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

Percentage Accurate: 85.4% → 92.2%

Time: 38.7s

Alternatives: 20

Speedup: 0.9×

• 50.4% 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: 85.4% 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: 92.2% accurate, 0.5× speedup

Math

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

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (-
           (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
           (* (* x 4.0) i))
          (* (* j 27.0) k))))
   (if (<= t_1 INFINITY) t_1 (* x (+ (* i -4.0) (* 18.0 (* y (* z t))))))))

C

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

Java

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

Python

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

Julia

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

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = x * ((i * -4.0) + (18.0 * (y * (z * t))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * 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]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.5%

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

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) 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- 0.0%

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

      2. associate-+l- 0.0%

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

      3. associate--l- 0.0%

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

      4. *-commutative 0.0%

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

      5. associate-*r* 11.5%

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

      6. associate-*l* 26.9%

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

      7. associate-*r* 23.1%

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

      8. *-commutative 23.1%

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

      9. associate-*l* 15.4%

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

      10. associate--l- 15.4%

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

      11. associate-+l- 15.4%

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

   3. Simplified 26.9%

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

   4. Taylor expanded in x around inf 69.3%

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

      1. cancel-sign-sub-inv 69.3%

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

      2. +-commutative 69.3%

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

      3. metadata-eval 69.3%

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

      4. *-commutative 69.3%

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

      5. *-commutative 69.3%

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

      6. associate-*l* 69.3%

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

      7. *-commutative 69.3%

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

   6. Applied egg-rr 69.3%

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

4. Final simplification 93.7%

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

Alternative 2: 87.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-174}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+93}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(z \cdot t\right) \cdot \left(x \cdot \left(18 \cdot y\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -5e-174)
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* j (* 27.0 k)) (* x (* 4.0 i))))
   (if (<= t 8.4e+93)
     (-
      (-
       (+ (* b c) (- (* (* z t) (* x (* 18.0 y))) (* t (* a 4.0))))
       (* (* x 4.0) i))
      (* (* j 27.0) k))
     (-
      (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
      (* 4.0 (* x i))))))

C

assert(y < z);
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 (t <= -5e-174) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
	} else if (t <= 8.4e+93) {
		tmp = (((b * c) + (((z * t) * (x * (18.0 * y))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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 (t <= (-5d-174)) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((j * (27.0d0 * k)) + (x * (4.0d0 * i)))
    else if (t <= 8.4d+93) then
        tmp = (((b * c) + (((z * t) * (x * (18.0d0 * y))) - (t * (a * 4.0d0)))) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
    else
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert y < z;
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 (t <= -5e-174) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
	} else if (t <= 8.4e+93) {
		tmp = (((b * c) + (((z * t) * (x * (18.0 * y))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -5e-174:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((j * (27.0 * k)) + (x * (4.0 * i)))
	elif t <= 8.4e+93:
		tmp = (((b * c) + (((z * t) * (x * (18.0 * y))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * k)
	else:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -5e-174)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(j * Float64(27.0 * k)) + Float64(x * Float64(4.0 * i))));
	elseif (t <= 8.4e+93)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(Float64(z * t) * Float64(x * Float64(18.0 * y))) - Float64(t * Float64(a * 4.0)))) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -5e-174)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
	elseif (t <= 8.4e+93)
		tmp = (((b * c) + (((z * t) * (x * (18.0 * y))) - (t * (a * 4.0)))) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	else
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -5e-174], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision] + N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.4e+93], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(N[(z * t), $MachinePrecision] * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.0000000000000002e-174

   1. Initial program 92.1%

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

      1. associate--l- 92.1%

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

      2. associate-+l- 92.1%

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

      3. associate--l- 92.1%

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

      4. *-commutative 92.1%

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

      5. associate-*r* 89.3%

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

      6. associate-*l* 87.4%

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

      7. associate-*r* 86.5%

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

      8. *-commutative 86.5%

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

      9. associate-*l* 91.9%

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

      10. associate--l- 91.9%

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

      11. associate-+l- 91.9%

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

   3. Simplified 93.2%

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

   if -5.0000000000000002e-174 < t < 8.39999999999999921e93

   1. Initial program 84.7%

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

      1. add-exp-log_binary64 56.7%

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

   3. Applied rewrite-once 56.7%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 84.7%

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

      2. associate-*l* 89.2%

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

      3. associate-*r* 89.2%

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

      4. *-commutative 89.2%

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

   5. Simplified 89.2%

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

   if 8.39999999999999921e93 < t

   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. Step-by-step derivation

      1. associate--l- 79.0%

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

      2. associate-+l- 79.0%

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

      3. associate--l- 79.0%

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

      4. *-commutative 79.0%

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

      5. associate-*r* 76.8%

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

      6. associate-*l* 76.9%

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

      7. associate-*r* 76.7%

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

      8. *-commutative 76.7%

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

      9. associate-*l* 76.7%

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

      10. associate--l- 76.7%

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

      11. associate-+l- 76.7%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in j around 0 93.3%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-174}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+93}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(z \cdot t\right) \cdot \left(x \cdot \left(18 \cdot y\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 3: 87.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq 1.12 \cdot 10^{+285}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) 1.12e+285)
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* j (* 27.0 k)) (* x (* 4.0 i))))
   (+ (* b c) (* j (* k -27.0)))))

C

assert(y < z);
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) <= 1.12e+285) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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) <= 1.12d+285) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((j * (27.0d0 * k)) + (x * (4.0d0 * i)))
    else
        tmp = (b * c) + (j * (k * (-27.0d0)))
    end if
    code = tmp
end function

Java

assert y < z;
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) <= 1.12e+285) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
	} else {
		tmp = (b * c) + (j * (k * -27.0));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= 1.12e+285:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((j * (27.0 * k)) + (x * (4.0 * i)))
	else:
		tmp = (b * c) + (j * (k * -27.0))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= 1.12e+285)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(j * Float64(27.0 * k)) + Float64(x * Float64(4.0 * i))));
	else
		tmp = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= 1.12e+285)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((j * (27.0 * k)) + (x * (4.0 * i)));
	else
		tmp = (b * c) + (j * (k * -27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], 1.12e+285], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision] + N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < 1.11999999999999998e285

   1. Initial program 88.3%

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

      1. associate--l- 88.3%

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

      2. associate-+l- 88.3%

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

      3. associate--l- 88.3%

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

      4. *-commutative 88.3%

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

      5. associate-*r* 88.8%

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

      6. associate-*l* 89.6%

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

      7. associate-*r* 87.6%

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

      8. *-commutative 87.6%

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

      9. associate-*l* 88.3%

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

      10. associate--l- 88.3%

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

      11. associate-+l- 88.3%

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

   3. Simplified 90.9%

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

   if 1.11999999999999998e285 < (*.f64 b c)

   1. Initial program 62.5%

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

   3. Simplified 68.8%

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

   4. Taylor expanded in b around inf 93.8%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq 1.12 \cdot 10^{+285}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(4 \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 4: 58.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ t_3 := t_1 + t_2\\ t_4 := -4 \cdot \left(t \cdot a\right) + \left(b \cdot c + t_2\right)\\ t_5 := t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -1.92 \cdot 10^{+27}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-106}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-190}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-211}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-20}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (* -4.0 (* x i)))
        (t_3 (+ t_1 t_2))
        (t_4 (+ (* -4.0 (* t a)) (+ (* b c) t_2)))
        (t_5 (* t (+ (* (* x 18.0) (* y z)) (* a -4.0)))))
   (if (<= t -1.92e+27)
     t_5
     (if (<= t -7.5e-106)
       (+ (* b c) t_1)
       (if (<= t -3.7e-190)
         t_4
         (if (<= t 4.8e-211)
           t_3
           (if (<= t 6.2e-20)
             t_4
             (if (<= t 1.25e+39)
               t_3
               (if (<= t 1.65e+184)
                 (* x (+ (* i -4.0) (* 18.0 (* y (* z t)))))
                 t_5)))))))))

C

assert(y < z);
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 * (k * -27.0);
	double t_2 = -4.0 * (x * i);
	double t_3 = t_1 + t_2;
	double t_4 = (-4.0 * (t * a)) + ((b * c) + t_2);
	double t_5 = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	double tmp;
	if (t <= -1.92e+27) {
		tmp = t_5;
	} else if (t <= -7.5e-106) {
		tmp = (b * c) + t_1;
	} else if (t <= -3.7e-190) {
		tmp = t_4;
	} else if (t <= 4.8e-211) {
		tmp = t_3;
	} else if (t <= 6.2e-20) {
		tmp = t_4;
	} else if (t <= 1.25e+39) {
		tmp = t_3;
	} else if (t <= 1.65e+184) {
		tmp = x * ((i * -4.0) + (18.0 * (y * (z * t))));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (-4.0d0) * (x * i)
    t_3 = t_1 + t_2
    t_4 = ((-4.0d0) * (t * a)) + ((b * c) + t_2)
    t_5 = t * (((x * 18.0d0) * (y * z)) + (a * (-4.0d0)))
    if (t <= (-1.92d+27)) then
        tmp = t_5
    else if (t <= (-7.5d-106)) then
        tmp = (b * c) + t_1
    else if (t <= (-3.7d-190)) then
        tmp = t_4
    else if (t <= 4.8d-211) then
        tmp = t_3
    else if (t <= 6.2d-20) then
        tmp = t_4
    else if (t <= 1.25d+39) then
        tmp = t_3
    else if (t <= 1.65d+184) then
        tmp = x * ((i * (-4.0d0)) + (18.0d0 * (y * (z * t))))
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

assert y < z;
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 * (k * -27.0);
	double t_2 = -4.0 * (x * i);
	double t_3 = t_1 + t_2;
	double t_4 = (-4.0 * (t * a)) + ((b * c) + t_2);
	double t_5 = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	double tmp;
	if (t <= -1.92e+27) {
		tmp = t_5;
	} else if (t <= -7.5e-106) {
		tmp = (b * c) + t_1;
	} else if (t <= -3.7e-190) {
		tmp = t_4;
	} else if (t <= 4.8e-211) {
		tmp = t_3;
	} else if (t <= 6.2e-20) {
		tmp = t_4;
	} else if (t <= 1.25e+39) {
		tmp = t_3;
	} else if (t <= 1.65e+184) {
		tmp = x * ((i * -4.0) + (18.0 * (y * (z * t))));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = -4.0 * (x * i)
	t_3 = t_1 + t_2
	t_4 = (-4.0 * (t * a)) + ((b * c) + t_2)
	t_5 = t * (((x * 18.0) * (y * z)) + (a * -4.0))
	tmp = 0
	if t <= -1.92e+27:
		tmp = t_5
	elif t <= -7.5e-106:
		tmp = (b * c) + t_1
	elif t <= -3.7e-190:
		tmp = t_4
	elif t <= 4.8e-211:
		tmp = t_3
	elif t <= 6.2e-20:
		tmp = t_4
	elif t <= 1.25e+39:
		tmp = t_3
	elif t <= 1.65e+184:
		tmp = x * ((i * -4.0) + (18.0 * (y * (z * t))))
	else:
		tmp = t_5
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(-4.0 * Float64(x * i))
	t_3 = Float64(t_1 + t_2)
	t_4 = Float64(Float64(-4.0 * Float64(t * a)) + Float64(Float64(b * c) + t_2))
	t_5 = Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) + Float64(a * -4.0)))
	tmp = 0.0
	if (t <= -1.92e+27)
		tmp = t_5;
	elseif (t <= -7.5e-106)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (t <= -3.7e-190)
		tmp = t_4;
	elseif (t <= 4.8e-211)
		tmp = t_3;
	elseif (t <= 6.2e-20)
		tmp = t_4;
	elseif (t <= 1.25e+39)
		tmp = t_3;
	elseif (t <= 1.65e+184)
		tmp = Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(y * Float64(z * t)))));
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = -4.0 * (x * i);
	t_3 = t_1 + t_2;
	t_4 = (-4.0 * (t * a)) + ((b * c) + t_2);
	t_5 = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	tmp = 0.0;
	if (t <= -1.92e+27)
		tmp = t_5;
	elseif (t <= -7.5e-106)
		tmp = (b * c) + t_1;
	elseif (t <= -3.7e-190)
		tmp = t_4;
	elseif (t <= 4.8e-211)
		tmp = t_3;
	elseif (t <= 6.2e-20)
		tmp = t_4;
	elseif (t <= 1.25e+39)
		tmp = t_3;
	elseif (t <= 1.65e+184)
		tmp = x * ((i * -4.0) + (18.0 * (y * (z * t))));
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.92e+27], t$95$5, If[LessEqual[t, -7.5e-106], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, -3.7e-190], t$95$4, If[LessEqual[t, 4.8e-211], t$95$3, If[LessEqual[t, 6.2e-20], t$95$4, If[LessEqual[t, 1.25e+39], t$95$3, If[LessEqual[t, 1.65e+184], N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.92000000000000004e27 or 1.6499999999999999e184 < t

