * y) * z) + (a * (-4.0d0))))
    if (t <= (-3.4d-29)) then
        tmp = t_1
    else if (t <= 1.4d-63) then
        tmp = ((b * c) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    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 k) {
	double t_1 = (b * c) + (t * ((((x * 18.0) * y) * z) + (a * -4.0)));
	double tmp;
	if (t <= -3.4e-29) {
		tmp = t_1;
	} else if (t <= 1.4e-63) {
		tmp = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (t * ((((x * 18.0) * y) * z) + (a * -4.0)))
	tmp = 0
	if t <= -3.4e-29:
		tmp = t_1
	elif t <= 1.4e-63:
		tmp = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(Float64(x * 18.0) * y) * z) + Float64(a * -4.0))))
	tmp = 0.0
	if (t <= -3.4e-29)
		tmp = t_1;
	elseif (t <= 1.4e-63)
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (t * ((((x * 18.0) * y) * z) + (a * -4.0)));
	tmp = 0.0;
	if (t <= -3.4e-29)
		tmp = t_1;
	elseif (t <= 1.4e-63)
		tmp = ((b * c) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e-29], t$95$1, If[LessEqual[t, 1.4e-63], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.39999999999999972e-29 or 1.4000000000000001e-63 < t

   1. Initial program 85.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \color{blue}{\left(b \cdot c\right)}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 77.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{c}\right)\right) \]

   7. Simplified 77.7%

      \[\leadsto t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \color{blue}{b \cdot c} \]

   if -3.39999999999999972e-29 < t < 1.4000000000000001e-63

   1. Initial program 86.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 84.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 4\right), i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 84.3%

      \[\leadsto \left(\color{blue}{b \cdot c} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-29}:\\ \;\;\;\;b \cdot c + t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-63}:\\ \;\;\;\;\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 75.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+18}:\\ \;\;\;\;\left(b \cdot c + a \cdot \left(t \cdot -4\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* x (+ (* i -4.0) (* 18.0 (* t (* y z))))))))
   (if (<= x -3.9e+65)
     t_1
     (if (<= x 1.85e+18)
       (- (+ (* b c) (* a (* t -4.0))) (* (* j 27.0) k))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) + (x * ((i * -4.0) + (18.0 * (t * (y * z)))));
	double tmp;
	if (x <= -3.9e+65) {
		tmp = t_1;
	} else if (x <= 1.85e+18) {
		tmp = ((b * c) + (a * (t * -4.0))) - ((j * 27.0) * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) + (x * ((i * (-4.0d0)) + (18.0d0 * (t * (y * z)))))
    if (x <= (-3.9d+65)) then
        tmp = t_1
    else if (x <= 1.85d+18) then
        tmp = ((b * c) + (a * (t * (-4.0d0)))) - ((j * 27.0d0) * k)
    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 k) {
	double t_1 = (b * c) + (x * ((i * -4.0) + (18.0 * (t * (y * z)))));
	double tmp;
	if (x <= -3.9e+65) {
		tmp = t_1;
	} else if (x <= 1.85e+18) {
		tmp = ((b * c) + (a * (t * -4.0))) - ((j * 27.0) * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (x * ((i * -4.0) + (18.0 * (t * (y * z)))))
	tmp = 0
	if x <= -3.9e+65:
		tmp = t_1
	elif x <= 1.85e+18:
		tmp = ((b * c) + (a * (t * -4.0))) - ((j * 27.0) * k)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(t * Float64(y * z))))))
	tmp = 0.0
	if (x <= -3.9e+65)
		tmp = t_1;
	elseif (x <= 1.85e+18)
		tmp = Float64(Float64(Float64(b * c) + Float64(a * Float64(t * -4.0))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (x * ((i * -4.0) + (18.0 * (t * (y * z)))));
	tmp = 0.0;
	if (x <= -3.9e+65)
		tmp = t_1;
	elseif (x <= 1.85e+18)
		tmp = ((b * c) + (a * (t * -4.0))) - ((j * 27.0) * k);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.9e+65], t$95$1, If[LessEqual[x, 1.85e+18], N[(N[(N[(b * c), $MachinePrecision] + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.8999999999999998e65 or 1.85e18 < x

   1. Initial program 79.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 91.2%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(-4 \cdot i + \left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{x} \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 88.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 88.5%

