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

Percentage Accurate: 84.7% → 93.1%

Time: 29.9s

Alternatives: 22

Speedup: 0.8×

• 51.1% 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: 84.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - t\_1\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \mathsf{fma}\left(18 \cdot t, y \cdot z, i \cdot -4\right) - 4 \cdot \left(t \cdot a\right)\right)\right) - t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+288}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(18, z \cdot \left(y \cdot t\right), i \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 27.0) k))
        (t_2
         (-
          (-
           (+ (- (* t (* (* (* x 18.0) y) z)) (* t (* a 4.0))) (* b c))
           (* (* x 4.0) i))
          t_1)))
   (if (<= t_2 (- INFINITY))
     (-
      (+ (* b c) (- (* x (fma (* 18.0 t) (* y z) (* i -4.0))) (* 4.0 (* t a))))
      t_1)
     (if (<= t_2 5e+288)
       t_2
       (if (<= t_2 INFINITY)
         (-
          (+
           (* t (- (* (* x 18.0) (* y z)) (* a 4.0)))
           (- (* b c) (* x (* 4.0 i))))
          (* j (* 27.0 k)))
         (* x (fma 18.0 (* z (* y t)) (* i -4.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = ((((t * (((x * 18.0) * y) * z)) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((b * c) + ((x * fma((18.0 * t), (y * z), (i * -4.0))) - (4.0 * (t * a)))) - t_1;
	} else if (t_2 <= 5e+288) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + ((b * c) - (x * (4.0 * i)))) - (j * (27.0 * k));
	} else {
		tmp = x * fma(18.0, (z * (y * t)), (i * -4.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(Float64(Float64(Float64(t * Float64(Float64(Float64(x * 18.0) * y) * z)) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(b * c) + Float64(Float64(x * fma(Float64(18.0 * t), Float64(y * z), Float64(i * -4.0))) - Float64(4.0 * Float64(t * a)))) - t_1);
	elseif (t_2 <= 5e+288)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0))) + Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)))) - Float64(j * Float64(27.0 * k)));
	else
		tmp = Float64(x * fma(18.0, Float64(z * Float64(y * t)), Float64(i * -4.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(b * c), $MachinePrecision] + N[(N[(x * N[(N[(18.0 * t), $MachinePrecision] * N[(y * z), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 5e+288], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(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[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 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 89.0%

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

   3. Taylor expanded in x around 0 93.7%

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

      1. associate--l+ 93.7%

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

      2. cancel-sign-sub-inv 93.7%

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

      3. associate-*r* 93.7%

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

      4. fma-define 93.7%

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

      5. metadata-eval 93.7%

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

      6. *-commutative 93.7%

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

   5. Applied egg-rr 93.7%

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

   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)) < 5.0000000000000003e288

   1. Initial program 99.8%

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

   if 5.0000000000000003e288 < (-.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 94.1%

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

   3. Simplified 94.1%

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

   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%

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

   3. Simplified 23.3%

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

   5. Taylor expanded in x around inf 73.8%

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

      1. +-commutative 73.8%

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

      2. metadata-eval 73.8%

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

      3. cancel-sign-sub-inv 73.8%

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

      4. cancel-sign-sub-inv 73.8%

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

      5. metadata-eval 73.8%

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

      6. fma-undefine 73.8%

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

      7. associate-*r* 77.2%

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

   7. Simplified 77.2%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq -\infty:\\ \;\;\;\;\left(b \cdot c + \left(x \cdot \mathsf{fma}\left(18 \cdot t, y \cdot z, i \cdot -4\right) - 4 \cdot \left(t \cdot a\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(18, z \cdot \left(y \cdot t\right), i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - t\_1\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+288}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(18, z \cdot \left(y \cdot t\right), i \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 27.0) k))
        (t_2
         (-
          (-
           (+ (- (* t (* (* (* x 18.0) y) z)) (* t (* a 4.0))) (* b c))
           (* (* x 4.0) i))
          t_1)))
   (if (<= t_2 (- INFINITY))
     (-
      (-
       (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
       (* 4.0 (* t a)))
      t_1)
     (if (<= t_2 5e+288)
       t_2
       (if (<= t_2 INFINITY)
         (-
          (+
           (* t (- (* (* x 18.0) (* y z)) (* a 4.0)))
           (- (* b c) (* x (* 4.0 i))))
          (* j (* 27.0 k)))
         (* x (fma 18.0 (* z (* y t)) (* i -4.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = ((((t * (((x * 18.0) * y) * z)) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - t_1;
	} else if (t_2 <= 5e+288) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + ((b * c) - (x * (4.0 * i)))) - (j * (27.0 * k));
	} else {
		tmp = x * fma(18.0, (z * (y * t)), (i * -4.0));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(Float64(Float64(Float64(t * Float64(Float64(Float64(x * 18.0) * y) * z)) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (t_2 <= 5e+288)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0))) + Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)))) - Float64(j * Float64(27.0 * k)));
	else
		tmp = Float64(x * fma(18.0, Float64(z * Float64(y * t)), Float64(i * -4.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 5e+288], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(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[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 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 89.0%

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

   3. Taylor expanded in x around 0 93.7%

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

   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)) < 5.0000000000000003e288

   1. Initial program 99.8%

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

   if 5.0000000000000003e288 < (-.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 94.1%

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

   3. Simplified 94.1%

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

   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%

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

   3. Simplified 23.3%

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

   5. Taylor expanded in x around inf 73.8%

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

      1. +-commutative 73.8%

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

      2. metadata-eval 73.8%

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

      3. cancel-sign-sub-inv 73.8%

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

      4. cancel-sign-sub-inv 73.8%

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

      5. metadata-eval 73.8%

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

      6. fma-undefine 73.8%

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

      7. associate-*r* 77.2%

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

   7. Simplified 77.2%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq -\infty:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(18, z \cdot \left(y \cdot t\right), i \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - t\_1\\ t_3 := 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(t\_3 - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+288}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + t\_3\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 27.0) k))
        (t_2
         (-
          (-
           (+ (- (* t (* (* (* x 18.0) y) z)) (* t (* a 4.0))) (* b c))
           (* (* x 4.0) i))
          t_1))
        (t_3 (* 18.0 (* t (* y z)))))
   (if (<= t_2 (- INFINITY))
     (- (- (+ (* b c) (* x (- t_3 (* 4.0 i)))) (* 4.0 (* t a))) t_1)
     (if (<= t_2 5e+288)
       t_2
       (if (<= t_2 INFINITY)
         (-
          (+
           (* t (- (* (* x 18.0) (* y z)) (* a 4.0)))
           (- (* b c) (* x (* 4.0 i))))
          (* j (* 27.0 k)))
         (* x (+ (* i -4.0) t_3)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = ((((t * (((x * 18.0) * y) * z)) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1;
	double t_3 = 18.0 * (t * (y * z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (((b * c) + (x * (t_3 - (4.0 * i)))) - (4.0 * (t * a))) - t_1;
	} else if (t_2 <= 5e+288) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + ((b * c) - (x * (4.0 * i)))) - (j * (27.0 * k));
	} else {
		tmp = x * ((i * -4.0) + t_3);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = ((((t * (((x * 18.0) * y) * z)) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1;
	double t_3 = 18.0 * (t * (y * z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (((b * c) + (x * (t_3 - (4.0 * i)))) - (4.0 * (t * a))) - t_1;
	} else if (t_2 <= 5e+288) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + ((b * c) - (x * (4.0 * i)))) - (j * (27.0 * k));
	} else {
		tmp = x * ((i * -4.0) + t_3);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = ((((t * (((x * 18.0) * y) * z)) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1
	t_3 = 18.0 * (t * (y * z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (((b * c) + (x * (t_3 - (4.0 * i)))) - (4.0 * (t * a))) - t_1
	elif t_2 <= 5e+288:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + ((b * c) - (x * (4.0 * i)))) - (j * (27.0 * k))
	else:
		tmp = x * ((i * -4.0) + t_3)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(Float64(Float64(Float64(t * Float64(Float64(Float64(x * 18.0) * y) * z)) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - t_1)
	t_3 = Float64(18.0 * Float64(t * Float64(y * z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(x * Float64(t_3 - Float64(4.0 * i)))) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (t_2 <= 5e+288)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0))) + Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)))) - Float64(j * Float64(27.0 * k)));
	else
		tmp = Float64(x * Float64(Float64(i * -4.0) + t_3));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = ((((t * (((x * 18.0) * y) * z)) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1;
	t_3 = 18.0 * (t * (y * z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (((b * c) + (x * (t_3 - (4.0 * i)))) - (4.0 * (t * a))) - t_1;
	elseif (t_2 <= 5e+288)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + ((b * c) - (x * (4.0 * i)))) - (j * (27.0 * k));
	else
		tmp = x * ((i * -4.0) + t_3);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(t$95$3 - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 5e+288], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(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[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(i * -4.0), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 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 89.0%