   1. Initial program 85.1%

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

      1. add-exp-log_binary64 43.8%

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

   3. Applied rewrite-once 43.8%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 85.1%

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

      2. associate-*l* 77.4%

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

      3. associate-*r* 77.4%

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

      4. *-commutative 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in t around inf 79.7%

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

      1. cancel-sign-sub-inv 79.7%

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

      2. associate-*r* 79.7%

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

      3. metadata-eval 79.7%

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

      4. *-commutative 79.7%

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

   8. Simplified 79.7%

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

   if -1.92000000000000004e27 < t < -7.5000000000000002e-106

   1. Initial program 99.6%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in b around inf 62.1%

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

   if -7.5000000000000002e-106 < t < -3.7000000000000002e-190 or 4.8000000000000004e-211 < t < 6.19999999999999999e-20

   1. Initial program 85.7%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in x around 0 90.6%

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

   5. Taylor expanded in j around 0 79.2%

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

   if -3.7000000000000002e-190 < t < 4.8000000000000004e-211 or 6.19999999999999999e-20 < t < 1.25000000000000004e39

   1. Initial program 79.7%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in i around inf 77.3%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} + j \cdot \left(k \cdot -27\right) \]

   if 1.25000000000000004e39 < t < 1.6499999999999999e184

   1. Initial program 96.0%

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

      1. associate--l- 96.0%

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

      2. associate-+l- 96.0%

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

      3. associate--l- 96.0%

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

      4. *-commutative 96.0%

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

      5. associate-*r* 92.4%

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

      6. associate-*l* 92.5%

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

      7. associate-*r* 92.3%

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

      8. *-commutative 92.3%

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

      9. associate-*l* 92.2%

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

      10. associate--l- 92.2%

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

      11. associate-+l- 92.2%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in x around inf 69.8%

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

      1. cancel-sign-sub-inv 69.8%

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

      2. +-commutative 69.8%

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

      3. metadata-eval 69.8%

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

      4. *-commutative 69.8%

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

      5. *-commutative 69.8%

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

      6. associate-*l* 69.8%

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

      7. *-commutative 69.8%

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

   6. Applied egg-rr 69.8%

      \[\leadsto x \cdot \color{blue}{\left(i \cdot -4 + 18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.92 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-106}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-190}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-211}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-20}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+39}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 5: 59.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := -4 \cdot \left(t \cdot a\right) + \left(b \cdot c + t_1\right)\\ t_3 := t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ t_4 := j \cdot \left(k \cdot -27\right)\\ t_5 := t_4 + t_1\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+30}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-103}:\\ \;\;\;\;t_4 + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-210}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+39}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i)))
        (t_2 (+ (* -4.0 (* t a)) (+ (* b c) t_1)))
        (t_3 (* t (+ (* (* x 18.0) (* y z)) (* a -4.0))))
        (t_4 (* j (* k -27.0)))
        (t_5 (+ t_4 t_1)))
   (if (<= t -1.8e+30)
     t_3
     (if (<= t -2.7e-103)
       (+ t_4 (* 18.0 (* (* y z) (* x t))))
       (if (<= t -1.15e-189)
         t_2
         (if (<= t 4e-210)
           t_5
           (if (<= t 4.7e-19)
             t_2
             (if (<= t 7.6e+39)
               t_5
               (if (<= t 4.6e+184)
                 (* x (+ (* i -4.0) (* 18.0 (* y (* z t)))))
                 t_3)))))))))

C

assert(y < z);
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 t_2 = (-4.0 * (t * a)) + ((b * c) + t_1);
	double t_3 = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	double t_4 = j * (k * -27.0);
	double t_5 = t_4 + t_1;
	double tmp;
	if (t <= -1.8e+30) {
		tmp = t_3;
	} else if (t <= -2.7e-103) {
		tmp = t_4 + (18.0 * ((y * z) * (x * t)));
	} else if (t <= -1.15e-189) {
		tmp = t_2;
	} else if (t <= 4e-210) {
		tmp = t_5;
	} else if (t <= 4.7e-19) {
		tmp = t_2;
	} else if (t <= 7.6e+39) {
		tmp = t_5;
	} else if (t <= 4.6e+184) {
		tmp = x * ((i * -4.0) + (18.0 * (y * (z * t))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (-4.0d0) * (x * i)
    t_2 = ((-4.0d0) * (t * a)) + ((b * c) + t_1)
    t_3 = t * (((x * 18.0d0) * (y * z)) + (a * (-4.0d0)))
    t_4 = j * (k * (-27.0d0))
    t_5 = t_4 + t_1
    if (t <= (-1.8d+30)) then
        tmp = t_3
    else if (t <= (-2.7d-103)) then
        tmp = t_4 + (18.0d0 * ((y * z) * (x * t)))
    else if (t <= (-1.15d-189)) then
        tmp = t_2
    else if (t <= 4d-210) then
        tmp = t_5
    else if (t <= 4.7d-19) then
        tmp = t_2
    else if (t <= 7.6d+39) then
        tmp = t_5
    else if (t <= 4.6d+184) then
        tmp = x * ((i * (-4.0d0)) + (18.0d0 * (y * (z * t))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert y < z;
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 t_2 = (-4.0 * (t * a)) + ((b * c) + t_1);
	double t_3 = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	double t_4 = j * (k * -27.0);
	double t_5 = t_4 + t_1;
	double tmp;
	if (t <= -1.8e+30) {
		tmp = t_3;
	} else if (t <= -2.7e-103) {
		tmp = t_4 + (18.0 * ((y * z) * (x * t)));
	} else if (t <= -1.15e-189) {
		tmp = t_2;
	} else if (t <= 4e-210) {
		tmp = t_5;
	} else if (t <= 4.7e-19) {
		tmp = t_2;
	} else if (t <= 7.6e+39) {
		tmp = t_5;
	} else if (t <= 4.6e+184) {
		tmp = x * ((i * -4.0) + (18.0 * (y * (z * t))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	t_2 = (-4.0 * (t * a)) + ((b * c) + t_1)
	t_3 = t * (((x * 18.0) * (y * z)) + (a * -4.0))
	t_4 = j * (k * -27.0)
	t_5 = t_4 + t_1
	tmp = 0
	if t <= -1.8e+30:
		tmp = t_3
	elif t <= -2.7e-103:
		tmp = t_4 + (18.0 * ((y * z) * (x * t)))
	elif t <= -1.15e-189:
		tmp = t_2
	elif t <= 4e-210:
		tmp = t_5
	elif t <= 4.7e-19:
		tmp = t_2
	elif t <= 7.6e+39:
		tmp = t_5
	elif t <= 4.6e+184:
		tmp = x * ((i * -4.0) + (18.0 * (y * (z * t))))
	else:
		tmp = t_3
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	t_2 = Float64(Float64(-4.0 * Float64(t * a)) + Float64(Float64(b * c) + t_1))
	t_3 = Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) + Float64(a * -4.0)))
	t_4 = Float64(j * Float64(k * -27.0))
	t_5 = Float64(t_4 + t_1)
	tmp = 0.0
	if (t <= -1.8e+30)
		tmp = t_3;
	elseif (t <= -2.7e-103)
		tmp = Float64(t_4 + Float64(18.0 * Float64(Float64(y * z) * Float64(x * t))));
	elseif (t <= -1.15e-189)
		tmp = t_2;
	elseif (t <= 4e-210)
		tmp = t_5;
	elseif (t <= 4.7e-19)
		tmp = t_2;
	elseif (t <= 7.6e+39)
		tmp = t_5;
	elseif (t <= 4.6e+184)
		tmp = Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(y * Float64(z * t)))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	t_2 = (-4.0 * (t * a)) + ((b * c) + t_1);
	t_3 = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	t_4 = j * (k * -27.0);
	t_5 = t_4 + t_1;
	tmp = 0.0;
	if (t <= -1.8e+30)
		tmp = t_3;
	elseif (t <= -2.7e-103)
		tmp = t_4 + (18.0 * ((y * z) * (x * t)));
	elseif (t <= -1.15e-189)
		tmp = t_2;
	elseif (t <= 4e-210)
		tmp = t_5;
	elseif (t <= 4.7e-19)
		tmp = t_2;
	elseif (t <= 7.6e+39)
		tmp = t_5;
	elseif (t <= 4.6e+184)
		tmp = x * ((i * -4.0) + (18.0 * (y * (z * t))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 + t$95$1), $MachinePrecision]}, If[LessEqual[t, -1.8e+30], t$95$3, If[LessEqual[t, -2.7e-103], N[(t$95$4 + N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.15e-189], t$95$2, If[LessEqual[t, 4e-210], t$95$5, If[LessEqual[t, 4.7e-19], t$95$2, If[LessEqual[t, 7.6e+39], t$95$5, If[LessEqual[t, 4.6e+184], N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.8000000000000001e30 or 4.6e184 < t

   1. Initial program 84.7%

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

      1. add-exp-log_binary64 43.7%

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

   3. Applied rewrite-once 43.7%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 84.7%

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

      2. associate-*l* 76.9%

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

      3. associate-*r* 76.9%

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

      4. *-commutative 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in t around inf 80.3%

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

      1. cancel-sign-sub-inv 80.3%

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

      2. associate-*r* 80.3%

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

      3. metadata-eval 80.3%

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

      4. *-commutative 80.3%

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

   8. Simplified 80.3%

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

   if -1.8000000000000001e30 < t < -2.7000000000000001e-103

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 64.8%

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

      1. associate-*r* 68.1%

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

   6. Simplified 68.1%

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

   if -2.7000000000000001e-103 < t < -1.1499999999999999e-189 or 4.0000000000000002e-210 < t < 4.7e-19

   1. Initial program 85.7%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in x around 0 90.6%

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

   5. Taylor expanded in j around 0 79.2%

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

   if -1.1499999999999999e-189 < t < 4.0000000000000002e-210 or 4.7e-19 < t < 7.5999999999999996e39

   1. Initial program 79.7%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in i around inf 77.3%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} + j \cdot \left(k \cdot -27\right) \]

   if 7.5999999999999996e39 < t < 4.6e184

   1. Initial program 96.0%

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

      1. associate--l- 96.0%

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

      2. associate-+l- 96.0%

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

      3. associate--l- 96.0%

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

      4. *-commutative 96.0%

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

      5. associate-*r* 92.4%

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

      6. associate-*l* 92.5%

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

      7. associate-*r* 92.3%

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

      8. *-commutative 92.3%

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

      9. associate-*l* 92.2%

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

      10. associate--l- 92.2%

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

      11. associate-+l- 92.2%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in x around inf 69.8%

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

      1. cancel-sign-sub-inv 69.8%

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

      2. +-commutative 69.8%

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

      3. metadata-eval 69.8%

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

      4. *-commutative 69.8%

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

      5. *-commutative 69.8%

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

      6. associate-*l* 69.8%

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

      7. *-commutative 69.8%

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

   6. Applied egg-rr 69.8%

      \[\leadsto x \cdot \color{blue}{\left(i \cdot -4 + 18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-189}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-210}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-19}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+39}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 6: 81.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\\ t_2 := 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+45}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(t_1 + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+38}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(t_2 + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(t_1 - a \cdot 4\right)\right) - t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* x (* y z)))) (t_2 (* 4.0 (* x i))))
   (if (<= t -3.6e+45)
     (+ (* j (* k -27.0)) (* t (+ t_1 (* a -4.0))))
     (if (<= t 8.6e+38)
       (- (+ (* b c) (* -4.0 (* t a))) (+ t_2 (* 27.0 (* j k))))
       (- (+ (* b c) (* t (- t_1 (* a 4.0)))) t_2)))))