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

   if -3.8999999999999998e65 < x < 1.85e18

   1. Initial program 91.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot a\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(a \cdot -4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(a \cdot \left(-4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      9. *-lowering-*.f64 73.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(-4, t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 73.2%

      \[\leadsto \color{blue}{\left(b \cdot c + a \cdot \left(-4 \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+65}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+18}:\\ \;\;\;\;\left(b \cdot c + a \cdot \left(t \cdot -4\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 45.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+47}:\\ \;\;\;\;\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-240}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+117}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(x \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z -6.5e+47)
   (* (* 18.0 t) (* y (* x z)))
   (if (<= z -1.2e-240)
     (+ (* b c) (* -4.0 (* t a)))
     (if (<= z 3.5e+117)
       (- (* -4.0 (* x i)) (* (* j 27.0) k))
       (* 18.0 (* z (* x (* y t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= -6.5e+47) {
		tmp = (18.0 * t) * (y * (x * z));
	} else if (z <= -1.2e-240) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (z <= 3.5e+117) {
		tmp = (-4.0 * (x * i)) - ((j * 27.0) * k);
	} else {
		tmp = 18.0 * (z * (x * (y * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: tmp
    if (z <= (-6.5d+47)) then
        tmp = (18.0d0 * t) * (y * (x * z))
    else if (z <= (-1.2d-240)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (z <= 3.5d+117) then
        tmp = ((-4.0d0) * (x * i)) - ((j * 27.0d0) * k)
    else
        tmp = 18.0d0 * (z * (x * (y * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= -6.5e+47) {
		tmp = (18.0 * t) * (y * (x * z));
	} else if (z <= -1.2e-240) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (z <= 3.5e+117) {
		tmp = (-4.0 * (x * i)) - ((j * 27.0) * k);
	} else {
		tmp = 18.0 * (z * (x * (y * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if z <= -6.5e+47:
		tmp = (18.0 * t) * (y * (x * z))
	elif z <= -1.2e-240:
		tmp = (b * c) + (-4.0 * (t * a))
	elif z <= 3.5e+117:
		tmp = (-4.0 * (x * i)) - ((j * 27.0) * k)
	else:
		tmp = 18.0 * (z * (x * (y * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= -6.5e+47)
		tmp = Float64(Float64(18.0 * t) * Float64(y * Float64(x * z)));
	elseif (z <= -1.2e-240)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (z <= 3.5e+117)
		tmp = Float64(Float64(-4.0 * Float64(x * i)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(18.0 * Float64(z * Float64(x * Float64(y * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (z <= -6.5e+47)
		tmp = (18.0 * t) * (y * (x * z));
	elseif (z <= -1.2e-240)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (z <= 3.5e+117)
		tmp = (-4.0 * (x * i)) - ((j * 27.0) * k);
	else
		tmp = 18.0 * (z * (x * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, -6.5e+47], N[(N[(18.0 * t), $MachinePrecision] * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e-240], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+117], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(18.0 * N[(z * N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.49999999999999988e47

   1. Initial program 86.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 89.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{x}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right) \]

      6. *-lowering-*.f64 51.1%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right) \]

   7. Simplified 51.1%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(18 \cdot t\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(18 \cdot t\right), \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(\color{blue}{\left(y \cdot z\right)} \cdot x\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(y \cdot \color{blue}{\left(z \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(y \cdot \left(x \cdot \color{blue}{z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      8. *-lowering-*.f64 54.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   9. Applied egg-rr 54.2%

      \[\leadsto \color{blue}{\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)} \]

   if -6.49999999999999988e47 < z < -1.2e-240

   1. Initial program 83.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot a\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(a \cdot -4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(a \cdot \left(-4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      9. *-lowering-*.f64 58.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(-4, t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 58.7%

      \[\leadsto \color{blue}{\left(b \cdot c + a \cdot \left(-4 \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

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

      1. +-commutative N/A

         \[\leadsto b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(a \cdot t\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot \color{blue}{a}\right)\right)\right) \]

      6. *-lowering-*.f64 41.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   8. Simplified 41.7%

      \[\leadsto \color{blue}{b \cdot c + -4 \cdot \left(t \cdot a\right)} \]

   if -1.2e-240 < z < 3.49999999999999983e117

   1. Initial program 88.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. *-lowering-*.f64 54.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