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

   3. Taylor expanded in x around 0 93.7%

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

   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)) < 5.0000000000000003e288

   1. Initial program 99.8%

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

   if 5.0000000000000003e288 < (-.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 94.1%

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

   3. Simplified 94.1%

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

   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%

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

   3. Simplified 23.3%

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

   5. Taylor expanded in x around inf 73.8%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq -\infty:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \leq \infty:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 33.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(\left(z \cdot t\right) \cdot \left(18 \cdot y\right)\right)\\ t_2 := i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.14 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-305}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-258}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{-181}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+35}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 (* (* z t) (* 18.0 y)))) (t_2 (* i (* x -4.0))))
   (if (<= x -1e+125)
     t_2
     (if (<= x -1.14e-38)
       t_1
       (if (<= x 6e-305)
         (* k (* j -27.0))
         (if (<= x 2.5e-258)
           (* b c)
           (if (<= x 9.4e-181)
             (* j (* k -27.0))
             (if (<= x 9.8e+35) (* b c) (if (<= x 2.6e+148) t_1 t_2)))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 * ((z * t) * (18.0 * y));
	double t_2 = i * (x * -4.0);
	double tmp;
	if (x <= -1e+125) {
		tmp = t_2;
	} else if (x <= -1.14e-38) {
		tmp = t_1;
	} else if (x <= 6e-305) {
		tmp = k * (j * -27.0);
	} else if (x <= 2.5e-258) {
		tmp = b * c;
	} else if (x <= 9.4e-181) {
		tmp = j * (k * -27.0);
	} else if (x <= 9.8e+35) {
		tmp = b * c;
	} else if (x <= 2.6e+148) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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 * ((z * t) * (18.0d0 * y))
    t_2 = i * (x * (-4.0d0))
    if (x <= (-1d+125)) then
        tmp = t_2
    else if (x <= (-1.14d-38)) then
        tmp = t_1
    else if (x <= 6d-305) then
        tmp = k * (j * (-27.0d0))
    else if (x <= 2.5d-258) then
        tmp = b * c
    else if (x <= 9.4d-181) then
        tmp = j * (k * (-27.0d0))
    else if (x <= 9.8d+35) then
        tmp = b * c
    else if (x <= 2.6d+148) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 * ((z * t) * (18.0 * y));
	double t_2 = i * (x * -4.0);
	double tmp;
	if (x <= -1e+125) {
		tmp = t_2;
	} else if (x <= -1.14e-38) {
		tmp = t_1;
	} else if (x <= 6e-305) {
		tmp = k * (j * -27.0);
	} else if (x <= 2.5e-258) {
		tmp = b * c;
	} else if (x <= 9.4e-181) {
		tmp = j * (k * -27.0);
	} else if (x <= 9.8e+35) {
		tmp = b * c;
	} else if (x <= 2.6e+148) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((z * t) * (18.0 * y))
	t_2 = i * (x * -4.0)
	tmp = 0
	if x <= -1e+125:
		tmp = t_2
	elif x <= -1.14e-38:
		tmp = t_1
	elif x <= 6e-305:
		tmp = k * (j * -27.0)
	elif x <= 2.5e-258:
		tmp = b * c
	elif x <= 9.4e-181:
		tmp = j * (k * -27.0)
	elif x <= 9.8e+35:
		tmp = b * c
	elif x <= 2.6e+148:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(z * t) * Float64(18.0 * y)))
	t_2 = Float64(i * Float64(x * -4.0))
	tmp = 0.0
	if (x <= -1e+125)
		tmp = t_2;
	elseif (x <= -1.14e-38)
		tmp = t_1;
	elseif (x <= 6e-305)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (x <= 2.5e-258)
		tmp = Float64(b * c);
	elseif (x <= 9.4e-181)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (x <= 9.8e+35)
		tmp = Float64(b * c);
	elseif (x <= 2.6e+148)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((z * t) * (18.0 * y));
	t_2 = i * (x * -4.0);
	tmp = 0.0;
	if (x <= -1e+125)
		tmp = t_2;
	elseif (x <= -1.14e-38)
		tmp = t_1;
	elseif (x <= 6e-305)
		tmp = k * (j * -27.0);
	elseif (x <= 2.5e-258)
		tmp = b * c;
	elseif (x <= 9.4e-181)
		tmp = j * (k * -27.0);
	elseif (x <= 9.8e+35)
		tmp = b * c;
	elseif (x <= 2.6e+148)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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[(N[(z * t), $MachinePrecision] * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+125], t$95$2, If[LessEqual[x, -1.14e-38], t$95$1, If[LessEqual[x, 6e-305], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-258], N[(b * c), $MachinePrecision], If[LessEqual[x, 9.4e-181], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e+35], N[(b * c), $MachinePrecision], If[LessEqual[x, 2.6e+148], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -9.9999999999999992e124 or 2.6e148 < x

   1. Initial program 66.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in i around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. associate-*r* 57.6%

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

   7. Simplified 57.6%

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

   if -9.9999999999999992e124 < x < -1.1399999999999999e-38 or 9.8000000000000005e35 < x < 2.6e148

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0 93.5%

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

   4. Taylor expanded in a around 0 76.5%

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

   5. Taylor expanded in t around inf 37.9%

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

      1. *-commutative 37.9%

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

      2. associate-*r* 41.9%

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

      3. *-commutative 41.9%

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

      4. associate-*r* 48.3%

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

      5. associate-*r* 48.3%

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

      6. *-commutative 48.3%

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

      7. associate-*l* 48.3%

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

      8. associate-*r* 48.3%

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

      9. *-commutative 48.3%

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

      10. *-commutative 48.3%

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

      11. associate-*l* 44.1%

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

   7. Simplified 44.1%

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

   if -1.1399999999999999e-38 < x < 6.0000000000000002e-305

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 83.5%

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

      1. associate--l+ 83.5%

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

      2. cancel-sign-sub-inv 83.5%

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

      3. associate-*r* 83.5%

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

      4. fma-define 83.5%

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

      5. metadata-eval 83.5%

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

      6. *-commutative 83.5%

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

   5. Applied egg-rr 83.5%

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

   6. Taylor expanded in j around inf 37.8%

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

      1. *-commutative 37.8%

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

      2. *-commutative 37.8%

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

      3. associate-*r* 37.7%

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

   8. Simplified 37.7%

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

   if 6.0000000000000002e-305 < x < 2.4999999999999999e-258 or 9.3999999999999995e-181 < x < 9.8000000000000005e35