C

assert(y < z);
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 * (y * z));
	double t_2 = 4.0 * (x * i);
	double tmp;
	if (t <= -3.6e+45) {
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	} else if (t <= 8.6e+38) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_2 + (27.0 * (j * k)));
	} else {
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - t_2;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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 * (y * z))
    t_2 = 4.0d0 * (x * i)
    if (t <= (-3.6d+45)) then
        tmp = (j * (k * (-27.0d0))) + (t * (t_1 + (a * (-4.0d0))))
    else if (t <= 8.6d+38) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (t_2 + (27.0d0 * (j * k)))
    else
        tmp = ((b * c) + (t * (t_1 - (a * 4.0d0)))) - t_2
    end if
    code = tmp
end function

Java

assert y < z;
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 * (y * z));
	double t_2 = 4.0 * (x * i);
	double tmp;
	if (t <= -3.6e+45) {
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	} else if (t <= 8.6e+38) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_2 + (27.0 * (j * k)));
	} else {
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - t_2;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (x * (y * z))
	t_2 = 4.0 * (x * i)
	tmp = 0
	if t <= -3.6e+45:
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)))
	elif t <= 8.6e+38:
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_2 + (27.0 * (j * k)))
	else:
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - t_2
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(x * Float64(y * z)))
	t_2 = Float64(4.0 * Float64(x * i))
	tmp = 0.0
	if (t <= -3.6e+45)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(t_1 + Float64(a * -4.0))));
	elseif (t <= 8.6e+38)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(t_2 + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(t_1 - Float64(a * 4.0)))) - t_2);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (x * (y * z));
	t_2 = 4.0 * (x * i);
	tmp = 0.0;
	if (t <= -3.6e+45)
		tmp = (j * (k * -27.0)) + (t * (t_1 + (a * -4.0)));
	elseif (t <= 8.6e+38)
		tmp = ((b * c) + (-4.0 * (t * a))) - (t_2 + (27.0 * (j * k)));
	else
		tmp = ((b * c) + (t * (t_1 - (a * 4.0)))) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+45], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(t$95$1 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.6e+38], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$2 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(t$95$1 - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.6e45

   1. Initial program 92.6%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in t around inf 89.2%

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

   if -3.6e45 < t < 8.5999999999999994e38

   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- 85.8%

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

      2. associate-+l- 85.8%

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

      3. associate--l- 85.8%

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

      4. *-commutative 85.8%

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

      5. associate-*r* 91.1%

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

      6. associate-*l* 95.1%

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

      7. associate-*r* 91.2%

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

      8. *-commutative 91.2%

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

      9. associate-*l* 87.2%

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

      10. associate--l- 87.2%

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

      11. associate-+l- 87.2%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around 0 88.1%

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

   if 8.5999999999999994e38 < t

   1. Initial program 82.9%

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

      1. associate--l- 82.9%

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

      2. associate-+l- 82.9%

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

      3. associate--l- 82.9%

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

      4. *-commutative 82.9%

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

      5. associate-*r* 81.2%

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

      6. associate-*l* 81.2%

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

      7. associate-*r* 81.1%

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

      8. *-commutative 81.1%

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

      9. associate-*l* 81.1%

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

      10. associate--l- 81.1%

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

      11. associate-+l- 81.1%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in j around 0 92.8%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+45}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+38}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 7: 32.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{if}\;t \leq -2.95 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-106}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-211}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-112}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+281} \lor \neg \left(t \leq 6.2 \cdot 10^{+294}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* i -4.0))) (t_2 (* 18.0 (* (* y z) (* x t)))))
   (if (<= t -2.95e+26)
     t_2
     (if (<= t -5.5e-106)
       (* -27.0 (* j k))
       (if (<= t -4.5e-198)
         t_1
         (if (<= t 6.8e-211)
           (* j (* k -27.0))
           (if (<= t 1.8e-112)
             (* b c)
             (if (<= t 2.6e+121)
               t_1
               (if (or (<= t 2.6e+281) (not (<= t 6.2e+294)))
                 t_2
                 (* t (* a -4.0)))))))))))

C

assert(y < z);
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);
	double t_2 = 18.0 * ((y * z) * (x * t));
	double tmp;
	if (t <= -2.95e+26) {
		tmp = t_2;
	} else if (t <= -5.5e-106) {
		tmp = -27.0 * (j * k);
	} else if (t <= -4.5e-198) {
		tmp = t_1;
	} else if (t <= 6.8e-211) {
		tmp = j * (k * -27.0);
	} else if (t <= 1.8e-112) {
		tmp = b * c;
	} else if (t <= 2.6e+121) {
		tmp = t_1;
	} else if ((t <= 2.6e+281) || !(t <= 6.2e+294)) {
		tmp = t_2;
	} else {
		tmp = t * (a * -4.0);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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 = x * (i * (-4.0d0))
    t_2 = 18.0d0 * ((y * z) * (x * t))
    if (t <= (-2.95d+26)) then
        tmp = t_2
    else if (t <= (-5.5d-106)) then
        tmp = (-27.0d0) * (j * k)
    else if (t <= (-4.5d-198)) then
        tmp = t_1
    else if (t <= 6.8d-211) then
        tmp = j * (k * (-27.0d0))
    else if (t <= 1.8d-112) then
        tmp = b * c
    else if (t <= 2.6d+121) then
        tmp = t_1
    else if ((t <= 2.6d+281) .or. (.not. (t <= 6.2d+294))) then
        tmp = t_2
    else
        tmp = t * (a * (-4.0d0))
    end if
    code = tmp
end function

Java

assert y < z;
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);
	double t_2 = 18.0 * ((y * z) * (x * t));
	double tmp;
	if (t <= -2.95e+26) {
		tmp = t_2;
	} else if (t <= -5.5e-106) {
		tmp = -27.0 * (j * k);
	} else if (t <= -4.5e-198) {
		tmp = t_1;
	} else if (t <= 6.8e-211) {
		tmp = j * (k * -27.0);
	} else if (t <= 1.8e-112) {
		tmp = b * c;
	} else if (t <= 2.6e+121) {
		tmp = t_1;
	} else if ((t <= 2.6e+281) || !(t <= 6.2e+294)) {
		tmp = t_2;
	} else {
		tmp = t * (a * -4.0);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (i * -4.0)
	t_2 = 18.0 * ((y * z) * (x * t))
	tmp = 0
	if t <= -2.95e+26:
		tmp = t_2
	elif t <= -5.5e-106:
		tmp = -27.0 * (j * k)
	elif t <= -4.5e-198:
		tmp = t_1
	elif t <= 6.8e-211:
		tmp = j * (k * -27.0)
	elif t <= 1.8e-112:
		tmp = b * c
	elif t <= 2.6e+121:
		tmp = t_1
	elif (t <= 2.6e+281) or not (t <= 6.2e+294):
		tmp = t_2
	else:
		tmp = t * (a * -4.0)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(i * -4.0))
	t_2 = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)))
	tmp = 0.0
	if (t <= -2.95e+26)
		tmp = t_2;
	elseif (t <= -5.5e-106)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (t <= -4.5e-198)
		tmp = t_1;
	elseif (t <= 6.8e-211)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (t <= 1.8e-112)
		tmp = Float64(b * c);
	elseif (t <= 2.6e+121)
		tmp = t_1;
	elseif ((t <= 2.6e+281) || !(t <= 6.2e+294))
		tmp = t_2;
	else
		tmp = Float64(t * Float64(a * -4.0));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (i * -4.0);
	t_2 = 18.0 * ((y * z) * (x * t));
	tmp = 0.0;
	if (t <= -2.95e+26)
		tmp = t_2;
	elseif (t <= -5.5e-106)
		tmp = -27.0 * (j * k);
	elseif (t <= -4.5e-198)
		tmp = t_1;
	elseif (t <= 6.8e-211)
		tmp = j * (k * -27.0);
	elseif (t <= 1.8e-112)
		tmp = b * c;
	elseif (t <= 2.6e+121)
		tmp = t_1;
	elseif ((t <= 2.6e+281) || ~((t <= 6.2e+294)))
		tmp = t_2;
	else
		tmp = t * (a * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.95e+26], t$95$2, If[LessEqual[t, -5.5e-106], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.5e-198], t$95$1, If[LessEqual[t, 6.8e-211], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-112], N[(b * c), $MachinePrecision], If[LessEqual[t, 2.6e+121], t$95$1, If[Or[LessEqual[t, 2.6e+281], N[Not[LessEqual[t, 6.2e+294]], $MachinePrecision]], t$95$2, N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.95000000000000015e26 or 2.5999999999999999e121 < t < 2.6000000000000001e281 or 6.20000000000000038e294 < t

   1. Initial program 86.1%

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

      1. associate--l- 86.1%

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

      2. associate-+l- 86.1%

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

      3. associate--l- 86.1%

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

      4. *-commutative 86.1%

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

      5. associate-*r* 80.2%

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

      6. associate-*l* 77.2%

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

      7. associate-*r* 80.2%

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

      8. *-commutative 80.2%

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

      9. associate-*l* 86.0%

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

      10. associate--l- 86.0%

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

      11. associate-+l- 86.0%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in x around inf 64.1%

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

   5. Taylor expanded in t around inf 58.9%

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

   6. Taylor expanded in x around 0 58.9%

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

      1. associate-*r* 59.0%

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

   8. Simplified 59.0%

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

   9. Taylor expanded in t around 0 58.9%

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

       1. associate-*r* 58.9%

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

       2. *-commutative 58.9%

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

       3. *-commutative 58.9%

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

   11. Simplified 58.9%

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

   if -2.95000000000000015e26 < t < -5.5000000000000001e-106

   1. Initial program 99.6%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in j around inf 42.9%

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

   if -5.5000000000000001e-106 < t < -4.4999999999999998e-198 or 1.8e-112 < t < 2.5999999999999999e121

   1. Initial program 84.6%

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

      1. associate--l- 84.6%

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

      2. associate-+l- 84.6%

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

      3. associate--l- 84.6%

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

      4. *-commutative 84.6%

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

      5. associate-*r* 88.3%

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

      6. associate-*l* 92.0%

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

      7. associate-*r* 86.0%

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

      8. *-commutative 86.0%

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

      9. associate-*l* 84.7%

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

      10. associate--l- 84.7%

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

      11. associate-+l- 84.7%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in x around inf 49.9%

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

   5. Taylor expanded in t around 0 42.5%

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

      1. *-commutative 42.5%

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

   7. Simplified 42.5%

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

   if -4.4999999999999998e-198 < t < 6.8000000000000002e-211

   1. Initial program 78.8%

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

      1. add-exp-log_binary64 60.7%

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

   3. Applied rewrite-once 60.7%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 78.8%

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

      2. associate-*l* 87.8%

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

      3. associate-*r* 87.8%

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

      4. *-commutative 87.8%

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

   5. Simplified 87.8%

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

   6. Taylor expanded in j around inf 58.2%

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

      1. *-commutative 58.2%

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

      2. associate-*r* 58.2%

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

   8. Simplified 58.2%

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

   if 6.8000000000000002e-211 < t < 1.8e-112

   1. Initial program 94.9%

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

      1. add-exp-log_binary64 64.9%

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

   3. Applied rewrite-once 64.9%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 94.9%

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

      2. associate-*l* 99.9%

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

      3. associate-*r* 99.8%

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

      4. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around inf 59.5%

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

   if 2.6000000000000001e281 < t < 6.20000000000000038e294

   1. Initial program 80.0%

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

      1. add-exp-log_binary64 60.0%

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

   3. Applied rewrite-once 60.0%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 80.0%

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

      2. associate-*l* 60.0%

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

      3. associate-*r* 60.0%

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

      4. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in a around inf 100.0%

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

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot t \]

      3. *-commutative 100.0%

         \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{+26}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-106}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-211}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-112}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+281} \lor \neg \left(t \leq 6.2 \cdot 10^{+294}\right):\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]