   5. Simplified 54.9%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]

   if 3.49999999999999983e117 < z

   1. Initial program 84.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{x}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right) \]

      6. *-lowering-*.f64 47.9%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right) \]

   7. Simplified 47.9%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(x \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(x \cdot \left(\left(t \cdot y\right) \cdot \color{blue}{z}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(x \cdot \left(t \cdot y\right)\right) \cdot \color{blue}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(x \cdot \left(t \cdot y\right)\right), \color{blue}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(t \cdot y\right)\right), z\right)\right) \]

      6. *-lowering-*.f64 49.6%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, y\right)\right), z\right)\right) \]

   9. Applied egg-rr 49.6%

      \[\leadsto 18 \cdot \color{blue}{\left(\left(x \cdot \left(t \cdot y\right)\right) \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+47}:\\ \;\;\;\;\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-240}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+117}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(x \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 72.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4 + z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+37}:\\ \;\;\;\;\left(b \cdot c + a \cdot \left(t \cdot -4\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (+ (* i -4.0) (* z (* y (* 18.0 t)))))))
   (if (<= x -3.4e+65)
     t_1
     (if (<= x 1.35e+37)
       (- (+ (* b c) (* a (* t -4.0))) (* (* j 27.0) k))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((i * -4.0) + (z * (y * (18.0 * t))));
	double tmp;
	if (x <= -3.4e+65) {
		tmp = t_1;
	} else if (x <= 1.35e+37) {
		tmp = ((b * c) + (a * (t * -4.0))) - ((j * 27.0) * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((i * (-4.0d0)) + (z * (y * (18.0d0 * t))))
    if (x <= (-3.4d+65)) then
        tmp = t_1
    else if (x <= 1.35d+37) then
        tmp = ((b * c) + (a * (t * (-4.0d0)))) - ((j * 27.0d0) * k)
    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 k) {
	double t_1 = x * ((i * -4.0) + (z * (y * (18.0 * t))));
	double tmp;
	if (x <= -3.4e+65) {
		tmp = t_1;
	} else if (x <= 1.35e+37) {
		tmp = ((b * c) + (a * (t * -4.0))) - ((j * 27.0) * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((i * -4.0) + (z * (y * (18.0 * t))))
	tmp = 0
	if x <= -3.4e+65:
		tmp = t_1
	elif x <= 1.35e+37:
		tmp = ((b * c) + (a * (t * -4.0))) - ((j * 27.0) * k)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(i * -4.0) + Float64(z * Float64(y * Float64(18.0 * t)))))
	tmp = 0.0
	if (x <= -3.4e+65)
		tmp = t_1;
	elseif (x <= 1.35e+37)
		tmp = Float64(Float64(Float64(b * c) + Float64(a * Float64(t * -4.0))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((i * -4.0) + (z * (y * (18.0 * t))));
	tmp = 0.0;
	if (x <= -3.4e+65)
		tmp = t_1;
	elseif (x <= 1.35e+37)
		tmp = ((b * c) + (a * (t * -4.0))) - ((j * 27.0) * k);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(z * N[(y * N[(18.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e+65], t$95$1, If[LessEqual[x, 1.35e+37], N[(N[(N[(b * c), $MachinePrecision] + N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3999999999999999e65 or 1.34999999999999993e37 < x

   1. Initial program 78.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\left(\left(18 \cdot t\right) \cdot y\right) \cdot \color{blue}{z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\left(\left(18 \cdot t\right) \cdot y\right), \color{blue}{z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(18 \cdot t\right), y\right), z\right)\right)\right) \]

      8. *-lowering-*.f64 83.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), y\right), z\right)\right)\right) \]