   1. Initial program 90.1%

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

   3. Simplified 85.4%

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

   5. Taylor expanded in b around inf 45.5%

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

   if 2.4999999999999999e-258 < x < 9.3999999999999995e-181

   1. Initial program 99.9%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in j around inf 58.2%

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

      1. metadata-eval 58.2%

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

      2. distribute-lft-neg-in 58.2%

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

      3. associate-*r* 58.1%

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

      4. *-commutative 58.1%

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

      5. associate-*r* 58.2%

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

      6. distribute-rgt-neg-in 58.2%

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

      7. *-commutative 58.2%

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

      8. distribute-rgt-neg-in 58.2%

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

      9. metadata-eval 58.2%

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

   7. Simplified 58.2%

      \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+125}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;x \leq -1.14 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(\left(z \cdot t\right) \cdot \left(18 \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-305}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-258}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{-181}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+35}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \left(\left(z \cdot t\right) \cdot \left(18 \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+201}:\\ \;\;\;\;b \cdot c + x \cdot \left(t\_1 - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+189}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + t\_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 (* t (* y z)))))
   (if (<= x -1.75e+201)
     (+ (* b c) (* x (- t_1 (* 4.0 i))))
     (if (<= x 3.7e+189)
       (-
        (+
         (* t (- (* (* x 18.0) (* y z)) (* a 4.0)))
         (- (* b c) (* x (* 4.0 i))))
        (* j (* 27.0 k)))
       (* x (+ (* i -4.0) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 * (t * (y * z));
	double tmp;
	if (x <= -1.75e+201) {
		tmp = (b * c) + (x * (t_1 - (4.0 * i)));
	} else if (x <= 3.7e+189) {
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + ((b * c) - (x * (4.0 * i)))) - (j * (27.0 * k));
	} else {
		tmp = x * ((i * -4.0) + t_1);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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) :: tmp
    t_1 = 18.0d0 * (t * (y * z))
    if (x <= (-1.75d+201)) then
        tmp = (b * c) + (x * (t_1 - (4.0d0 * i)))
    else if (x <= 3.7d+189) then
        tmp = ((t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0))) + ((b * c) - (x * (4.0d0 * i)))) - (j * (27.0d0 * k))
    else
        tmp = x * ((i * (-4.0d0)) + t_1)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 * (t * (y * z));
	double tmp;
	if (x <= -1.75e+201) {
		tmp = (b * c) + (x * (t_1 - (4.0 * i)));
	} else if (x <= 3.7e+189) {
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + ((b * c) - (x * (4.0 * i)))) - (j * (27.0 * k));
	} else {
		tmp = x * ((i * -4.0) + t_1);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (y * z))
	tmp = 0
	if x <= -1.75e+201:
		tmp = (b * c) + (x * (t_1 - (4.0 * i)))
	elif x <= 3.7e+189:
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + ((b * c) - (x * (4.0 * i)))) - (j * (27.0 * k))
	else:
		tmp = x * ((i * -4.0) + t_1)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(y * z)))
	tmp = 0.0
	if (x <= -1.75e+201)
		tmp = Float64(Float64(b * c) + Float64(x * Float64(t_1 - Float64(4.0 * i))));
	elseif (x <= 3.7e+189)
		tmp = Float64(Float64(Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0))) + Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)))) - Float64(j * Float64(27.0 * k)));
	else
		tmp = Float64(x * Float64(Float64(i * -4.0) + t_1));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (t * (y * z));
	tmp = 0.0;
	if (x <= -1.75e+201)
		tmp = (b * c) + (x * (t_1 - (4.0 * i)));
	elseif (x <= 3.7e+189)
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + ((b * c) - (x * (4.0 * i)))) - (j * (27.0 * k));
	else
		tmp = x * ((i * -4.0) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.75e+201], N[(N[(b * c), $MachinePrecision] + N[(x * N[(t$95$1 - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e+189], N[(N[(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[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(i * -4.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7500000000000001e201

   1. Initial program 52.2%

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

   3. Taylor expanded in x around 0 77.8%

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

   4. Taylor expanded in a around 0 85.2%

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

   5. Taylor expanded in j around 0 88.9%

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

   if -1.7500000000000001e201 < x < 3.70000000000000021e189

   1. Initial program 91.4%

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

   3. Simplified 90.0%

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

   if 3.70000000000000021e189 < x

   1. Initial program 56.8%

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

   3. Simplified 65.4%

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

   5. Taylor expanded in x around inf 95.6%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+201}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+189}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ t_2 := x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -1.56 \cdot 10^{+140}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+33}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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) (* 4.0 (* t a))) (* (* j 27.0) k)))
        (t_2 (* x (+ (* i -4.0) (* 18.0 (* t (* y z)))))))
   (if (<= x -1.56e+140)
     t_2
     (if (<= x 4.2e-156)
       t_1
       (if (<= x 7.5e+33)
         (- (- (* b c) (* 4.0 (* x i))) (* j (* 27.0 k)))
         (if (<= x 1.25e+54) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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) - (4.0 * (t * a))) - ((j * 27.0) * k);
	double t_2 = x * ((i * -4.0) + (18.0 * (t * (y * z))));
	double tmp;
	if (x <= -1.56e+140) {
		tmp = t_2;
	} else if (x <= 4.2e-156) {
		tmp = t_1;
	} else if (x <= 7.5e+33) {
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (27.0 * k));
	} else if (x <= 1.25e+54) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    t_2 = x * ((i * (-4.0d0)) + (18.0d0 * (t * (y * z))))
    if (x <= (-1.56d+140)) then
        tmp = t_2
    else if (x <= 4.2d-156) then
        tmp = t_1
    else if (x <= 7.5d+33) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - (j * (27.0d0 * k))
    else if (x <= 1.25d+54) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) - (4.0 * (t * a))) - ((j * 27.0) * k);
	double t_2 = x * ((i * -4.0) + (18.0 * (t * (y * z))));
	double tmp;
	if (x <= -1.56e+140) {
		tmp = t_2;
	} else if (x <= 4.2e-156) {
		tmp = t_1;
	} else if (x <= 7.5e+33) {
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (27.0 * k));
	} else if (x <= 1.25e+54) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	t_2 = x * ((i * -4.0) + (18.0 * (t * (y * z))))
	tmp = 0
	if x <= -1.56e+140:
		tmp = t_2
	elif x <= 4.2e-156:
		tmp = t_1
	elif x <= 7.5e+33:
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (27.0 * k))
	elif x <= 1.25e+54:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k))
	t_2 = Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(t * Float64(y * z)))))
	tmp = 0.0
	if (x <= -1.56e+140)
		tmp = t_2;
	elseif (x <= 4.2e-156)
		tmp = t_1;
	elseif (x <= 7.5e+33)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(j * Float64(27.0 * k)));
	elseif (x <= 1.25e+54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	t_2 = x * ((i * -4.0) + (18.0 * (t * (y * z))));
	tmp = 0.0;
	if (x <= -1.56e+140)
		tmp = t_2;
	elseif (x <= 4.2e-156)
		tmp = t_1;
	elseif (x <= 7.5e+33)
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (27.0 * k));
	elseif (x <= 1.25e+54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.56e+140], t$95$2, If[LessEqual[x, 4.2e-156], t$95$1, If[LessEqual[x, 7.5e+33], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e+54], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.56000000000000002e140 or 1.25000000000000001e54 < x

   1. Initial program 68.6%

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

   3. Simplified 74.2%

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

   5. Taylor expanded in x around inf 80.5%

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

   if -1.56000000000000002e140 < x < 4.20000000000000025e-156 or 7.50000000000000046e33 < x < 1.25000000000000001e54

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0 78.8%

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

   if 4.20000000000000025e-156 < x < 7.50000000000000046e33

   1. Initial program 88.5%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in t around 0 73.0%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.56 \cdot 10^{+140}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-156}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+33}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+54}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 32.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-197}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-101}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-36}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+252}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 (* t (* a -4.0))))
   (if (<= t -2.8e+78)
     t_1
     (if (<= t -1.65e-197)
       (* b c)
       (if (<= t 6.2e-101)
         (* i (* x -4.0))
         (if (<= t 2.8e-36)
           (* b c)
           (if (<= t 5.4e+252) (* 18.0 (* t (* x (* y z)))) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = t * (a * -4.0);
	double tmp;
	if (t <= -2.8e+78) {
		tmp = t_1;
	} else if (t <= -1.65e-197) {
		tmp = b * c;
	} else if (t <= 6.2e-101) {
		tmp = i * (x * -4.0);
	} else if (t <= 2.8e-36) {
		tmp = b * c;
	} else if (t <= 5.4e+252) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (t <= (-2.8d+78)) then
        tmp = t_1
    else if (t <= (-1.65d-197)) then
        tmp = b * c
    else if (t <= 6.2d-101) then
        tmp = i * (x * (-4.0d0))
    else if (t <= 2.8d-36) then
        tmp = b * c
    else if (t <= 5.4d+252) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = t * (a * -4.0);
	double tmp;
	if (t <= -2.8e+78) {
		tmp = t_1;
	} else if (t <= -1.65e-197) {
		tmp = b * c;
	} else if (t <= 6.2e-101) {
		tmp = i * (x * -4.0);
	} else if (t <= 2.8e-36) {
		tmp = b * c;
	} else if (t <= 5.4e+252) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if t <= -2.8e+78:
		tmp = t_1
	elif t <= -1.65e-197:
		tmp = b * c
	elif t <= 6.2e-101:
		tmp = i * (x * -4.0)
	elif t <= 2.8e-36:
		tmp = b * c
	elif t <= 5.4e+252:
		tmp = 18.0 * (t * (x * (y * z)))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (t <= -2.8e+78)
		tmp = t_1;
	elseif (t <= -1.65e-197)
		tmp = Float64(b * c);
	elseif (t <= 6.2e-101)
		tmp = Float64(i * Float64(x * -4.0));
	elseif (t <= 2.8e-36)
		tmp = Float64(b * c);
	elseif (t <= 5.4e+252)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (t <= -2.8e+78)
		tmp = t_1;
	elseif (t <= -1.65e-197)
		tmp = b * c;
	elseif (t <= 6.2e-101)
		tmp = i * (x * -4.0);
	elseif (t <= 2.8e-36)
		tmp = b * c;
	elseif (t <= 5.4e+252)
		tmp = 18.0 * (t * (x * (y * z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+78], t$95$1, If[LessEqual[t, -1.65e-197], N[(b * c), $MachinePrecision], If[LessEqual[t, 6.2e-101], N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-36], N[(b * c), $MachinePrecision], If[LessEqual[t, 5.4e+252], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.8000000000000001e78 or 5.40000000000000021e252 < t