Alternative 8: 32.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-107}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -6.7 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-209}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-114}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+277}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+294}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* i -4.0))) (t_2 (* 18.0 (* (* y z) (* x t)))))
   (if (<= t -3.4e+27)
     t_2
     (if (<= t -7.6e-107)
       (* -27.0 (* j k))
       (if (<= t -6.7e-198)
         t_1
         (if (<= t 1e-209)
           (* j (* k -27.0))
           (if (<= t 4.8e-114)
             (* b c)
             (if (<= t 7.5e+120)
               t_1
               (if (<= t 2.8e+277)
                 (* x (* 18.0 (* t (* y z))))
                 (if (<= t 7.8e+294) (* t (* a -4.0)) t_2))))))))))

C

assert(y < z);
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);
	double t_2 = 18.0 * ((y * z) * (x * t));
	double tmp;
	if (t <= -3.4e+27) {
		tmp = t_2;
	} else if (t <= -7.6e-107) {
		tmp = -27.0 * (j * k);
	} else if (t <= -6.7e-198) {
		tmp = t_1;
	} else if (t <= 1e-209) {
		tmp = j * (k * -27.0);
	} else if (t <= 4.8e-114) {
		tmp = b * c;
	} else if (t <= 7.5e+120) {
		tmp = t_1;
	} else if (t <= 2.8e+277) {
		tmp = x * (18.0 * (t * (y * z)));
	} else if (t <= 7.8e+294) {
		tmp = t * (a * -4.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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 = x * (i * (-4.0d0))
    t_2 = 18.0d0 * ((y * z) * (x * t))
    if (t <= (-3.4d+27)) then
        tmp = t_2
    else if (t <= (-7.6d-107)) then
        tmp = (-27.0d0) * (j * k)
    else if (t <= (-6.7d-198)) then
        tmp = t_1
    else if (t <= 1d-209) then
        tmp = j * (k * (-27.0d0))
    else if (t <= 4.8d-114) then
        tmp = b * c
    else if (t <= 7.5d+120) then
        tmp = t_1
    else if (t <= 2.8d+277) then
        tmp = x * (18.0d0 * (t * (y * z)))
    else if (t <= 7.8d+294) then
        tmp = t * (a * (-4.0d0))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z;
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);
	double t_2 = 18.0 * ((y * z) * (x * t));
	double tmp;
	if (t <= -3.4e+27) {
		tmp = t_2;
	} else if (t <= -7.6e-107) {
		tmp = -27.0 * (j * k);
	} else if (t <= -6.7e-198) {
		tmp = t_1;
	} else if (t <= 1e-209) {
		tmp = j * (k * -27.0);
	} else if (t <= 4.8e-114) {
		tmp = b * c;
	} else if (t <= 7.5e+120) {
		tmp = t_1;
	} else if (t <= 2.8e+277) {
		tmp = x * (18.0 * (t * (y * z)));
	} else if (t <= 7.8e+294) {
		tmp = t * (a * -4.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (i * -4.0)
	t_2 = 18.0 * ((y * z) * (x * t))
	tmp = 0
	if t <= -3.4e+27:
		tmp = t_2
	elif t <= -7.6e-107:
		tmp = -27.0 * (j * k)
	elif t <= -6.7e-198:
		tmp = t_1
	elif t <= 1e-209:
		tmp = j * (k * -27.0)
	elif t <= 4.8e-114:
		tmp = b * c
	elif t <= 7.5e+120:
		tmp = t_1
	elif t <= 2.8e+277:
		tmp = x * (18.0 * (t * (y * z)))
	elif t <= 7.8e+294:
		tmp = t * (a * -4.0)
	else:
		tmp = t_2
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(i * -4.0))
	t_2 = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)))
	tmp = 0.0
	if (t <= -3.4e+27)
		tmp = t_2;
	elseif (t <= -7.6e-107)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (t <= -6.7e-198)
		tmp = t_1;
	elseif (t <= 1e-209)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (t <= 4.8e-114)
		tmp = Float64(b * c);
	elseif (t <= 7.5e+120)
		tmp = t_1;
	elseif (t <= 2.8e+277)
		tmp = Float64(x * Float64(18.0 * Float64(t * Float64(y * z))));
	elseif (t <= 7.8e+294)
		tmp = Float64(t * Float64(a * -4.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (i * -4.0);
	t_2 = 18.0 * ((y * z) * (x * t));
	tmp = 0.0;
	if (t <= -3.4e+27)
		tmp = t_2;
	elseif (t <= -7.6e-107)
		tmp = -27.0 * (j * k);
	elseif (t <= -6.7e-198)
		tmp = t_1;
	elseif (t <= 1e-209)
		tmp = j * (k * -27.0);
	elseif (t <= 4.8e-114)
		tmp = b * c;
	elseif (t <= 7.5e+120)
		tmp = t_1;
	elseif (t <= 2.8e+277)
		tmp = x * (18.0 * (t * (y * z)));
	elseif (t <= 7.8e+294)
		tmp = t * (a * -4.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+27], t$95$2, If[LessEqual[t, -7.6e-107], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.7e-198], t$95$1, If[LessEqual[t, 1e-209], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-114], N[(b * c), $MachinePrecision], If[LessEqual[t, 7.5e+120], t$95$1, If[LessEqual[t, 2.8e+277], N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e+294], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -3.4e27 or 7.80000000000000026e294 < t

   1. Initial program 90.4%

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

      1. associate--l- 90.4%

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

      2. associate-+l- 90.4%

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

      3. associate--l- 90.4%

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

      4. *-commutative 90.4%

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

      5. associate-*r* 83.1%

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

      6. associate-*l* 78.6%

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

      7. associate-*r* 81.5%

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

      8. *-commutative 81.5%

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

      9. associate-*l* 90.1%

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

      10. associate--l- 90.1%

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

      11. associate-+l- 90.1%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in x around inf 58.9%

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

   5. Taylor expanded in t around inf 55.6%

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

   6. Taylor expanded in x around 0 55.6%

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

      1. associate-*r* 55.6%

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

   8. Simplified 55.6%

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

   9. Taylor expanded in t around 0 55.6%

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

       1. associate-*r* 57.1%

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

       2. *-commutative 57.1%

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

       3. *-commutative 57.1%

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

   11. Simplified 57.1%

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

   if -3.4e27 < t < -7.6000000000000004e-107

   1. Initial program 99.6%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in j around inf 42.9%

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

   if -7.6000000000000004e-107 < t < -6.69999999999999982e-198 or 4.8000000000000002e-114 < t < 7.5000000000000006e120

   1. Initial program 84.6%

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

      1. associate--l- 84.6%

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

      2. associate-+l- 84.6%

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

      3. associate--l- 84.6%

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

      4. *-commutative 84.6%

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

      5. associate-*r* 88.3%

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

      6. associate-*l* 92.0%

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

      7. associate-*r* 86.0%

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

      8. *-commutative 86.0%

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

      9. associate-*l* 84.7%

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

      10. associate--l- 84.7%

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

      11. associate-+l- 84.7%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in x around inf 49.9%

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

   5. Taylor expanded in t around 0 42.5%

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

      1. *-commutative 42.5%

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

   7. Simplified 42.5%

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

   if -6.69999999999999982e-198 < t < 1e-209

   1. Initial program 78.8%

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

      1. add-exp-log_binary64 60.7%

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

   3. Applied rewrite-once 60.7%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 78.8%

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

      2. associate-*l* 87.8%

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

      3. associate-*r* 87.8%

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

      4. *-commutative 87.8%

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

   5. Simplified 87.8%

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

   6. Taylor expanded in j around inf 58.2%

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

      1. *-commutative 58.2%

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

      2. associate-*r* 58.2%

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

   8. Simplified 58.2%

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

   if 1e-209 < t < 4.8000000000000002e-114

   1. Initial program 94.9%

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

      1. add-exp-log_binary64 64.9%

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

   3. Applied rewrite-once 64.9%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 94.9%

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

      2. associate-*l* 99.9%

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

      3. associate-*r* 99.8%

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

      4. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around inf 59.5%

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

   if 7.5000000000000006e120 < t < 2.79999999999999985e277

   1. Initial program 77.4%

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

      1. associate--l- 77.4%

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

      2. associate-+l- 77.4%

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

      3. associate--l- 77.4%

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

      4. *-commutative 77.4%

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

      5. associate-*r* 74.3%

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

      6. associate-*l* 74.4%

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

      7. associate-*r* 77.4%

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

      8. *-commutative 77.4%

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

      9. associate-*l* 77.4%

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

      10. associate--l- 77.4%

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

      11. associate-+l- 77.4%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in x around inf 74.9%

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

   5. Taylor expanded in t around inf 65.6%

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

   if 2.79999999999999985e277 < t < 7.80000000000000026e294

   1. Initial program 80.0%

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

      1. add-exp-log_binary64 60.0%

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

   3. Applied rewrite-once 60.0%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 80.0%

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

      2. associate-*l* 60.0%

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

      3. associate-*r* 60.0%

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

      4. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in a around inf 100.0%

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

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot t \]

      3. *-commutative 100.0%

         \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+27}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-107}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -6.7 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 10^{-209}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-114}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+277}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+294}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \end{array} \]

Alternative 9: 32.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{if}\;t \leq -3.75 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-105}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-210}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-111}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+277}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+294}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* i -4.0))) (t_2 (* 18.0 (* (* y z) (* x t)))))
   (if (<= t -3.75e+26)
     t_2
     (if (<= t -1.3e-105)
       (* -27.0 (* j k))
       (if (<= t -3.5e-198)
         t_1
         (if (<= t 7.5e-210)
           (* j (* k -27.0))
           (if (<= t 8.5e-111)
             (* b c)
             (if (<= t 9.6e+120)
               t_1
               (if (<= t 5.4e+277)
                 (* x (* 18.0 (* y (* z t))))
                 (if (<= t 7.5e+294) (* t (* a -4.0)) t_2))))))))))

C

assert(y < z);
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);
	double t_2 = 18.0 * ((y * z) * (x * t));
	double tmp;
	if (t <= -3.75e+26) {
		tmp = t_2;
	} else if (t <= -1.3e-105) {
		tmp = -27.0 * (j * k);
	} else if (t <= -3.5e-198) {
		tmp = t_1;
	} else if (t <= 7.5e-210) {
		tmp = j * (k * -27.0);
	} else if (t <= 8.5e-111) {
		tmp = b * c;
	} else if (t <= 9.6e+120) {
		tmp = t_1;
	} else if (t <= 5.4e+277) {
		tmp = x * (18.0 * (y * (z * t)));
	} else if (t <= 7.5e+294) {
		tmp = t * (a * -4.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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 = x * (i * (-4.0d0))
    t_2 = 18.0d0 * ((y * z) * (x * t))
    if (t <= (-3.75d+26)) then
        tmp = t_2
    else if (t <= (-1.3d-105)) then
        tmp = (-27.0d0) * (j * k)
    else if (t <= (-3.5d-198)) then
        tmp = t_1
    else if (t <= 7.5d-210) then
        tmp = j * (k * (-27.0d0))
    else if (t <= 8.5d-111) then
        tmp = b * c
    else if (t <= 9.6d+120) then
        tmp = t_1
    else if (t <= 5.4d+277) then
        tmp = x * (18.0d0 * (y * (z * t)))
    else if (t <= 7.5d+294) then
        tmp = t * (a * (-4.0d0))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z;
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);
	double t_2 = 18.0 * ((y * z) * (x * t));
	double tmp;
	if (t <= -3.75e+26) {
		tmp = t_2;
	} else if (t <= -1.3e-105) {
		tmp = -27.0 * (j * k);
	} else if (t <= -3.5e-198) {
		tmp = t_1;
	} else if (t <= 7.5e-210) {
		tmp = j * (k * -27.0);
	} else if (t <= 8.5e-111) {
		tmp = b * c;
	} else if (t <= 9.6e+120) {
		tmp = t_1;
	} else if (t <= 5.4e+277) {
		tmp = x * (18.0 * (y * (z * t)));
	} else if (t <= 7.5e+294) {
		tmp = t * (a * -4.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (i * -4.0)
	t_2 = 18.0 * ((y * z) * (x * t))
	tmp = 0
	if t <= -3.75e+26:
		tmp = t_2
	elif t <= -1.3e-105:
		tmp = -27.0 * (j * k)
	elif t <= -3.5e-198:
		tmp = t_1
	elif t <= 7.5e-210:
		tmp = j * (k * -27.0)
	elif t <= 8.5e-111:
		tmp = b * c
	elif t <= 9.6e+120:
		tmp = t_1
	elif t <= 5.4e+277:
		tmp = x * (18.0 * (y * (z * t)))
	elif t <= 7.5e+294:
		tmp = t * (a * -4.0)
	else:
		tmp = t_2
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(i * -4.0))
	t_2 = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)))
	tmp = 0.0
	if (t <= -3.75e+26)
		tmp = t_2;
	elseif (t <= -1.3e-105)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (t <= -3.5e-198)
		tmp = t_1;
	elseif (t <= 7.5e-210)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (t <= 8.5e-111)
		tmp = Float64(b * c);
	elseif (t <= 9.6e+120)
		tmp = t_1;
	elseif (t <= 5.4e+277)
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))));
	elseif (t <= 7.5e+294)
		tmp = Float64(t * Float64(a * -4.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (i * -4.0);
	t_2 = 18.0 * ((y * z) * (x * t));
	tmp = 0.0;
	if (t <= -3.75e+26)
		tmp = t_2;
	elseif (t <= -1.3e-105)
		tmp = -27.0 * (j * k);
	elseif (t <= -3.5e-198)
		tmp = t_1;
	elseif (t <= 7.5e-210)
		tmp = j * (k * -27.0);
	elseif (t <= 8.5e-111)
		tmp = b * c;
	elseif (t <= 9.6e+120)
		tmp = t_1;
	elseif (t <= 5.4e+277)
		tmp = x * (18.0 * (y * (z * t)));
	elseif (t <= 7.5e+294)
		tmp = t * (a * -4.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.75e+26], t$95$2, If[LessEqual[t, -1.3e-105], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.5e-198], t$95$1, If[LessEqual[t, 7.5e-210], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-111], N[(b * c), $MachinePrecision], If[LessEqual[t, 9.6e+120], t$95$1, If[LessEqual[t, 5.4e+277], N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+294], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -3.74999999999999971e26 or 7.4999999999999999e294 < t