   7. Simplified 83.3%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i + \left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)} \]

   if -3.3999999999999999e65 < x < 1.34999999999999993e37

   1. Initial program 91.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot a\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(a \cdot -4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(a \cdot \left(-4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      9. *-lowering-*.f64 73.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(-4, t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 73.1%

      \[\leadsto \color{blue}{\left(b \cdot c + a \cdot \left(-4 \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+37}:\\ \;\;\;\;\left(b \cdot c + a \cdot \left(t \cdot -4\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + z \cdot \left(y \cdot \left(18 \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 45.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+48}:\\ \;\;\;\;\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-131}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+130}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(x \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z -1.2e+48)
   (* (* 18.0 t) (* y (* x z)))
   (if (<= z -1.8e-131)
     (+ (* b c) (* -4.0 (* t a)))
     (if (<= z 3.8e+130)
       (+ (* b c) (* x (* i -4.0)))
       (* 18.0 (* z (* x (* y t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= -1.2e+48) {
		tmp = (18.0 * t) * (y * (x * z));
	} else if (z <= -1.8e-131) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (z <= 3.8e+130) {
		tmp = (b * c) + (x * (i * -4.0));
	} else {
		tmp = 18.0 * (z * (x * (y * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: tmp
    if (z <= (-1.2d+48)) then
        tmp = (18.0d0 * t) * (y * (x * z))
    else if (z <= (-1.8d-131)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (z <= 3.8d+130) then
        tmp = (b * c) + (x * (i * (-4.0d0)))
    else
        tmp = 18.0d0 * (z * (x * (y * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= -1.2e+48) {
		tmp = (18.0 * t) * (y * (x * z));
	} else if (z <= -1.8e-131) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (z <= 3.8e+130) {
		tmp = (b * c) + (x * (i * -4.0));
	} else {
		tmp = 18.0 * (z * (x * (y * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if z <= -1.2e+48:
		tmp = (18.0 * t) * (y * (x * z))
	elif z <= -1.8e-131:
		tmp = (b * c) + (-4.0 * (t * a))
	elif z <= 3.8e+130:
		tmp = (b * c) + (x * (i * -4.0))
	else:
		tmp = 18.0 * (z * (x * (y * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= -1.2e+48)
		tmp = Float64(Float64(18.0 * t) * Float64(y * Float64(x * z)));
	elseif (z <= -1.8e-131)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (z <= 3.8e+130)
		tmp = Float64(Float64(b * c) + Float64(x * Float64(i * -4.0)));
	else
		tmp = Float64(18.0 * Float64(z * Float64(x * Float64(y * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (z <= -1.2e+48)
		tmp = (18.0 * t) * (y * (x * z));
	elseif (z <= -1.8e-131)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (z <= 3.8e+130)
		tmp = (b * c) + (x * (i * -4.0));
	else
		tmp = 18.0 * (z * (x * (y * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, -1.2e+48], N[(N[(18.0 * t), $MachinePrecision] * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.8e-131], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+130], N[(N[(b * c), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(18.0 * N[(z * N[(x * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2000000000000001e48

   1. Initial program 86.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 89.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{x}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right) \]

      6. *-lowering-*.f64 51.1%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right) \]

   7. Simplified 51.1%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \left(18 \cdot t\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(18 \cdot t\right), \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(\color{blue}{\left(y \cdot z\right)} \cdot x\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(y \cdot \color{blue}{\left(z \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \left(y \cdot \left(x \cdot \color{blue}{z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      8. *-lowering-*.f64 54.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(18, t\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   9. Applied egg-rr 54.2%

      \[\leadsto \color{blue}{\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)} \]

   if -1.2000000000000001e48 < z < -1.8e-131

   1. Initial program 80.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(-4 \cdot \left(a \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot a\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(a \cdot -4\right) \cdot t\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(a \cdot \left(-4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(a, \left(-4 \cdot t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      9. *-lowering-*.f64 60.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(-4, t\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   5. Simplified 60.8%

      \[\leadsto \color{blue}{\left(b \cdot c + a \cdot \left(-4 \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

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

      1. +-commutative N/A

         \[\leadsto b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(a \cdot t\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(a \cdot t\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \left(t \cdot \color{blue}{a}\right)\right)\right) \]

      6. *-lowering-*.f64 45.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   8. Simplified 45.0%

      \[\leadsto \color{blue}{b \cdot c + -4 \cdot \left(t \cdot a\right)} \]

   if -1.8e-131 < z < 3.8000000000000002e130

   1. Initial program 88.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 81.1%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(-4 \cdot i + \left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{x} \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(\color{blue}{18} \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \color{blue}{\left(y \cdot z\right)}\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 59.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 59.5%

      \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \]