   1. Initial program 79.2%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in a around inf 50.8%

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

      1. *-commutative 50.8%

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

      2. *-commutative 50.8%

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

      3. associate-*r* 50.8%

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

      4. *-commutative 50.8%

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

   7. Simplified 50.8%

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

   if -2.8000000000000001e78 < t < -1.6499999999999999e-197 or 6.19999999999999946e-101 < t < 2.8000000000000001e-36

   1. Initial program 91.1%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in b around inf 40.1%

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

   if -1.6499999999999999e-197 < t < 6.19999999999999946e-101

   1. Initial program 81.6%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in i around inf 40.7%

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

      1. *-commutative 40.7%

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

      2. associate-*r* 40.7%

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

   7. Simplified 40.7%

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

   if 2.8000000000000001e-36 < t < 5.40000000000000021e252

   1. Initial program 83.7%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in y around inf 42.3%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-197}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-101}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-36}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+252}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 32.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-194}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-101}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-18}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+246}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 (* t (* a -4.0))))
   (if (<= t -1.1e+74)
     t_1
     (if (<= t -4.8e-194)
       (* b c)
       (if (<= t 6.8e-101)
         (* i (* x -4.0))
         (if (<= t 4.5e-18)
           (* b c)
           (if (<= t 1.45e+246) (* t (* 18.0 (* y (* x z)))) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = t * (a * -4.0);
	double tmp;
	if (t <= -1.1e+74) {
		tmp = t_1;
	} else if (t <= -4.8e-194) {
		tmp = b * c;
	} else if (t <= 6.8e-101) {
		tmp = i * (x * -4.0);
	} else if (t <= 4.5e-18) {
		tmp = b * c;
	} else if (t <= 1.45e+246) {
		tmp = t * (18.0 * (y * (x * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (t <= (-1.1d+74)) then
        tmp = t_1
    else if (t <= (-4.8d-194)) then
        tmp = b * c
    else if (t <= 6.8d-101) then
        tmp = i * (x * (-4.0d0))
    else if (t <= 4.5d-18) then
        tmp = b * c
    else if (t <= 1.45d+246) then
        tmp = t * (18.0d0 * (y * (x * z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = t * (a * -4.0);
	double tmp;
	if (t <= -1.1e+74) {
		tmp = t_1;
	} else if (t <= -4.8e-194) {
		tmp = b * c;
	} else if (t <= 6.8e-101) {
		tmp = i * (x * -4.0);
	} else if (t <= 4.5e-18) {
		tmp = b * c;
	} else if (t <= 1.45e+246) {
		tmp = t * (18.0 * (y * (x * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if t <= -1.1e+74:
		tmp = t_1
	elif t <= -4.8e-194:
		tmp = b * c
	elif t <= 6.8e-101:
		tmp = i * (x * -4.0)
	elif t <= 4.5e-18:
		tmp = b * c
	elif t <= 1.45e+246:
		tmp = t * (18.0 * (y * (x * z)))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (t <= -1.1e+74)
		tmp = t_1;
	elseif (t <= -4.8e-194)
		tmp = Float64(b * c);
	elseif (t <= 6.8e-101)
		tmp = Float64(i * Float64(x * -4.0));
	elseif (t <= 4.5e-18)
		tmp = Float64(b * c);
	elseif (t <= 1.45e+246)
		tmp = Float64(t * Float64(18.0 * Float64(y * Float64(x * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (t <= -1.1e+74)
		tmp = t_1;
	elseif (t <= -4.8e-194)
		tmp = b * c;
	elseif (t <= 6.8e-101)
		tmp = i * (x * -4.0);
	elseif (t <= 4.5e-18)
		tmp = b * c;
	elseif (t <= 1.45e+246)
		tmp = t * (18.0 * (y * (x * z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e+74], t$95$1, If[LessEqual[t, -4.8e-194], N[(b * c), $MachinePrecision], If[LessEqual[t, 6.8e-101], N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-18], N[(b * c), $MachinePrecision], If[LessEqual[t, 1.45e+246], N[(t * N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.1000000000000001e74 or 1.45000000000000007e246 < t

   1. Initial program 79.2%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in a around inf 50.8%

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

      1. *-commutative 50.8%

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

      2. *-commutative 50.8%

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

      3. associate-*r* 50.8%

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

      4. *-commutative 50.8%

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

   7. Simplified 50.8%

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

   if -1.1000000000000001e74 < t < -4.8e-194 or 6.79999999999999978e-101 < t < 4.49999999999999994e-18

   1. Initial program 91.5%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in b around inf 39.9%

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

   if -4.8e-194 < t < 6.79999999999999978e-101

   1. Initial program 81.6%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in i around inf 40.7%

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

      1. *-commutative 40.7%

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

      2. associate-*r* 40.7%

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

   7. Simplified 40.7%

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

   if 4.49999999999999994e-18 < t < 1.45000000000000007e246

   1. Initial program 82.9%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in y around inf 42.6%

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

      1. *-commutative 42.6%

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

      2. associate-*r* 42.6%

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

      3. *-commutative 42.6%

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

      4. associate-*r* 42.7%

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

      5. *-commutative 42.7%

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

      6. *-commutative 42.7%

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

      7. associate-*r* 42.6%

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

   7. Simplified 42.6%

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

   8. Taylor expanded in x around 0 42.6%

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

      1. associate-*r* 42.7%

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

      2. *-commutative 42.7%

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

      3. *-commutative 42.7%

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

      4. associate-*r* 42.6%

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

      5. *-commutative 42.6%

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

      6. associate-*l* 45.5%

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

   10. Simplified 45.5%

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

   11. Taylor expanded in z around 0 42.6%

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

       1. *-commutative 42.6%

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

       2. associate-*l* 44.1%

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

   13. Simplified 44.1%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-194}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-101}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-18}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+246}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 32.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-197}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-101}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-35}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+249}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 (* t (* a -4.0))))
   (if (<= t -1.6e+77)
     t_1
     (if (<= t -2.6e-197)
       (* b c)
       (if (<= t 6.5e-101)
         (* i (* x -4.0))
         (if (<= t 6e-35)
           (* b c)
           (if (<= t 7e+249) (* t (* (* (* x 18.0) y) z)) t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = t * (a * -4.0);
	double tmp;
	if (t <= -1.6e+77) {
		tmp = t_1;
	} else if (t <= -2.6e-197) {
		tmp = b * c;
	} else if (t <= 6.5e-101) {
		tmp = i * (x * -4.0);
	} else if (t <= 6e-35) {
		tmp = b * c;
	} else if (t <= 7e+249) {
		tmp = t * (((x * 18.0) * y) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (t <= (-1.6d+77)) then
        tmp = t_1
    else if (t <= (-2.6d-197)) then
        tmp = b * c
    else if (t <= 6.5d-101) then
        tmp = i * (x * (-4.0d0))
    else if (t <= 6d-35) then
        tmp = b * c
    else if (t <= 7d+249) then
        tmp = t * (((x * 18.0d0) * y) * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = t * (a * -4.0);
	double tmp;
	if (t <= -1.6e+77) {
		tmp = t_1;
	} else if (t <= -2.6e-197) {
		tmp = b * c;
	} else if (t <= 6.5e-101) {
		tmp = i * (x * -4.0);
	} else if (t <= 6e-35) {
		tmp = b * c;
	} else if (t <= 7e+249) {
		tmp = t * (((x * 18.0) * y) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if t <= -1.6e+77:
		tmp = t_1
	elif t <= -2.6e-197:
		tmp = b * c
	elif t <= 6.5e-101:
		tmp = i * (x * -4.0)
	elif t <= 6e-35:
		tmp = b * c
	elif t <= 7e+249:
		tmp = t * (((x * 18.0) * y) * z)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (t <= -1.6e+77)
		tmp = t_1;
	elseif (t <= -2.6e-197)
		tmp = Float64(b * c);
	elseif (t <= 6.5e-101)
		tmp = Float64(i * Float64(x * -4.0));
	elseif (t <= 6e-35)
		tmp = Float64(b * c);
	elseif (t <= 7e+249)
		tmp = Float64(t * Float64(Float64(Float64(x * 18.0) * y) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (t <= -1.6e+77)
		tmp = t_1;
	elseif (t <= -2.6e-197)
		tmp = b * c;
	elseif (t <= 6.5e-101)
		tmp = i * (x * -4.0);
	elseif (t <= 6e-35)
		tmp = b * c;
	elseif (t <= 7e+249)
		tmp = t * (((x * 18.0) * y) * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+77], t$95$1, If[LessEqual[t, -2.6e-197], N[(b * c), $MachinePrecision], If[LessEqual[t, 6.5e-101], N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-35], N[(b * c), $MachinePrecision], If[LessEqual[t, 7e+249], N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.6000000000000001e77 or 7.00000000000000024e249 < t