   1. Initial program 90.4%

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

      1. associate--l- 90.4%

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

      2. associate-+l- 90.4%

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

      3. associate--l- 90.4%

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

      4. *-commutative 90.4%

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

      5. associate-*r* 83.1%

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

      6. associate-*l* 78.6%

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

      7. associate-*r* 81.5%

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

      8. *-commutative 81.5%

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

      9. associate-*l* 90.1%

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

      10. associate--l- 90.1%

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

      11. associate-+l- 90.1%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in x around inf 58.9%

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

   5. Taylor expanded in t around inf 55.6%

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

   6. Taylor expanded in x around 0 55.6%

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

      1. associate-*r* 55.6%

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

   8. Simplified 55.6%

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

   9. Taylor expanded in t around 0 55.6%

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

       1. associate-*r* 57.1%

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

       2. *-commutative 57.1%

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

       3. *-commutative 57.1%

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

   11. Simplified 57.1%

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

   if -3.74999999999999971e26 < t < -1.2999999999999999e-105

   1. Initial program 99.6%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in j around inf 42.9%

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

   if -1.2999999999999999e-105 < t < -3.50000000000000025e-198 or 8.5000000000000003e-111 < t < 9.60000000000000004e120

   1. Initial program 84.6%

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

      1. associate--l- 84.6%

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

      2. associate-+l- 84.6%

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

      3. associate--l- 84.6%

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

      4. *-commutative 84.6%

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

      5. associate-*r* 88.3%

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

      6. associate-*l* 92.0%

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

      7. associate-*r* 86.0%

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

      8. *-commutative 86.0%

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

      9. associate-*l* 84.7%

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

      10. associate--l- 84.7%

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

      11. associate-+l- 84.7%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in x around inf 49.9%

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

   5. Taylor expanded in t around 0 42.5%

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

      1. *-commutative 42.5%

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

   7. Simplified 42.5%

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

   if -3.50000000000000025e-198 < t < 7.4999999999999997e-210

   1. Initial program 78.8%

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

      1. add-exp-log_binary64 60.7%

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

   3. Applied rewrite-once 60.7%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 78.8%

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

      2. associate-*l* 87.8%

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

      3. associate-*r* 87.8%

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

      4. *-commutative 87.8%

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

   5. Simplified 87.8%

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

   6. Taylor expanded in j around inf 58.2%

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

      1. *-commutative 58.2%

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

      2. associate-*r* 58.2%

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

   8. Simplified 58.2%

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

   if 7.4999999999999997e-210 < t < 8.5000000000000003e-111

   1. Initial program 94.9%

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

      1. add-exp-log_binary64 64.9%

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

   3. Applied rewrite-once 64.9%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 94.9%

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

      2. associate-*l* 99.9%

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

      3. associate-*r* 99.8%

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

      4. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around inf 59.5%

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

   if 9.60000000000000004e120 < t < 5.39999999999999974e277

   1. Initial program 77.4%

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

      1. associate--l- 77.4%

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

      2. associate-+l- 77.4%

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

      3. associate--l- 77.4%

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

      4. *-commutative 77.4%

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

      5. associate-*r* 74.3%

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

      6. associate-*l* 74.4%

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

      7. associate-*r* 77.4%

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

      8. *-commutative 77.4%

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

      9. associate-*l* 77.4%

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

      10. associate--l- 77.4%

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

      11. associate-+l- 77.4%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in x around inf 74.9%

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

   5. Taylor expanded in t around inf 65.6%

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

      1. associate-*r* 65.7%

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

      2. *-commutative 65.7%

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

      3. associate-*r* 68.8%

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

   7. Simplified 68.8%

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

   if 5.39999999999999974e277 < t < 7.4999999999999999e294

   1. Initial program 80.0%

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

      1. add-exp-log_binary64 60.0%

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

   3. Applied rewrite-once 60.0%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 80.0%

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

      2. associate-*l* 60.0%

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

      3. associate-*r* 60.0%

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

      4. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in a around inf 100.0%

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

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot t \]

      3. *-commutative 100.0%

         \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.75 \cdot 10^{+26}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-105}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-210}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-111}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+277}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+294}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \end{array} \]

Alternative 10: 58.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t_1\\ t_3 := t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+38}:\\ \;\;\;\;t_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ (* b c) t_1))
        (t_3 (* t (+ (* (* x 18.0) (* y z)) (* a -4.0)))))
   (if (<= t -2.4e+27)
     t_3
     (if (<= t -6e-104)
       t_2
       (if (<= t -3.4e-198)
         (- (* b c) (* x (* 4.0 i)))
         (if (<= t 2e-112)
           t_2
           (if (<= t 8.6e+38)
             (+ t_1 (* -4.0 (* x i)))
             (if (<= t 1.7e+184)
               (* x (+ (* i -4.0) (* 18.0 (* y (* z t)))))
               t_3))))))))

C

assert(y < z);
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 * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	double tmp;
	if (t <= -2.4e+27) {
		tmp = t_3;
	} else if (t <= -6e-104) {
		tmp = t_2;
	} else if (t <= -3.4e-198) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 2e-112) {
		tmp = t_2;
	} else if (t <= 8.6e+38) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if (t <= 1.7e+184) {
		tmp = x * ((i * -4.0) + (18.0 * (y * (z * t))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    t_3 = t * (((x * 18.0d0) * (y * z)) + (a * (-4.0d0)))
    if (t <= (-2.4d+27)) then
        tmp = t_3
    else if (t <= (-6d-104)) then
        tmp = t_2
    else if (t <= (-3.4d-198)) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if (t <= 2d-112) then
        tmp = t_2
    else if (t <= 8.6d+38) then
        tmp = t_1 + ((-4.0d0) * (x * i))
    else if (t <= 1.7d+184) then
        tmp = x * ((i * (-4.0d0)) + (18.0d0 * (y * (z * t))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert y < z;
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 * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	double tmp;
	if (t <= -2.4e+27) {
		tmp = t_3;
	} else if (t <= -6e-104) {
		tmp = t_2;
	} else if (t <= -3.4e-198) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 2e-112) {
		tmp = t_2;
	} else if (t <= 8.6e+38) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if (t <= 1.7e+184) {
		tmp = x * ((i * -4.0) + (18.0 * (y * (z * t))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	t_3 = t * (((x * 18.0) * (y * z)) + (a * -4.0))
	tmp = 0
	if t <= -2.4e+27:
		tmp = t_3
	elif t <= -6e-104:
		tmp = t_2
	elif t <= -3.4e-198:
		tmp = (b * c) - (x * (4.0 * i))
	elif t <= 2e-112:
		tmp = t_2
	elif t <= 8.6e+38:
		tmp = t_1 + (-4.0 * (x * i))
	elif t <= 1.7e+184:
		tmp = x * ((i * -4.0) + (18.0 * (y * (z * t))))
	else:
		tmp = t_3
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) + Float64(a * -4.0)))
	tmp = 0.0
	if (t <= -2.4e+27)
		tmp = t_3;
	elseif (t <= -6e-104)
		tmp = t_2;
	elseif (t <= -3.4e-198)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (t <= 2e-112)
		tmp = t_2;
	elseif (t <= 8.6e+38)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(x * i)));
	elseif (t <= 1.7e+184)
		tmp = Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(y * Float64(z * t)))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	t_3 = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	tmp = 0.0;
	if (t <= -2.4e+27)
		tmp = t_3;
	elseif (t <= -6e-104)
		tmp = t_2;
	elseif (t <= -3.4e-198)
		tmp = (b * c) - (x * (4.0 * i));
	elseif (t <= 2e-112)
		tmp = t_2;
	elseif (t <= 8.6e+38)
		tmp = t_1 + (-4.0 * (x * i));
	elseif (t <= 1.7e+184)
		tmp = x * ((i * -4.0) + (18.0 * (y * (z * t))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e+27], t$95$3, If[LessEqual[t, -6e-104], t$95$2, If[LessEqual[t, -3.4e-198], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-112], t$95$2, If[LessEqual[t, 8.6e+38], N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+184], N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.39999999999999998e27 or 1.7000000000000001e184 < t

   1. Initial program 85.1%

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

      1. add-exp-log_binary64 43.8%

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

   3. Applied rewrite-once 43.8%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 85.1%

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

      2. associate-*l* 77.4%

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

      3. associate-*r* 77.4%

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

      4. *-commutative 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in t around inf 79.7%

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

      1. cancel-sign-sub-inv 79.7%

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

      2. associate-*r* 79.7%

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

      3. metadata-eval 79.7%

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

      4. *-commutative 79.7%

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

   8. Simplified 79.7%

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

   if -2.39999999999999998e27 < t < -6.0000000000000005e-104 or -3.3999999999999998e-198 < t < 1.9999999999999999e-112

   1. Initial program 89.8%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in b around inf 68.5%

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

   if -6.0000000000000005e-104 < t < -3.3999999999999998e-198

   1. Initial program 72.4%

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

      1. associate--l- 72.4%

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

      2. associate-+l- 72.4%

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

      3. associate--l- 72.4%

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

      4. *-commutative 72.4%

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

      5. associate-*r* 85.9%

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

      6. associate-*l* 95.0%

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

      7. associate-*r* 77.1%

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

      8. *-commutative 77.1%

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

      9. associate-*l* 72.6%

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

      10. associate--l- 72.6%

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

      11. associate-+l- 72.6%

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

   3. Simplified 77.2%

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

   4. Taylor expanded in t around 0 77.7%

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

   5. Taylor expanded in i around inf 70.0%

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

      1. *-commutative 70.0%

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

      2. *-commutative 70.0%

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

      3. associate-*r* 70.0%

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

   7. Simplified 70.0%

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

   if 1.9999999999999999e-112 < t < 8.5999999999999994e38

   1. Initial program 85.6%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in i around inf 71.1%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} + j \cdot \left(k \cdot -27\right) \]

   if 8.5999999999999994e38 < t < 1.7000000000000001e184

   1. Initial program 96.0%

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

      1. associate--l- 96.0%

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

      2. associate-+l- 96.0%

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

      3. associate--l- 96.0%

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

      4. *-commutative 96.0%

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

      5. associate-*r* 92.4%

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

      6. associate-*l* 92.5%

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

      7. associate-*r* 92.3%

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

      8. *-commutative 92.3%

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

      9. associate-*l* 92.2%

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

      10. associate--l- 92.2%

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

      11. associate-+l- 92.2%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in x around inf 69.8%