   9. Taylor expanded in t around 0

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

       1. +-commutative N/A

          \[\leadsto b \cdot c + \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

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

          \[\leadsto \mathsf{+.f64}\left(\left(b \cdot c\right), \color{blue}{\left(-4 \cdot \left(i \cdot x\right)\right)}\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(\left(-4 \cdot i\right) \cdot \color{blue}{x}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \color{blue}{\left(-4 \cdot i\right)}\right)\right) \]

       7. *-lowering-*.f64 49.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(-4, \color{blue}{i}\right)\right)\right) \]

   11. Simplified 49.7%

       \[\leadsto \color{blue}{b \cdot c + x \cdot \left(-4 \cdot i\right)} \]

   if 3.8000000000000002e130 < z

   1. Initial program 83.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 91.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(18, \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(t \cdot \left(\left(y \cdot z\right) \cdot \color{blue}{x}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(t \cdot \left(y \cdot z\right)\right), \color{blue}{x}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \left(y \cdot z\right)\right), x\right)\right) \]

      6. *-lowering-*.f64 49.1%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right), x\right)\right) \]

   7. Simplified 49.1%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(x \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(x \cdot \left(\left(t \cdot y\right) \cdot \color{blue}{z}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(18, \left(\left(x \cdot \left(t \cdot y\right)\right) \cdot \color{blue}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\left(x \cdot \left(t \cdot y\right)\right), \color{blue}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(t \cdot y\right)\right), z\right)\right) \]

      6. *-lowering-*.f64 50.8%

         \[\leadsto \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(t, y\right)\right), z\right)\right) \]

   9. Applied egg-rr 50.8%

      \[\leadsto 18 \cdot \color{blue}{\left(\left(x \cdot \left(t \cdot y\right)\right) \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+48}:\\ \;\;\;\;\left(18 \cdot t\right) \cdot \left(y \cdot \left(x \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-131}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+130}:\\ \;\;\;\;b \cdot c + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(x \cdot \left(y \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;i \leq -1.52 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-281}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;i \leq 0.00135:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= i -1.52e+141)
     t_1
     (if (<= i -1.25e-281)
       (* a (* t -4.0))
       (if (<= i 0.00135) (* j (* k -27.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (i <= -1.52e+141) {
		tmp = t_1;
	} else if (i <= -1.25e-281) {
		tmp = a * (t * -4.0);
	} else if (i <= 0.00135) {
		tmp = j * (k * -27.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (x * i)
    if (i <= (-1.52d+141)) then
        tmp = t_1
    else if (i <= (-1.25d-281)) then
        tmp = a * (t * (-4.0d0))
    else if (i <= 0.00135d0) then
        tmp = j * (k * (-27.0d0))
    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 k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (i <= -1.52e+141) {
		tmp = t_1;
	} else if (i <= -1.25e-281) {
		tmp = a * (t * -4.0);
	} else if (i <= 0.00135) {
		tmp = j * (k * -27.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	tmp = 0
	if i <= -1.52e+141:
		tmp = t_1
	elif i <= -1.25e-281:
		tmp = a * (t * -4.0)
	elif i <= 0.00135:
		tmp = j * (k * -27.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (i <= -1.52e+141)
		tmp = t_1;
	elseif (i <= -1.25e-281)
		tmp = Float64(a * Float64(t * -4.0));
	elseif (i <= 0.00135)
		tmp = Float64(j * Float64(k * -27.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	tmp = 0.0;
	if (i <= -1.52e+141)
		tmp = t_1;
	elseif (i <= -1.25e-281)
		tmp = a * (t * -4.0);
	elseif (i <= 0.00135)
		tmp = j * (k * -27.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.52e+141], t$95$1, If[LessEqual[i, -1.25e-281], N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 0.00135], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.52e141 or 0.0013500000000000001 < i

   1. Initial program 83.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 85.9%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 46.6%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 46.6%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

   if -1.52e141 < i < -1.2499999999999999e-281

   1. Initial program 82.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf

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

      1. associate-*r* N/A

         \[\leadsto \left(-4 \cdot a\right) \cdot \color{blue}{t} \]

      2. *-commutative N/A

         \[\leadsto \left(a \cdot -4\right) \cdot t \]

      3. associate-*r* N/A

         \[\leadsto a \cdot \color{blue}{\left(-4 \cdot t\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-4 \cdot t\right)}\right) \]