   1. Initial program 79.2%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in a around inf 50.8%

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

      1. *-commutative 50.8%

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

      2. *-commutative 50.8%

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

      3. associate-*r* 50.8%

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

      4. *-commutative 50.8%

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

   7. Simplified 50.8%

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

   if -1.6000000000000001e77 < t < -2.6000000000000001e-197 or 6.4999999999999996e-101 < t < 5.99999999999999978e-35

   1. Initial program 91.1%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in b around inf 40.1%

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

   if -2.6000000000000001e-197 < t < 6.4999999999999996e-101

   1. Initial program 81.6%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in i around inf 40.7%

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

      1. *-commutative 40.7%

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

      2. associate-*r* 40.7%

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

   7. Simplified 40.7%

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

   if 5.99999999999999978e-35 < t < 7.00000000000000024e249

   1. Initial program 83.7%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in y around inf 42.3%

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

      1. *-commutative 42.3%

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

      2. associate-*r* 42.3%

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

      3. *-commutative 42.3%

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

      4. associate-*r* 42.4%

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

      5. *-commutative 42.4%

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

      6. *-commutative 42.4%

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

      7. associate-*r* 40.9%

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

   7. Simplified 40.9%

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

   8. Taylor expanded in x around 0 42.3%

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

      1. associate-*r* 42.4%

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

      2. *-commutative 42.4%

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

      3. *-commutative 42.4%

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

      4. associate-*r* 40.9%

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

      5. *-commutative 40.9%

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

      6. associate-*l* 45.1%

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

   10. Simplified 45.1%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-197}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-101}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-35}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+249}:\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-45}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+56}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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) (* 18.0 (* t (* y z)))))))
   (if (<= x -9.6e+50)
     t_1
     (if (<= x 1.15e-45)
       (- (* b c) (* (* j 27.0) k))
       (if (<= x 3.7e+56)
         (- (* b c) (* 4.0 (* x i)))
         (if (<= x 4.4e+70) (* y (* (* x 18.0) (* z t))) t_1))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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) + (18.0 * (t * (y * z))));
	double tmp;
	if (x <= -9.6e+50) {
		tmp = t_1;
	} else if (x <= 1.15e-45) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (x <= 3.7e+56) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (x <= 4.4e+70) {
		tmp = y * ((x * 18.0) * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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) :: tmp
    t_1 = x * ((i * (-4.0d0)) + (18.0d0 * (t * (y * z))))
    if (x <= (-9.6d+50)) then
        tmp = t_1
    else if (x <= 1.15d-45) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else if (x <= 3.7d+56) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (x <= 4.4d+70) then
        tmp = y * ((x * 18.0d0) * (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) + (18.0 * (t * (y * z))));
	double tmp;
	if (x <= -9.6e+50) {
		tmp = t_1;
	} else if (x <= 1.15e-45) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if (x <= 3.7e+56) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (x <= 4.4e+70) {
		tmp = y * ((x * 18.0) * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((i * -4.0) + (18.0 * (t * (y * z))))
	tmp = 0
	if x <= -9.6e+50:
		tmp = t_1
	elif x <= 1.15e-45:
		tmp = (b * c) - ((j * 27.0) * k)
	elif x <= 3.7e+56:
		tmp = (b * c) - (4.0 * (x * i))
	elif x <= 4.4e+70:
		tmp = y * ((x * 18.0) * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(t * Float64(y * z)))))
	tmp = 0.0
	if (x <= -9.6e+50)
		tmp = t_1;
	elseif (x <= 1.15e-45)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif (x <= 3.7e+56)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (x <= 4.4e+70)
		tmp = Float64(y * Float64(Float64(x * 18.0) * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((i * -4.0) + (18.0 * (t * (y * z))));
	tmp = 0.0;
	if (x <= -9.6e+50)
		tmp = t_1;
	elseif (x <= 1.15e-45)
		tmp = (b * c) - ((j * 27.0) * k);
	elseif (x <= 3.7e+56)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (x <= 4.4e+70)
		tmp = y * ((x * 18.0) * (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.6e+50], t$95$1, If[LessEqual[x, 1.15e-45], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e+56], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e+70], N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.6000000000000007e50 or 4.40000000000000001e70 < x

   1. Initial program 72.8%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in x around inf 75.4%

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

   if -9.6000000000000007e50 < x < 1.14999999999999996e-45

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0 86.9%

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

   4. Taylor expanded in b around inf 63.9%

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

   if 1.14999999999999996e-45 < x < 3.69999999999999997e56

   1. Initial program 78.7%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in t around 0 66.0%

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

   6. Taylor expanded in j around 0 60.6%

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

   if 3.69999999999999997e56 < x < 4.40000000000000001e70

   1. Initial program 69.1%

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

   3. Simplified 69.1%

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

   5. Taylor expanded in y around inf 40.1%

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

      1. *-commutative 40.1%

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

      2. associate-*r* 40.1%

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

      3. *-commutative 40.1%

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

      4. associate-*r* 40.1%

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

      5. *-commutative 40.1%

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

      6. *-commutative 40.1%

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

      7. associate-*r* 40.1%

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

   7. Simplified 40.1%

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

      1. add0 40.1%

         \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) + 0} \]

      2. associate-*r* 99.5%

         \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot z\right)\right) \cdot y} + 0 \]

      3. fma-define 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(\left(x \cdot 18\right) \cdot z\right), y, 0\right)} \]

      4. *-commutative 99.5%

         \[\leadsto \mathsf{fma}\left(t \cdot \color{blue}{\left(z \cdot \left(x \cdot 18\right)\right)}, y, 0\right) \]

   9. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(z \cdot \left(x \cdot 18\right)\right), y, 0\right)} \]
   10. Step-by-step derivation

       1. fma-undefine 99.5%

          \[\leadsto \color{blue}{\left(t \cdot \left(z \cdot \left(x \cdot 18\right)\right)\right) \cdot y + 0} \]

       2. associate-*r* 99.5%

          \[\leadsto \color{blue}{\left(\left(t \cdot z\right) \cdot \left(x \cdot 18\right)\right)} \cdot y + 0 \]

       3. *-commutative 99.5%

          \[\leadsto \left(\left(t \cdot z\right) \cdot \color{blue}{\left(18 \cdot x\right)}\right) \cdot y + 0 \]

   11. Applied egg-rr 99.5%

       \[\leadsto \color{blue}{\left(\left(t \cdot z\right) \cdot \left(18 \cdot x\right)\right) \cdot y + 0} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-45}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+56}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{-181} \lor \neg \left(x \leq 8 \cdot 10^{-122}\right):\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 27.0) k)))
   (if (or (<= x -1.2e-181) (not (<= x 8e-122)))
     (- (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))) t_1)
     (- (- (* b c) (* 4.0 (* t a))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((x <= -1.2e-181) || !(x <= 8e-122)) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((x <= (-1.2d-181)) .or. (.not. (x <= 8d-122))) then
        tmp = ((b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))) - t_1
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((x <= -1.2e-181) || !(x <= 8e-122)) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (x <= -1.2e-181) or not (x <= 8e-122):
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((x <= -1.2e-181) || !(x <= 8e-122))
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((x <= -1.2e-181) || ~((x <= 8e-122)))
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1;
	else
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[x, -1.2e-181], N[Not[LessEqual[x, 8e-122]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2000000000000001e-181 or 8.00000000000000047e-122 < x