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

      1. cancel-sign-sub-inv 69.8%

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

      2. +-commutative 69.8%

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

      3. metadata-eval 69.8%

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

      4. *-commutative 69.8%

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

      5. *-commutative 69.8%

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

      6. associate-*l* 69.8%

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

      7. *-commutative 69.8%

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

   6. Applied egg-rr 69.8%

      \[\leadsto x \cdot \color{blue}{\left(i \cdot -4 + 18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-104}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-112}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+38}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 11: 80.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+43}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+121}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -7e+43)
   (+ (* j (* k -27.0)) (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))
   (if (<= t 1.65e+121)
     (- (+ (* b c) (* -4.0 (* t a))) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
     (* t (+ (* (* x 18.0) (* y z)) (* a -4.0))))))

C

assert(y < z);
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 (t <= -7e+43) {
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	} else if (t <= 1.65e+121) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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 (t <= (-7d+43)) then
        tmp = (j * (k * (-27.0d0))) + (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0))))
    else if (t <= 1.65d+121) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    else
        tmp = t * (((x * 18.0d0) * (y * z)) + (a * (-4.0d0)))
    end if
    code = tmp
end function

Java

assert y < z;
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 (t <= -7e+43) {
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	} else if (t <= 1.65e+121) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -7e+43:
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)))
	elif t <= 1.65e+121:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	else:
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -7e+43)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))));
	elseif (t <= 1.65e+121)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) + Float64(a * -4.0)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -7e+43)
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	elseif (t <= 1.65e+121)
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	else
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -7e+43], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e+121], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.0000000000000002e43

   1. Initial program 92.6%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in t around inf 89.2%

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

   if -7.0000000000000002e43 < t < 1.6499999999999999e121

   1. Initial program 87.0%

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

      1. associate--l- 87.0%

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

      2. associate-+l- 87.0%

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

      3. associate--l- 87.0%

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

      4. *-commutative 87.0%

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

      5. associate-*r* 91.8%

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

      6. associate-*l* 95.5%

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

      7. associate-*r* 91.3%

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

      8. *-commutative 91.3%

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

      9. associate-*l* 87.7%

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

      10. associate--l- 87.7%

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

      11. associate-+l- 87.7%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in y around 0 86.8%

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

   if 1.6499999999999999e121 < t

   1. Initial program 76.9%

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

      1. add-exp-log_binary64 43.3%

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

   3. Applied rewrite-once 43.3%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 76.9%

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

      2. associate-*l* 69.3%

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

      3. associate-*r* 69.3%

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

      4. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in t around inf 85.4%

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

      1. cancel-sign-sub-inv 85.4%

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

      2. associate-*r* 85.4%

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

      3. metadata-eval 85.4%

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

      4. *-commutative 85.4%

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

   8. Simplified 85.4%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+43}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+121}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 12: 47.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t_1\\ t_3 := 18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{if}\;t \leq -9.6 \cdot 10^{+26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+128}:\\ \;\;\;\;t_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+279}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+294}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ (* b c) t_1))
        (t_3 (* 18.0 (* (* y z) (* x t)))))
   (if (<= t -9.6e+26)
     t_3
     (if (<= t -6.8e-105)
       t_2
       (if (<= t -3.4e-198)
         (- (* b c) (* x (* 4.0 i)))
         (if (<= t 3.15e-111)
           t_2
           (if (<= t 2.4e+128)
             (+ t_1 (* -4.0 (* x i)))
             (if (<= t 7e+279)
               (* x (* 18.0 (* y (* z t))))
               (if (<= t 6e+294) (* t (* a -4.0)) t_3)))))))))

C

assert(y < z);
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 * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = 18.0 * ((y * z) * (x * t));
	double tmp;
	if (t <= -9.6e+26) {
		tmp = t_3;
	} else if (t <= -6.8e-105) {
		tmp = t_2;
	} else if (t <= -3.4e-198) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 3.15e-111) {
		tmp = t_2;
	} else if (t <= 2.4e+128) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if (t <= 7e+279) {
		tmp = x * (18.0 * (y * (z * t)));
	} else if (t <= 6e+294) {
		tmp = t * (a * -4.0);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    t_3 = 18.0d0 * ((y * z) * (x * t))
    if (t <= (-9.6d+26)) then
        tmp = t_3
    else if (t <= (-6.8d-105)) then
        tmp = t_2
    else if (t <= (-3.4d-198)) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if (t <= 3.15d-111) then
        tmp = t_2
    else if (t <= 2.4d+128) then
        tmp = t_1 + ((-4.0d0) * (x * i))
    else if (t <= 7d+279) then
        tmp = x * (18.0d0 * (y * (z * t)))
    else if (t <= 6d+294) then
        tmp = t * (a * (-4.0d0))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert y < z;
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 * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = 18.0 * ((y * z) * (x * t));
	double tmp;
	if (t <= -9.6e+26) {
		tmp = t_3;
	} else if (t <= -6.8e-105) {
		tmp = t_2;
	} else if (t <= -3.4e-198) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 3.15e-111) {
		tmp = t_2;
	} else if (t <= 2.4e+128) {
		tmp = t_1 + (-4.0 * (x * i));
	} else if (t <= 7e+279) {
		tmp = x * (18.0 * (y * (z * t)));
	} else if (t <= 6e+294) {
		tmp = t * (a * -4.0);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	t_3 = 18.0 * ((y * z) * (x * t))
	tmp = 0
	if t <= -9.6e+26:
		tmp = t_3
	elif t <= -6.8e-105:
		tmp = t_2
	elif t <= -3.4e-198:
		tmp = (b * c) - (x * (4.0 * i))
	elif t <= 3.15e-111:
		tmp = t_2
	elif t <= 2.4e+128:
		tmp = t_1 + (-4.0 * (x * i))
	elif t <= 7e+279:
		tmp = x * (18.0 * (y * (z * t)))
	elif t <= 6e+294:
		tmp = t * (a * -4.0)
	else:
		tmp = t_3
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)))
	tmp = 0.0
	if (t <= -9.6e+26)
		tmp = t_3;
	elseif (t <= -6.8e-105)
		tmp = t_2;
	elseif (t <= -3.4e-198)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (t <= 3.15e-111)
		tmp = t_2;
	elseif (t <= 2.4e+128)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(x * i)));
	elseif (t <= 7e+279)
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))));
	elseif (t <= 6e+294)
		tmp = Float64(t * Float64(a * -4.0));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	t_3 = 18.0 * ((y * z) * (x * t));
	tmp = 0.0;
	if (t <= -9.6e+26)
		tmp = t_3;
	elseif (t <= -6.8e-105)
		tmp = t_2;
	elseif (t <= -3.4e-198)
		tmp = (b * c) - (x * (4.0 * i));
	elseif (t <= 3.15e-111)
		tmp = t_2;
	elseif (t <= 2.4e+128)
		tmp = t_1 + (-4.0 * (x * i));
	elseif (t <= 7e+279)
		tmp = x * (18.0 * (y * (z * t)));
	elseif (t <= 6e+294)
		tmp = t * (a * -4.0);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.6e+26], t$95$3, If[LessEqual[t, -6.8e-105], t$95$2, If[LessEqual[t, -3.4e-198], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.15e-111], t$95$2, If[LessEqual[t, 2.4e+128], N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+279], N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+294], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -9.60000000000000018e26 or 6.00000000000000011e294 < t

   1. Initial program 90.4%

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

      1. associate--l- 90.4%

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

      2. associate-+l- 90.4%

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

      3. associate--l- 90.4%

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

      4. *-commutative 90.4%

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

      5. associate-*r* 83.1%

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

      6. associate-*l* 78.6%

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

      7. associate-*r* 81.5%

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

      8. *-commutative 81.5%

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

      9. associate-*l* 90.1%

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

      10. associate--l- 90.1%

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

      11. associate-+l- 90.1%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in x around inf 58.9%

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

   5. Taylor expanded in t around inf 55.6%

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

   6. Taylor expanded in x around 0 55.6%

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

      1. associate-*r* 55.6%

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

   8. Simplified 55.6%

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

   9. Taylor expanded in t around 0 55.6%

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

       1. associate-*r* 57.1%

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

       2. *-commutative 57.1%

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

       3. *-commutative 57.1%

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

   11. Simplified 57.1%

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

   if -9.60000000000000018e26 < t < -6.79999999999999984e-105 or -3.3999999999999998e-198 < t < 3.1500000000000002e-111

   1. Initial program 89.8%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in b around inf 68.5%

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

   if -6.79999999999999984e-105 < t < -3.3999999999999998e-198

   1. Initial program 72.4%

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

      1. associate--l- 72.4%

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

      2. associate-+l- 72.4%

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

      3. associate--l- 72.4%

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

      4. *-commutative 72.4%

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

      5. associate-*r* 85.9%

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

      6. associate-*l* 95.0%

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

      7. associate-*r* 77.1%

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

      8. *-commutative 77.1%

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

      9. associate-*l* 72.6%

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

      10. associate--l- 72.6%

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

      11. associate-+l- 72.6%

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

   3. Simplified 77.2%

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

   4. Taylor expanded in t around 0 77.7%

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

   5. Taylor expanded in i around inf 70.0%

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

      1. *-commutative 70.0%

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

      2. *-commutative 70.0%

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

      3. associate-*r* 70.0%

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

   7. Simplified 70.0%

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

   if 3.1500000000000002e-111 < t < 2.4000000000000002e128

   1. Initial program 89.1%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in i around inf 64.5%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} + j \cdot \left(k \cdot -27\right) \]

   if 2.4000000000000002e128 < t < 7.00000000000000003e279

   1. Initial program 77.4%

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

      1. associate--l- 77.4%

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

      2. associate-+l- 77.4%

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

      3. associate--l- 77.4%

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

      4. *-commutative 77.4%

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

      5. associate-*r* 74.3%

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

      6. associate-*l* 74.4%

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

      7. associate-*r* 77.4%

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

      8. *-commutative 77.4%

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

      9. associate-*l* 77.4%

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

      10. associate--l- 77.4%

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

      11. associate-+l- 77.4%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in x around inf 74.9%

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

   5. Taylor expanded in t around inf 65.6%

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

      1. associate-*r* 65.7%

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

      2. *-commutative 65.7%

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

      3. associate-*r* 68.8%

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

   7. Simplified 68.8%

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

   if 7.00000000000000003e279 < t < 6.00000000000000011e294

   1. Initial program 80.0%

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

      1. add-exp-log_binary64 60.0%

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

   3. Applied rewrite-once 60.0%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 80.0%

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

      2. associate-*l* 60.0%

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

      3. associate-*r* 60.0%

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

      4. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in a around inf 100.0%

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

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-4 \cdot a\right) \cdot t} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(a \cdot -4\right)} \cdot t \]

      3. *-commutative 100.0%

         \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot -4\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{+26}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-105}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-111}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+128}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+279}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+294}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \end{array} \]

Alternative 13: 58.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + t_1\\ t_3 := t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \mathbf{if}\;t \leq -1.06 \cdot 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+120}:\\ \;\;\;\;t_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ (* b c) t_1))
        (t_3 (* t (+ (* (* x 18.0) (* y z)) (* a -4.0)))))
   (if (<= t -1.06e+27)
     t_3
     (if (<= t -2.15e-104)
       t_2
       (if (<= t -5e-198)
         (- (* b c) (* x (* 4.0 i)))
         (if (<= t 5.4e-114)
           t_2
           (if (<= t 7e+120) (+ t_1 (* -4.0 (* x i))) t_3)))))))