      5. *-lowering-*.f64 30.9%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(-4, \color{blue}{t}\right)\right) \]

   7. Simplified 30.9%

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot t\right)} \]

   if -1.2499999999999999e-281 < i < 0.0013500000000000001

   1. Initial program 95.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \left(\left(y \cdot z\right) \cdot x\right) + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + -4 \cdot \left(i \cdot x\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \left(-4 \cdot i\right) \cdot x\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      10. distribute-rgt-in N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(b \cdot c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, c\right), \left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(\color{blue}{j}, 27\right), k\right)\right) \]

   5. Simplified 90.1%

      \[\leadsto \color{blue}{\left(b \cdot c + x \cdot \left(-4 \cdot i + \left(\left(18 \cdot t\right) \cdot y\right) \cdot z\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(c \cdot \left(b + \frac{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}{c}\right)\right)}, \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]
   7. Step-by-step derivation

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \left(b + \frac{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}{c}\right)\right), \mathsf{*.f64}\left(\color{blue}{\mathsf{*.f64}\left(j, 27\right)}, k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{+.f64}\left(b, \left(\frac{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}{c}\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, \color{blue}{27}\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\left(x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right), c\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right), c\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-4 \cdot i\right), \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right), c\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right), c\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right), c\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \left(y \cdot z\right)\right)\right)\right)\right), c\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

      9. *-lowering-*.f64 85.7%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, \mathsf{+.f64}\left(b, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(-4, i\right), \mathsf{*.f64}\left(18, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(y, z\right)\right)\right)\right)\right), c\right)\right)\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, 27\right), k\right)\right) \]

   8. Simplified 85.7%

      \[\leadsto \color{blue}{c \cdot \left(b + \frac{x \cdot \left(-4 \cdot i + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)}{c}\right)} - \left(j \cdot 27\right) \cdot k \]

   9. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left(j \cdot k\right) \cdot \color{blue}{-27} \]

       2. associate-*l* N/A

          \[\leadsto j \cdot \color{blue}{\left(k \cdot -27\right)} \]

       3. *-commutative N/A

          \[\leadsto j \cdot \left(-27 \cdot \color{blue}{k}\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(-27 \cdot k\right)}\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(j, \left(k \cdot \color{blue}{-27}\right)\right) \]

       6. *-lowering-*.f64 39.3%

          \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(k, \color{blue}{-27}\right)\right) \]

   11. Simplified 39.3%

       \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.52 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-281}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;i \leq 0.00135:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 31.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;i \leq -1 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{+70}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= i -1e+141)
     t_1
     (if (<= i -2.4e-167) (* a (* t -4.0)) (if (<= i 8.5e+70) (* 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 k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (i <= -1e+141) {
		tmp = t_1;
	} else if (i <= -2.4e-167) {
		tmp = a * (t * -4.0);
	} else if (i <= 8.5e+70) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (x * i)
    if (i <= (-1d+141)) then
        tmp = t_1
    else if (i <= (-2.4d-167)) then
        tmp = a * (t * (-4.0d0))
    else if (i <= 8.5d+70) then
        tmp = 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 k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (i <= -1e+141) {
		tmp = t_1;
	} else if (i <= -2.4e-167) {
		tmp = a * (t * -4.0);
	} else if (i <= 8.5e+70) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	tmp = 0
	if i <= -1e+141:
		tmp = t_1
	elif i <= -2.4e-167:
		tmp = a * (t * -4.0)
	elif i <= 8.5e+70:
		tmp = b * c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (i <= -1e+141)
		tmp = t_1;
	elseif (i <= -2.4e-167)
		tmp = Float64(a * Float64(t * -4.0));
	elseif (i <= 8.5e+70)
		tmp = 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, k)
	t_1 = -4.0 * (x * i);
	tmp = 0.0;
	if (i <= -1e+141)
		tmp = t_1;
	elseif (i <= -2.4e-167)
		tmp = a * (t * -4.0);
	elseif (i <= 8.5e+70)
		tmp = b * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1e+141], t$95$1, If[LessEqual[i, -2.4e-167], N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.5e+70], N[(b * c), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.00000000000000002e141 or 8.4999999999999996e70 < i