   1. Initial program 79.7%

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

   3. Taylor expanded in x around 0 86.9%

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

   4. Taylor expanded in a around 0 83.0%

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

   if -1.2000000000000001e-181 < x < 8.00000000000000047e-122

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0 89.4%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-181} \lor \neg \left(x \leq 8 \cdot 10^{-122}\right):\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-36}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+55} \lor \neg \left(x \leq 1.5 \cdot 10^{+145}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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) (* 4.0 (* x i)))))
   (if (<= x -7e+123)
     t_1
     (if (<= x 1.65e-36)
       (- (* b c) (* (* j 27.0) k))
       (if (or (<= x 6.5e+55) (not (<= x 1.5e+145)))
         t_1
         (* y (* (* x 18.0) (* z t))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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) - (4.0 * (x * i));
	double tmp;
	if (x <= -7e+123) {
		tmp = t_1;
	} else if (x <= 1.65e-36) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if ((x <= 6.5e+55) || !(x <= 1.5e+145)) {
		tmp = t_1;
	} else {
		tmp = y * ((x * 18.0) * (z * t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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) :: tmp
    t_1 = (b * c) - (4.0d0 * (x * i))
    if (x <= (-7d+123)) then
        tmp = t_1
    else if (x <= 1.65d-36) then
        tmp = (b * c) - ((j * 27.0d0) * k)
    else if ((x <= 6.5d+55) .or. (.not. (x <= 1.5d+145))) then
        tmp = t_1
    else
        tmp = y * ((x * 18.0d0) * (z * t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) - (4.0 * (x * i));
	double tmp;
	if (x <= -7e+123) {
		tmp = t_1;
	} else if (x <= 1.65e-36) {
		tmp = (b * c) - ((j * 27.0) * k);
	} else if ((x <= 6.5e+55) || !(x <= 1.5e+145)) {
		tmp = t_1;
	} else {
		tmp = y * ((x * 18.0) * (z * t));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (x * i))
	tmp = 0
	if x <= -7e+123:
		tmp = t_1
	elif x <= 1.65e-36:
		tmp = (b * c) - ((j * 27.0) * k)
	elif (x <= 6.5e+55) or not (x <= 1.5e+145):
		tmp = t_1
	else:
		tmp = y * ((x * 18.0) * (z * t))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	tmp = 0.0
	if (x <= -7e+123)
		tmp = t_1;
	elseif (x <= 1.65e-36)
		tmp = Float64(Float64(b * c) - Float64(Float64(j * 27.0) * k));
	elseif ((x <= 6.5e+55) || !(x <= 1.5e+145))
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(x * 18.0) * Float64(z * t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (x * i));
	tmp = 0.0;
	if (x <= -7e+123)
		tmp = t_1;
	elseif (x <= 1.65e-36)
		tmp = (b * c) - ((j * 27.0) * k);
	elseif ((x <= 6.5e+55) || ~((x <= 1.5e+145)))
		tmp = t_1;
	else
		tmp = y * ((x * 18.0) * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e+123], t$95$1, If[LessEqual[x, 1.65e-36], N[(N[(b * c), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 6.5e+55], N[Not[LessEqual[x, 1.5e+145]], $MachinePrecision]], t$95$1, N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.99999999999999999e123 or 1.64999999999999995e-36 < x < 6.50000000000000027e55 or 1.5000000000000001e145 < x

   1. Initial program 69.2%

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

   3. Simplified 73.0%

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

   5. Taylor expanded in t around 0 68.4%

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

   6. Taylor expanded in j around 0 64.6%

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

   if -6.99999999999999999e123 < x < 1.64999999999999995e-36

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0 87.1%

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

   4. Taylor expanded in b around inf 60.6%

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

   if 6.50000000000000027e55 < x < 1.5000000000000001e145

   1. Initial program 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in y around inf 52.8%

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

      1. *-commutative 52.8%

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

      2. associate-*r* 52.8%

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

      3. *-commutative 52.8%

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

      4. associate-*r* 52.9%

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

      5. *-commutative 52.9%

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

      6. *-commutative 52.9%

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

      7. associate-*r* 52.9%

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

   7. Simplified 52.9%

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

      1. add0 52.9%

         \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) + 0} \]

      2. associate-*r* 75.8%

         \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot z\right)\right) \cdot y} + 0 \]

      3. fma-define 75.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(\left(x \cdot 18\right) \cdot z\right), y, 0\right)} \]

      4. *-commutative 75.8%

         \[\leadsto \mathsf{fma}\left(t \cdot \color{blue}{\left(z \cdot \left(x \cdot 18\right)\right)}, y, 0\right) \]

   9. Applied egg-rr 75.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t \cdot \left(z \cdot \left(x \cdot 18\right)\right), y, 0\right)} \]
   10. Step-by-step derivation

       1. fma-undefine 75.8%

          \[\leadsto \color{blue}{\left(t \cdot \left(z \cdot \left(x \cdot 18\right)\right)\right) \cdot y + 0} \]

       2. associate-*r* 75.7%

          \[\leadsto \color{blue}{\left(\left(t \cdot z\right) \cdot \left(x \cdot 18\right)\right)} \cdot y + 0 \]

       3. *-commutative 75.7%

          \[\leadsto \left(\left(t \cdot z\right) \cdot \color{blue}{\left(18 \cdot x\right)}\right) \cdot y + 0 \]

   11. Applied egg-rr 75.7%

       \[\leadsto \color{blue}{\left(\left(t \cdot z\right) \cdot \left(18 \cdot x\right)\right) \cdot y + 0} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+123}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-36}:\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+55} \lor \neg \left(x \leq 1.5 \cdot 10^{+145}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x \cdot 18\right) \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+102} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+49}\right):\\ \;\;\;\;b \cdot c - t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 27.0) k)))
   (if (or (<= t_1 -4e+102) (not (<= t_1 5e+49)))
     (- (* b c) t_1)
     (- (* b c) (* 4.0 (* x i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -4e+102) || !(t_1 <= 5e+49)) {
		tmp = (b * c) - t_1;
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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) :: tmp
    t_1 = (j * 27.0d0) * k
    if ((t_1 <= (-4d+102)) .or. (.not. (t_1 <= 5d+49))) then
        tmp = (b * c) - t_1
    else
        tmp = (b * c) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -4e+102) || !(t_1 <= 5e+49)) {
		tmp = (b * c) - t_1;
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if (t_1 <= -4e+102) or not (t_1 <= 5e+49):
		tmp = (b * c) - t_1
	else:
		tmp = (b * c) - (4.0 * (x * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_1 <= -4e+102) || !(t_1 <= 5e+49))
		tmp = Float64(Float64(b * c) - t_1);
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_1 <= -4e+102) || ~((t_1 <= 5e+49)))
		tmp = (b * c) - t_1;
	else
		tmp = (b * c) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+102], N[Not[LessEqual[t$95$1, 5e+49]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j 27) k) < -3.99999999999999991e102 or 5.0000000000000004e49 < (*.f64 (*.f64 j 27) k)

   1. Initial program 83.4%

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

   3. Taylor expanded in x around 0 84.6%

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

   4. Taylor expanded in b around inf 63.6%

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

   if -3.99999999999999991e102 < (*.f64 (*.f64 j 27) k) < 5.0000000000000004e49

   1. Initial program 84.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in t around 0 61.0%

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

   6. Taylor expanded in j around 0 56.6%

      \[\leadsto \color{blue}{b \cdot c - 4 \cdot \left(i \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -4 \cdot 10^{+102} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+49}\right):\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 75.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+78} \lor \neg \left(x \leq 8.2 \cdot 10^{-41}\right):\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 -4.2e+78) (not (<= x 8.2e-41)))
   (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
   (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -4.2e+78) || !(x <= 8.2e-41)) {
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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 <= (-4.2d+78)) .or. (.not. (x <= 8.2d-41))) then
        tmp = (b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -4.2e+78) || !(x <= 8.2e-41)) {
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -4.2e+78) or not (x <= 8.2e-41):
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -4.2e+78) || !(x <= 8.2e-41))
		tmp = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -4.2e+78) || ~((x <= 8.2e-41)))
		tmp = (b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)));
	else
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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, -4.2e+78], N[Not[LessEqual[x, 8.2e-41]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2000000000000002e78 or 8.20000000000000028e-41 < x