C

assert(y < z);
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 * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	double tmp;
	if (t <= -1.06e+27) {
		tmp = t_3;
	} else if (t <= -2.15e-104) {
		tmp = t_2;
	} else if (t <= -5e-198) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 5.4e-114) {
		tmp = t_2;
	} else if (t <= 7e+120) {
		tmp = t_1 + (-4.0 * (x * i));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + t_1
    t_3 = t * (((x * 18.0d0) * (y * z)) + (a * (-4.0d0)))
    if (t <= (-1.06d+27)) then
        tmp = t_3
    else if (t <= (-2.15d-104)) then
        tmp = t_2
    else if (t <= (-5d-198)) then
        tmp = (b * c) - (x * (4.0d0 * i))
    else if (t <= 5.4d-114) then
        tmp = t_2
    else if (t <= 7d+120) then
        tmp = t_1 + ((-4.0d0) * (x * i))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert y < z;
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 * (k * -27.0);
	double t_2 = (b * c) + t_1;
	double t_3 = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	double tmp;
	if (t <= -1.06e+27) {
		tmp = t_3;
	} else if (t <= -2.15e-104) {
		tmp = t_2;
	} else if (t <= -5e-198) {
		tmp = (b * c) - (x * (4.0 * i));
	} else if (t <= 5.4e-114) {
		tmp = t_2;
	} else if (t <= 7e+120) {
		tmp = t_1 + (-4.0 * (x * i));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + t_1
	t_3 = t * (((x * 18.0) * (y * z)) + (a * -4.0))
	tmp = 0
	if t <= -1.06e+27:
		tmp = t_3
	elif t <= -2.15e-104:
		tmp = t_2
	elif t <= -5e-198:
		tmp = (b * c) - (x * (4.0 * i))
	elif t <= 5.4e-114:
		tmp = t_2
	elif t <= 7e+120:
		tmp = t_1 + (-4.0 * (x * i))
	else:
		tmp = t_3
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) + Float64(a * -4.0)))
	tmp = 0.0
	if (t <= -1.06e+27)
		tmp = t_3;
	elseif (t <= -2.15e-104)
		tmp = t_2;
	elseif (t <= -5e-198)
		tmp = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)));
	elseif (t <= 5.4e-114)
		tmp = t_2;
	elseif (t <= 7e+120)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(x * i)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + t_1;
	t_3 = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	tmp = 0.0;
	if (t <= -1.06e+27)
		tmp = t_3;
	elseif (t <= -2.15e-104)
		tmp = t_2;
	elseif (t <= -5e-198)
		tmp = (b * c) - (x * (4.0 * i));
	elseif (t <= 5.4e-114)
		tmp = t_2;
	elseif (t <= 7e+120)
		tmp = t_1 + (-4.0 * (x * i));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.06e+27], t$95$3, If[LessEqual[t, -2.15e-104], t$95$2, If[LessEqual[t, -5e-198], N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e-114], t$95$2, If[LessEqual[t, 7e+120], N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.05999999999999994e27 or 7.00000000000000015e120 < t

   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. add-exp-log_binary64 43.4%

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

   3. Applied rewrite-once 43.4%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 85.8%

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

      2. associate-*l* 78.2%

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

      3. associate-*r* 78.2%

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

      4. *-commutative 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in t around inf 77.4%

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

      1. cancel-sign-sub-inv 77.4%

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

      2. associate-*r* 77.4%

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

      3. metadata-eval 77.4%

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

      4. *-commutative 77.4%

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

   8. Simplified 77.4%

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

   if -1.05999999999999994e27 < t < -2.15000000000000005e-104 or -4.9999999999999999e-198 < t < 5.3999999999999999e-114

   1. Initial program 89.8%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in b around inf 68.5%

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

   if -2.15000000000000005e-104 < t < -4.9999999999999999e-198

   1. Initial program 72.4%

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

      1. associate--l- 72.4%

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

      2. associate-+l- 72.4%

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

      3. associate--l- 72.4%

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

      4. *-commutative 72.4%

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

      5. associate-*r* 85.9%

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

      6. associate-*l* 95.0%

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

      7. associate-*r* 77.1%

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

      8. *-commutative 77.1%

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

      9. associate-*l* 72.6%

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

      10. associate--l- 72.6%

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

      11. associate-+l- 72.6%

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

   3. Simplified 77.2%

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

   4. Taylor expanded in t around 0 77.7%

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

   5. Taylor expanded in i around inf 70.0%

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

      1. *-commutative 70.0%

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

      2. *-commutative 70.0%

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

      3. associate-*r* 70.0%

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

   7. Simplified 70.0%

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

   if 5.3999999999999999e-114 < t < 7.00000000000000015e120

   1. Initial program 89.1%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in i around inf 64.5%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-104}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-114}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+120}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 14: 74.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+125}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= t -8.6e+44)
   (+ (* j (* k -27.0)) (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))
   (if (<= t 5e+125)
     (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
     (* t (+ (* (* x 18.0) (* y z)) (* a -4.0))))))

C

assert(y < z);
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 (t <= -8.6e+44) {
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	} else if (t <= 5e+125) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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 (t <= (-8.6d+44)) then
        tmp = (j * (k * (-27.0d0))) + (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0))))
    else if (t <= 5d+125) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    else
        tmp = t * (((x * 18.0d0) * (y * z)) + (a * (-4.0d0)))
    end if
    code = tmp
end function

Java

assert y < z;
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 (t <= -8.6e+44) {
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	} else if (t <= 5e+125) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -8.6e+44:
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)))
	elif t <= 5e+125:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	else:
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -8.6e+44)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))));
	elseif (t <= 5e+125)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) + Float64(a * -4.0)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -8.6e+44)
		tmp = (j * (k * -27.0)) + (t * ((18.0 * (x * (y * z))) + (a * -4.0)));
	elseif (t <= 5e+125)
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	else
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[t, -8.6e+44], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+125], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.59999999999999965e44

   1. Initial program 92.6%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in t around inf 89.2%

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

   if -8.59999999999999965e44 < t < 4.99999999999999962e125

   1. Initial program 87.0%

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

      1. associate--l- 87.0%

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

      2. associate-+l- 87.0%

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

      3. associate--l- 87.0%

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

      4. *-commutative 87.0%

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

      5. associate-*r* 91.8%

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

      6. associate-*l* 95.5%

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

      7. associate-*r* 91.3%

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

      8. *-commutative 91.3%

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

      9. associate-*l* 87.7%

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

      10. associate--l- 87.7%

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

      11. associate-+l- 87.7%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in t around 0 79.8%

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

   if 4.99999999999999962e125 < t

   1. Initial program 76.9%

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

      1. add-exp-log_binary64 43.3%

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

   3. Applied rewrite-once 43.3%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 76.9%

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

      2. associate-*l* 69.3%

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

      3. associate-*r* 69.3%

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

      4. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in t around inf 85.4%

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

      1. cancel-sign-sub-inv 85.4%

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

      2. associate-*r* 85.4%

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

      3. metadata-eval 85.4%

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

      4. *-commutative 85.4%

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

   8. Simplified 85.4%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+125}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 15: 47.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ t_2 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -14000000000:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-76}:\\ \;\;\;\;\left(x \cdot 18\right) \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* j (* k -27.0)))) (t_2 (* x (* i -4.0))))
   (if (<= x -1.5e+246)
     t_2
     (if (<= x -14000000000.0)
       (* x (* 18.0 (* y (* z t))))
       (if (<= x -3.6e-22)
         t_1
         (if (<= x -8e-76)
           (* (* x 18.0) (* t (* y z)))
           (if (<= x 3.6e+151) t_1 t_2)))))))

C

assert(y < z);
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) + (j * (k * -27.0));
	double t_2 = x * (i * -4.0);
	double tmp;
	if (x <= -1.5e+246) {
		tmp = t_2;
	} else if (x <= -14000000000.0) {
		tmp = x * (18.0 * (y * (z * t)));
	} else if (x <= -3.6e-22) {
		tmp = t_1;
	} else if (x <= -8e-76) {
		tmp = (x * 18.0) * (t * (y * z));
	} else if (x <= 3.6e+151) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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 = (b * c) + (j * (k * (-27.0d0)))
    t_2 = x * (i * (-4.0d0))
    if (x <= (-1.5d+246)) then
        tmp = t_2
    else if (x <= (-14000000000.0d0)) then
        tmp = x * (18.0d0 * (y * (z * t)))
    else if (x <= (-3.6d-22)) then
        tmp = t_1
    else if (x <= (-8d-76)) then
        tmp = (x * 18.0d0) * (t * (y * z))
    else if (x <= 3.6d+151) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z;
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) + (j * (k * -27.0));
	double t_2 = x * (i * -4.0);
	double tmp;
	if (x <= -1.5e+246) {
		tmp = t_2;
	} else if (x <= -14000000000.0) {
		tmp = x * (18.0 * (y * (z * t)));
	} else if (x <= -3.6e-22) {
		tmp = t_1;
	} else if (x <= -8e-76) {
		tmp = (x * 18.0) * (t * (y * z));
	} else if (x <= 3.6e+151) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	t_2 = x * (i * -4.0)
	tmp = 0
	if x <= -1.5e+246:
		tmp = t_2
	elif x <= -14000000000.0:
		tmp = x * (18.0 * (y * (z * t)))
	elif x <= -3.6e-22:
		tmp = t_1
	elif x <= -8e-76:
		tmp = (x * 18.0) * (t * (y * z))
	elif x <= 3.6e+151:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	t_2 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (x <= -1.5e+246)
		tmp = t_2;
	elseif (x <= -14000000000.0)
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))));
	elseif (x <= -3.6e-22)
		tmp = t_1;
	elseif (x <= -8e-76)
		tmp = Float64(Float64(x * 18.0) * Float64(t * Float64(y * z)));
	elseif (x <= 3.6e+151)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (k * -27.0));
	t_2 = x * (i * -4.0);
	tmp = 0.0;
	if (x <= -1.5e+246)
		tmp = t_2;
	elseif (x <= -14000000000.0)
		tmp = x * (18.0 * (y * (z * t)));
	elseif (x <= -3.6e-22)
		tmp = t_1;
	elseif (x <= -8e-76)
		tmp = (x * 18.0) * (t * (y * z));
	elseif (x <= 3.6e+151)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e+246], t$95$2, If[LessEqual[x, -14000000000.0], N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.6e-22], t$95$1, If[LessEqual[x, -8e-76], N[(N[(x * 18.0), $MachinePrecision] * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+151], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.5e246 or 3.6e151 < x

   1. Initial program 70.6%

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

      1. associate--l- 70.6%

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

      2. associate-+l- 70.6%

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

      3. associate--l- 70.6%

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

      4. *-commutative 70.6%

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

      5. associate-*r* 73.0%

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

      6. associate-*l* 84.2%

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

      7. associate-*r* 79.5%

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

      8. *-commutative 79.5%

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

      9. associate-*l* 77.4%

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

      10. associate--l- 77.4%

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

      11. associate-+l- 77.4%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in x around inf 87.6%

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

   5. Taylor expanded in t around 0 65.7%

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

      1. *-commutative 65.7%

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

   7. Simplified 65.7%

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

   if -1.5e246 < x < -1.4e10

   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- 84.1%

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

      2. associate-+l- 84.1%

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

      3. associate--l- 84.1%

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

      4. *-commutative 84.1%

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

      5. associate-*r* 83.9%

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

      6. associate-*l* 83.9%

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

      7. associate-*r* 82.2%

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

      8. *-commutative 82.2%

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

      9. associate-*l* 82.2%

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

      10. associate--l- 82.2%

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

      11. associate-+l- 82.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in x around inf 60.9%

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

   5. Taylor expanded in t around inf 45.9%

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

      1. associate-*r* 49.8%

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

      2. *-commutative 49.8%

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

      3. associate-*r* 49.8%

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

   7. Simplified 49.8%

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

   if -1.4e10 < x < -3.5999999999999998e-22 or -7.99999999999999942e-76 < x < 3.6e151

   1. Initial program 91.9%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in b around inf 57.8%

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

   if -3.5999999999999998e-22 < x < -7.99999999999999942e-76

   1. Initial program 90.5%

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

      1. associate--l- 90.5%

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

      2. associate-+l- 90.5%

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

      3. associate--l- 90.5%

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

      4. *-commutative 90.5%

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

      5. associate-*r* 82.0%

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

      6. associate-*l* 82.1%

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

      7. associate-*r* 81.8%

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

      8. *-commutative 81.8%

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

      9. associate-*l* 81.9%

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

      10. associate--l- 81.9%

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

      11. associate-+l- 81.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in x around inf 79.3%

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

   5. Taylor expanded in t around inf 63.1%

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

      1. add-exp-log_binary64 27.7%

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

   7. Applied rewrite-once 27.7%

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

      1. rem-exp-log 63.1%

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

      2. associate-*r* 63.3%

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

   9. Simplified 63.3%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+246}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq -14000000000:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-22}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-76}:\\ \;\;\;\;\left(x \cdot 18\right) \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+151}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \]