   1. Initial program 79.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 50.3%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 50.3%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]

   if -1.00000000000000002e141 < i < -2.39999999999999993e-167

   1. Initial program 84.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf

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

      1. associate-*r* N/A

         \[\leadsto \left(-4 \cdot a\right) \cdot \color{blue}{t} \]

      2. *-commutative N/A

         \[\leadsto \left(a \cdot -4\right) \cdot t \]

      3. associate-*r* N/A

         \[\leadsto a \cdot \color{blue}{\left(-4 \cdot t\right)} \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-4 \cdot t\right)}\right) \]

      5. *-lowering-*.f64 34.8%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(-4, \color{blue}{t}\right)\right) \]

   7. Simplified 34.8%

      \[\leadsto \color{blue}{a \cdot \left(-4 \cdot t\right)} \]

   if -2.39999999999999993e-167 < i < 8.4999999999999996e70

   1. Initial program 92.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 92.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 27.7%

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

   7. Simplified 27.7%

      \[\leadsto \color{blue}{b \cdot c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+141}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{+70}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 35.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.5 \cdot 10^{+109}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.45 \cdot 10^{+138}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -4.5e+109)
   (* b c)
   (if (<= (* b c) 1.45e+138) (* -4.0 (* x i)) (* b c))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -4.5e+109) {
		tmp = b * c;
	} else if ((b * c) <= 1.45e+138) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-4.5d+109)) then
        tmp = b * c
    else if ((b * c) <= 1.45d+138) then
        tmp = (-4.0d0) * (x * i)
    else
        tmp = 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 k) {
	double tmp;
	if ((b * c) <= -4.5e+109) {
		tmp = b * c;
	} else if ((b * c) <= 1.45e+138) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -4.5e+109:
		tmp = b * c
	elif (b * c) <= 1.45e+138:
		tmp = -4.0 * (x * i)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -4.5e+109)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 1.45e+138)
		tmp = Float64(-4.0 * Float64(x * i));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -4.5e+109)
		tmp = b * c;
	elseif ((b * c) <= 1.45e+138)
		tmp = -4.0 * (x * i);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -4.5e+109], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.45e+138], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -4.4999999999999996e109 or 1.45000000000000005e138 < (*.f64 b c)

   1. Initial program 86.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 48.5%

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

   7. Simplified 48.5%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -4.4999999999999996e109 < (*.f64 b c) < 1.45000000000000005e138

   1. Initial program 85.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

      2. associate--l+ N/A

         \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   3. Simplified 89.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(i \cdot x\right)}\right) \]

      2. *-lowering-*.f64 26.2%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(i, \color{blue}{x}\right)\right) \]

   7. Simplified 26.2%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.5 \cdot 10^{+109}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.45 \cdot 10^{+138}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 23.6% accurate, 10.3× speedup

Math

\[\begin{array}{l} \\ b \cdot c \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    code = b * c
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 k) {
	return b * c;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.0%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Step-by-step derivation

   1. associate--l+ N/A

      \[\leadsto \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right) - \color{blue}{\left(j \cdot 27\right)} \cdot k \]

   2. associate--l+ N/A

      \[\leadsto \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)} \]

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

      \[\leadsto \mathsf{+.f64}\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right), \color{blue}{\left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)}\right) \]

   4. distribute-rgt-out-- N/A

      \[\leadsto \mathsf{+.f64}\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)\right), \left(\color{blue}{\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)} - \left(j \cdot 27\right) \cdot k\right)\right) \]

   6. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right) \cdot i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\left(x \cdot 18\right) \cdot y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \color{blue}{\left(x \cdot 4\right)} \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(x \cdot 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(\color{blue}{x} \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(\mathsf{neg}\left(a \cdot 4\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \left(a \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

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

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot \color{blue}{i}\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 18\right), y\right), z\right), \mathsf{*.f64}\left(a, -4\right)\right)\right), \left(\left(b \cdot c - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\right)\right) \]

3. Simplified 88.8%

   \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z + a \cdot -4\right) + \left(-27 \cdot \left(j \cdot k\right) + \left(b \cdot c + x \cdot \left(i \cdot -4\right)\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot c} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 19.9%

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

7. Simplified 19.9%

   \[\leadsto \color{blue}{b \cdot c} \]
8. Add Preprocessing

Developer Target 1: 89.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    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), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024161 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8105407698770699/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 8284013971902611/50000000000000) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))