   1. Initial program 73.3%

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

   3. Taylor expanded in x around 0 85.4%

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

   4. Taylor expanded in a around 0 84.0%

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

   5. Taylor expanded in j around 0 79.6%

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

   if -4.2000000000000002e78 < x < 8.20000000000000028e-41

   1. Initial program 95.1%

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

   3. Taylor expanded in x around 0 81.5%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+78} \lor \neg \left(x \leq 8.2 \cdot 10^{-41}\right):\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{-41}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-112}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 (* i (* x -4.0))))
   (if (<= c -1.15e-41)
     (* b c)
     (if (<= c -1e-231)
       t_1
       (if (<= c 2.5e-112)
         (* j (* k -27.0))
         (if (<= c 1.85e+118) t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = i * (x * -4.0);
	double tmp;
	if (c <= -1.15e-41) {
		tmp = b * c;
	} else if (c <= -1e-231) {
		tmp = t_1;
	} else if (c <= 2.5e-112) {
		tmp = j * (k * -27.0);
	} else if (c <= 1.85e+118) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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) :: tmp
    t_1 = i * (x * (-4.0d0))
    if (c <= (-1.15d-41)) then
        tmp = b * c
    else if (c <= (-1d-231)) then
        tmp = t_1
    else if (c <= 2.5d-112) then
        tmp = j * (k * (-27.0d0))
    else if (c <= 1.85d+118) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = i * (x * -4.0);
	double tmp;
	if (c <= -1.15e-41) {
		tmp = b * c;
	} else if (c <= -1e-231) {
		tmp = t_1;
	} else if (c <= 2.5e-112) {
		tmp = j * (k * -27.0);
	} else if (c <= 1.85e+118) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = i * (x * -4.0)
	tmp = 0
	if c <= -1.15e-41:
		tmp = b * c
	elif c <= -1e-231:
		tmp = t_1
	elif c <= 2.5e-112:
		tmp = j * (k * -27.0)
	elif c <= 1.85e+118:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(i * Float64(x * -4.0))
	tmp = 0.0
	if (c <= -1.15e-41)
		tmp = Float64(b * c);
	elseif (c <= -1e-231)
		tmp = t_1;
	elseif (c <= 2.5e-112)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (c <= 1.85e+118)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = i * (x * -4.0);
	tmp = 0.0;
	if (c <= -1.15e-41)
		tmp = b * c;
	elseif (c <= -1e-231)
		tmp = t_1;
	elseif (c <= 2.5e-112)
		tmp = j * (k * -27.0);
	elseif (c <= 1.85e+118)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e-41], N[(b * c), $MachinePrecision], If[LessEqual[c, -1e-231], t$95$1, If[LessEqual[c, 2.5e-112], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.85e+118], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.15000000000000005e-41 or 1.84999999999999993e118 < c

   1. Initial program 82.5%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in b around inf 42.7%

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

   if -1.15000000000000005e-41 < c < -9.9999999999999999e-232 or 2.50000000000000022e-112 < c < 1.84999999999999993e118

   1. Initial program 85.0%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in i around inf 32.7%

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

      1. *-commutative 32.7%

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

      2. associate-*r* 32.7%

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

   7. Simplified 32.7%

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

   if -9.9999999999999999e-232 < c < 2.50000000000000022e-112

   1. Initial program 85.5%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in j around inf 33.6%

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

      1. metadata-eval 33.6%

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

      2. distribute-lft-neg-in 33.6%

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

      3. associate-*r* 33.5%

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

      4. *-commutative 33.5%

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

      5. associate-*r* 33.6%

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

      6. distribute-rgt-neg-in 33.6%

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

      7. *-commutative 33.6%

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

      8. distribute-rgt-neg-in 33.6%

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

      9. metadata-eval 33.6%

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

   7. Simplified 33.6%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{-41}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-231}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-112}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{+118}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;c \leq -1.1 \cdot 10^{-41}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-116}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 (* i (* x -4.0))))
   (if (<= c -1.1e-41)
     (* b c)
     (if (<= c -4.8e-231)
       t_1
       (if (<= c 9.5e-116)
         (* k (* j -27.0))
         (if (<= c 1.1e+118) t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = i * (x * -4.0);
	double tmp;
	if (c <= -1.1e-41) {
		tmp = b * c;
	} else if (c <= -4.8e-231) {
		tmp = t_1;
	} else if (c <= 9.5e-116) {
		tmp = k * (j * -27.0);
	} else if (c <= 1.1e+118) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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) :: tmp
    t_1 = i * (x * (-4.0d0))
    if (c <= (-1.1d-41)) then
        tmp = b * c
    else if (c <= (-4.8d-231)) then
        tmp = t_1
    else if (c <= 9.5d-116) then
        tmp = k * (j * (-27.0d0))
    else if (c <= 1.1d+118) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = i * (x * -4.0);
	double tmp;
	if (c <= -1.1e-41) {
		tmp = b * c;
	} else if (c <= -4.8e-231) {
		tmp = t_1;
	} else if (c <= 9.5e-116) {
		tmp = k * (j * -27.0);
	} else if (c <= 1.1e+118) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = i * (x * -4.0)
	tmp = 0
	if c <= -1.1e-41:
		tmp = b * c
	elif c <= -4.8e-231:
		tmp = t_1
	elif c <= 9.5e-116:
		tmp = k * (j * -27.0)
	elif c <= 1.1e+118:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(i * Float64(x * -4.0))
	tmp = 0.0
	if (c <= -1.1e-41)
		tmp = Float64(b * c);
	elseif (c <= -4.8e-231)
		tmp = t_1;
	elseif (c <= 9.5e-116)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (c <= 1.1e+118)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = i * (x * -4.0);
	tmp = 0.0;
	if (c <= -1.1e-41)
		tmp = b * c;
	elseif (c <= -4.8e-231)
		tmp = t_1;
	elseif (c <= 9.5e-116)
		tmp = k * (j * -27.0);
	elseif (c <= 1.1e+118)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.1e-41], N[(b * c), $MachinePrecision], If[LessEqual[c, -4.8e-231], t$95$1, If[LessEqual[c, 9.5e-116], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.1e+118], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.1e-41 or 1.09999999999999993e118 < c

   1. Initial program 82.5%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in b around inf 42.7%

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

   if -1.1e-41 < c < -4.79999999999999983e-231 or 9.4999999999999998e-116 < c < 1.09999999999999993e118