Alternative 16: 72.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+52} \lor \neg \left(t \leq 4.2 \cdot 10^{+126}\right):\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.5e+52) (not (<= t 4.2e+126)))
   (* t (+ (* (* x 18.0) (* y z)) (* a -4.0)))
   (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))))

C

assert(y < z);
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 ((t <= -1.5e+52) || !(t <= 4.2e+126)) {
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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 ((t <= (-1.5d+52)) .or. (.not. (t <= 4.2d+126))) then
        tmp = t * (((x * 18.0d0) * (y * z)) + (a * (-4.0d0)))
    else
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    end if
    code = tmp
end function

Java

assert y < z;
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 ((t <= -1.5e+52) || !(t <= 4.2e+126)) {
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.5e+52) or not (t <= 4.2e+126):
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0))
	else:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.5e+52) || !(t <= 4.2e+126))
		tmp = Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) + Float64(a * -4.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1.5e+52) || ~((t <= 4.2e+126)))
		tmp = t * (((x * 18.0) * (y * z)) + (a * -4.0));
	else
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.5e+52], N[Not[LessEqual[t, 4.2e+126]], $MachinePrecision]], N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5e52 or 4.1999999999999998e126 < t

   1. Initial program 86.1%

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

      1. add-exp-log_binary64 42.6%

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

   3. Applied rewrite-once 42.6%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 86.1%

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

      2. associate-*l* 78.1%

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

      3. associate-*r* 78.1%

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

      4. *-commutative 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in t around inf 79.3%

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

      1. cancel-sign-sub-inv 79.3%

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

      2. associate-*r* 79.3%

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

      3. metadata-eval 79.3%

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

      4. *-commutative 79.3%

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

   8. Simplified 79.3%

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

   if -1.5e52 < t < 4.1999999999999998e126

   1. Initial program 87.0%

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

      1. associate--l- 87.0%

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

      2. associate-+l- 87.0%

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

      3. associate--l- 87.0%

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

      4. *-commutative 87.0%

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

      5. associate-*r* 91.8%

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

      6. associate-*l* 95.5%

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

      7. associate-*r* 91.3%

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

      8. *-commutative 91.3%

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

      9. associate-*l* 87.7%

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

      10. associate--l- 87.7%

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

      11. associate-+l- 87.7%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in t around 0 79.8%

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+52} \lor \neg \left(t \leq 4.2 \cdot 10^{+126}\right):\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]

Alternative 17: 49.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{if}\;i \leq -18.5:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* j (* k -27.0)))) (t_2 (- (* b c) (* x (* 4.0 i)))))
   (if (<= i -18.5)
     t_2
     (if (<= i 5.2e-85)
       t_1
       (if (<= i 1.6e-18)
         (* x (* 18.0 (* t (* y z))))
         (if (<= i 8.5e+147) t_1 t_2))))))

C

assert(y < z);
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) + (j * (k * -27.0));
	double t_2 = (b * c) - (x * (4.0 * i));
	double tmp;
	if (i <= -18.5) {
		tmp = t_2;
	} else if (i <= 5.2e-85) {
		tmp = t_1;
	} else if (i <= 1.6e-18) {
		tmp = x * (18.0 * (t * (y * z)));
	} else if (i <= 8.5e+147) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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 = (b * c) + (j * (k * (-27.0d0)))
    t_2 = (b * c) - (x * (4.0d0 * i))
    if (i <= (-18.5d0)) then
        tmp = t_2
    else if (i <= 5.2d-85) then
        tmp = t_1
    else if (i <= 1.6d-18) then
        tmp = x * (18.0d0 * (t * (y * z)))
    else if (i <= 8.5d+147) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z;
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) + (j * (k * -27.0));
	double t_2 = (b * c) - (x * (4.0 * i));
	double tmp;
	if (i <= -18.5) {
		tmp = t_2;
	} else if (i <= 5.2e-85) {
		tmp = t_1;
	} else if (i <= 1.6e-18) {
		tmp = x * (18.0 * (t * (y * z)));
	} else if (i <= 8.5e+147) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	t_2 = (b * c) - (x * (4.0 * i))
	tmp = 0
	if i <= -18.5:
		tmp = t_2
	elif i <= 5.2e-85:
		tmp = t_1
	elif i <= 1.6e-18:
		tmp = x * (18.0 * (t * (y * z)))
	elif i <= 8.5e+147:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	t_2 = Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)))
	tmp = 0.0
	if (i <= -18.5)
		tmp = t_2;
	elseif (i <= 5.2e-85)
		tmp = t_1;
	elseif (i <= 1.6e-18)
		tmp = Float64(x * Float64(18.0 * Float64(t * Float64(y * z))));
	elseif (i <= 8.5e+147)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (k * -27.0));
	t_2 = (b * c) - (x * (4.0 * i));
	tmp = 0.0;
	if (i <= -18.5)
		tmp = t_2;
	elseif (i <= 5.2e-85)
		tmp = t_1;
	elseif (i <= 1.6e-18)
		tmp = x * (18.0 * (t * (y * z)));
	elseif (i <= 8.5e+147)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -18.5], t$95$2, If[LessEqual[i, 5.2e-85], t$95$1, If[LessEqual[i, 1.6e-18], N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.5e+147], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -18.5 or 8.5000000000000007e147 < i

   1. Initial program 85.9%

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

      1. associate--l- 85.9%

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

      2. associate-+l- 85.9%

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

      3. associate--l- 85.9%

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

      4. *-commutative 85.9%

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

      5. associate-*r* 88.0%

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

      6. associate-*l* 91.2%

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

      7. associate-*r* 87.0%

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

      8. *-commutative 87.0%

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

      9. associate-*l* 85.9%

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

      10. associate--l- 85.9%

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

      11. associate-+l- 85.9%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in t around 0 76.0%

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

   5. Taylor expanded in i around inf 65.4%

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

      1. *-commutative 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-*r* 65.4%

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

   7. Simplified 65.4%

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

   if -18.5 < i < 5.20000000000000023e-85 or 1.6e-18 < i < 8.5000000000000007e147

   1. Initial program 86.9%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in b around inf 55.2%

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

   if 5.20000000000000023e-85 < i < 1.6e-18

   1. Initial program 88.9%

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

      1. associate--l- 88.9%

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

      2. associate-+l- 88.9%

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

      3. associate--l- 88.9%

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

      4. *-commutative 88.9%

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

      5. associate-*r* 78.5%

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

      6. associate-*l* 72.9%

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

      7. associate-*r* 78.2%

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

      8. *-commutative 78.2%

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

      9. associate-*l* 88.8%

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

      10. associate--l- 88.8%

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

      11. associate-+l- 88.8%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in x around inf 73.1%

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

   5. Taylor expanded in t around inf 62.3%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -18.5:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{-85}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{+147}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - x \cdot \left(4 \cdot i\right)\\ \end{array} \]

Alternative 18: 36.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+60}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 6 \cdot 10^{+64}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -5e+60)
   (* b c)
   (if (<= (* b c) 6e+64) (* -27.0 (* j k)) (* b c))))

C

assert(y < z);
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) <= -5e+60) {
		tmp = b * c;
	} else if ((b * c) <= 6e+64) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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) <= (-5d+60)) then
        tmp = b * c
    else if ((b * c) <= 6d+64) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert y < z;
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) <= -5e+60) {
		tmp = b * c;
	} else if ((b * c) <= 6e+64) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -5e+60:
		tmp = b * c
	elif (b * c) <= 6e+64:
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -5e+60)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 6e+64)
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -5e+60)
		tmp = b * c;
	elseif ((b * c) <= 6e+64)
		tmp = -27.0 * (j * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -5e+60], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6e+64], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -4.99999999999999975e60 or 6.0000000000000004e64 < (*.f64 b c)

   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. add-exp-log_binary64 54.2%

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

   3. Applied rewrite-once 54.2%

      \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. rem-exp-log 83.0%

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

      2. associate-*l* 85.1%

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

      3. associate-*r* 85.1%

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

      4. *-commutative 85.1%

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

   5. Simplified 85.1%

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

   6. Taylor expanded in b around inf 50.9%

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

   if -4.99999999999999975e60 < (*.f64 b c) < 6.0000000000000004e64

   1. Initial program 88.8%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in j around inf 31.2%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+60}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 6 \cdot 10^{+64}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 19: 31.4% accurate, 3.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-68} \lor \neg \left(x \leq 2.08 \cdot 10^{+37}\right):\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -4.5e-68) (not (<= x 2.08e+37)))
   (* x (* i -4.0))
   (* -27.0 (* j k))))

C

assert(y < z);
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 <= -4.5e-68) || !(x <= 2.08e+37)) {
		tmp = x * (i * -4.0);
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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 <= (-4.5d-68)) .or. (.not. (x <= 2.08d+37))) then
        tmp = x * (i * (-4.0d0))
    else
        tmp = (-27.0d0) * (j * k)
    end if
    code = tmp
end function

Java

assert y < z;
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 <= -4.5e-68) || !(x <= 2.08e+37)) {
		tmp = x * (i * -4.0);
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -4.5e-68) or not (x <= 2.08e+37):
		tmp = x * (i * -4.0)
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -4.5e-68) || !(x <= 2.08e+37))
		tmp = Float64(x * Float64(i * -4.0));
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -4.5e-68) || ~((x <= 2.08e+37)))
		tmp = x * (i * -4.0);
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -4.5e-68], N[Not[LessEqual[x, 2.08e+37]], $MachinePrecision]], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.49999999999999999e-68 or 2.0800000000000001e37 < x

   1. Initial program 80.8%

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

      1. associate--l- 80.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 80.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

      3. associate--l- 80.8%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-commutative 80.8%

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)} \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. associate-*r* 81.5%

         \[\leadsto \color{blue}{z \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 85.7%

         \[\leadsto z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot t\right)\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. associate-*r* 82.3%

         \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot 18\right)\right) \cdot \left(y \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-commutative 82.3%

         \[\leadsto \color{blue}{\left(\left(x \cdot 18\right) \cdot z\right)} \cdot \left(y \cdot t\right) - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. associate-*l* 80.9%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. associate--l- 80.9%

          \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      11. associate-+l- 80.9%

          \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

   3. Simplified 85.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 65.4%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]

   5. Taylor expanded in t around 0 38.2%

      \[\leadsto x \cdot \color{blue}{\left(-4 \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 38.2%

         \[\leadsto x \cdot \color{blue}{\left(i \cdot -4\right)} \]

   7. Simplified 38.2%

      \[\leadsto x \cdot \color{blue}{\left(i \cdot -4\right)} \]

   if -4.49999999999999999e-68 < x < 2.0800000000000001e37

   1. Initial program 93.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 93.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x \cdot 18, y \cdot z, a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in j around inf 38.9%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-68} \lor \neg \left(x \leq 2.08 \cdot 10^{+37}\right):\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 20: 23.9% accurate, 10.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ b \cdot c \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* b c))

C

assert(y < z);
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

NOTE: y and z should be sorted in increasing order before calling this function.
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

assert y < z;
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

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = b * c;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(b * c), $MachinePrecision]

Derivation

1. Initial program 86.7%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Step-by-step derivation

   1. add-exp-log_binary64 50.2%

      \[\leadsto \color{blue}{\left(\left(\left(e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k} \]

3. Applied rewrite-once 50.2%

   \[\leadsto \left(\left(\left(\color{blue}{e^{\log \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\right)}} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
4. Step-by-step derivation

   1. rem-exp-log 86.7%

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. associate-*l* 86.3%

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. associate-*r* 86.3%

      \[\leadsto \left(\left(\left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot \left(z \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. *-commutative 86.3%

      \[\leadsto \left(\left(\left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot \color{blue}{\left(t \cdot z\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

5. Simplified 86.3%

   \[\leadsto \left(\left(\left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right) \cdot \left(t \cdot z\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

6. Taylor expanded in b around inf 21.7%

   \[\leadsto \color{blue}{b \cdot c} \]

7. Final simplification 21.7%

   \[\leadsto b \cdot c \]

Developer target: 89.4% accurate, 0.9× 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 2023297 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))