   1. Initial program 85.1%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in i around inf 32.5%

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

      1. *-commutative 32.5%

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

      2. associate-*r* 32.5%

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

   7. Simplified 32.5%

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

   if -4.79999999999999983e-231 < c < 9.4999999999999998e-116

   1. Initial program 85.3%

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

   3. Taylor expanded in x around 0 87.2%

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

      1. associate--l+ 87.2%

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

      2. cancel-sign-sub-inv 87.2%

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

      3. associate-*r* 87.3%

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

      4. fma-define 87.3%

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

      5. metadata-eval 87.3%

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

      6. *-commutative 87.3%

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

   5. Applied egg-rr 87.3%

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

   6. Taylor expanded in j around inf 34.1%

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

      1. *-commutative 34.1%

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

      2. *-commutative 34.1%

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

      3. associate-*r* 34.1%

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

   8. Simplified 34.1%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.1 \cdot 10^{-41}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-231}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-116}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+118}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 31.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{-41}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-234}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-115}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 (* i (* x -4.0))))
   (if (<= c -1.15e-41)
     (* b c)
     (if (<= c -1.6e-234)
       t_1
       (if (<= c 1.05e-115)
         (* -27.0 (* j k))
         (if (<= c 1.05e+118) t_1 (* b c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 = i * (x * -4.0);
	double tmp;
	if (c <= -1.15e-41) {
		tmp = b * c;
	} else if (c <= -1.6e-234) {
		tmp = t_1;
	} else if (c <= 1.05e-115) {
		tmp = -27.0 * (j * k);
	} else if (c <= 1.05e+118) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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) :: tmp
    t_1 = i * (x * (-4.0d0))
    if (c <= (-1.15d-41)) then
        tmp = b * c
    else if (c <= (-1.6d-234)) then
        tmp = t_1
    else if (c <= 1.05d-115) then
        tmp = (-27.0d0) * (j * k)
    else if (c <= 1.05d+118) then
        tmp = t_1
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 = i * (x * -4.0);
	double tmp;
	if (c <= -1.15e-41) {
		tmp = b * c;
	} else if (c <= -1.6e-234) {
		tmp = t_1;
	} else if (c <= 1.05e-115) {
		tmp = -27.0 * (j * k);
	} else if (c <= 1.05e+118) {
		tmp = t_1;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = i * (x * -4.0)
	tmp = 0
	if c <= -1.15e-41:
		tmp = b * c
	elif c <= -1.6e-234:
		tmp = t_1
	elif c <= 1.05e-115:
		tmp = -27.0 * (j * k)
	elif c <= 1.05e+118:
		tmp = t_1
	else:
		tmp = b * c
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(i * Float64(x * -4.0))
	tmp = 0.0
	if (c <= -1.15e-41)
		tmp = Float64(b * c);
	elseif (c <= -1.6e-234)
		tmp = t_1;
	elseif (c <= 1.05e-115)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (c <= 1.05e+118)
		tmp = t_1;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = i * (x * -4.0);
	tmp = 0.0;
	if (c <= -1.15e-41)
		tmp = b * c;
	elseif (c <= -1.6e-234)
		tmp = t_1;
	elseif (c <= 1.05e-115)
		tmp = -27.0 * (j * k);
	elseif (c <= 1.05e+118)
		tmp = t_1;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e-41], N[(b * c), $MachinePrecision], If[LessEqual[c, -1.6e-234], t$95$1, If[LessEqual[c, 1.05e-115], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.05e+118], t$95$1, N[(b * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.15000000000000005e-41 or 1.05e118 < c

   1. Initial program 82.5%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in b around inf 42.7%

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

   if -1.15000000000000005e-41 < c < -1.5999999999999999e-234 or 1.05000000000000001e-115 < c < 1.05e118

   1. Initial program 85.1%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in i around inf 32.5%

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

      1. *-commutative 32.5%

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

      2. associate-*r* 32.5%

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

   7. Simplified 32.5%

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

   if -1.5999999999999999e-234 < c < 1.05000000000000001e-115

   1. Initial program 85.3%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in j around inf 34.1%

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

      1. *-commutative 34.1%

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

   7. Simplified 34.1%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{-41}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-234}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-115}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{+118}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 55.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.5 \cdot 10^{+80} \lor \neg \left(b \cdot c \leq 7.2 \cdot 10^{+128}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) - x \cdot \left(4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 (<= (* b c) -2.5e+80) (not (<= (* b c) 7.2e+128)))
   (- (* b c) (* 4.0 (* x i)))
   (- (* j (* k -27.0)) (* x (* 4.0 i)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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) <= -2.5e+80) || !((b * c) <= 7.2e+128)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (j * (k * -27.0)) - (x * (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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) <= (-2.5d+80)) .or. (.not. ((b * c) <= 7.2d+128))) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = (j * (k * (-27.0d0))) - (x * (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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) <= -2.5e+80) || !((b * c) <= 7.2e+128)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (j * (k * -27.0)) - (x * (4.0 * i));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -2.5e+80) or not ((b * c) <= 7.2e+128):
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = (j * (k * -27.0)) - (x * (4.0 * i))
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -2.5e+80) || !(Float64(b * c) <= 7.2e+128))
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(j * Float64(k * -27.0)) - Float64(x * Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -2.5e+80) || ~(((b * c) <= 7.2e+128)))
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = (j * (k * -27.0)) - (x * (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -2.5e+80], N[Not[LessEqual[N[(b * c), $MachinePrecision], 7.2e+128]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.4999999999999998e80 or 7.20000000000000054e128 < (*.f64 b c)

   1. Initial program 83.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in t around 0 73.2%

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

   6. Taylor expanded in j around 0 69.2%

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

   if -2.4999999999999998e80 < (*.f64 b c) < 7.20000000000000054e128

   1. Initial program 84.6%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in t around 0 60.7%

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

   6. Taylor expanded in b around 0 57.2%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 57.2%

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

      2. neg-sub0 57.2%

         \[\leadsto \color{blue}{0 - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)} \]

      3. +-commutative 57.2%

         \[\leadsto 0 - \color{blue}{\left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(i \cdot x\right)\right)} \]

      4. associate-*r* 57.2%

         \[\leadsto 0 - \left(\color{blue}{\left(27 \cdot j\right) \cdot k} + 4 \cdot \left(i \cdot x\right)\right) \]

      5. *-commutative 57.2%

         \[\leadsto 0 - \left(\color{blue}{\left(j \cdot 27\right)} \cdot k + 4 \cdot \left(i \cdot x\right)\right) \]

      6. *-commutative 57.2%

         \[\leadsto 0 - \left(\left(j \cdot 27\right) \cdot k + 4 \cdot \color{blue}{\left(x \cdot i\right)}\right) \]

      7. associate--r+ 57.2%

         \[\leadsto \color{blue}{\left(0 - \left(j \cdot 27\right) \cdot k\right) - 4 \cdot \left(x \cdot i\right)} \]

      8. neg-sub0 57.2%

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

      9. associate-*l* 57.2%

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

      10. distribute-rgt-neg-in 57.2%

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

      11. *-commutative 57.2%

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

      12. distribute-rgt-neg-in 57.2%

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

      13. metadata-eval 57.2%

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

      14. *-commutative 57.2%

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

      15. associate-*r* 57.2%

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

   8. Simplified 57.2%

      \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right) - x \cdot \left(i \cdot 4\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2.5 \cdot 10^{+80} \lor \neg \left(b \cdot c \leq 7.2 \cdot 10^{+128}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) - x \cdot \left(4 \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 71.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+138} \lor \neg \left(x \leq 1.4 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 -1.5e+138) (not (<= x 1.4e+51)))
   (* x (+ (* i -4.0) (* 18.0 (* t (* y z)))))
   (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 <= -1.5e+138) || !(x <= 1.4e+51)) {
		tmp = x * ((i * -4.0) + (18.0 * (t * (y * z))));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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 <= (-1.5d+138)) .or. (.not. (x <= 1.4d+51))) then
        tmp = x * ((i * (-4.0d0)) + (18.0d0 * (t * (y * z))))
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 <= -1.5e+138) || !(x <= 1.4e+51)) {
		tmp = x * ((i * -4.0) + (18.0 * (t * (y * z))));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -1.5e+138) or not (x <= 1.4e+51):
		tmp = x * ((i * -4.0) + (18.0 * (t * (y * z))))
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -1.5e+138) || !(x <= 1.4e+51))
		tmp = Float64(x * Float64(Float64(i * -4.0) + Float64(18.0 * Float64(t * Float64(y * z)))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -1.5e+138) || ~((x <= 1.4e+51)))
		tmp = x * ((i * -4.0) + (18.0 * (t * (y * z))));
	else
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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, -1.5e+138], N[Not[LessEqual[x, 1.4e+51]], $MachinePrecision]], N[(x * N[(N[(i * -4.0), $MachinePrecision] + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.50000000000000005e138 or 1.40000000000000002e51 < x

   1. Initial program 68.6%

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

   3. Simplified 74.2%

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

   5. Taylor expanded in x around inf 80.5%

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

   if -1.50000000000000005e138 < x < 1.40000000000000002e51

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0 74.5%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+138} \lor \neg \left(x \leq 1.4 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \left(i \cdot -4 + 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 43.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1.9 \cdot 10^{-33}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 8 \cdot 10^{+239}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -1.9e-33)
   (* k (* j -27.0))
   (if (<= k 8e+239) (- (* b c) (* 4.0 (* x i))) (* j (* k -27.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 (k <= -1.9e-33) {
		tmp = k * (j * -27.0);
	} else if (k <= 8e+239) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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 (k <= (-1.9d-33)) then
        tmp = k * (j * (-27.0d0))
    else if (k <= 8d+239) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = j * (k * (-27.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 (k <= -1.9e-33) {
		tmp = k * (j * -27.0);
	} else if (k <= 8e+239) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -1.9e-33:
		tmp = k * (j * -27.0)
	elif k <= 8e+239:
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -1.9e-33)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (k <= 8e+239)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -1.9e-33)
		tmp = k * (j * -27.0);
	elseif (k <= 8e+239)
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -1.9e-33], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8e+239], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -1.89999999999999997e-33

   1. Initial program 82.2%

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

   3. Taylor expanded in x around 0 85.0%

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

      1. associate--l+ 85.0%

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

      2. cancel-sign-sub-inv 85.0%

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

      3. associate-*r* 85.0%

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

      4. fma-define 85.0%

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

      5. metadata-eval 85.0%

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

      6. *-commutative 85.0%

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

   5. Applied egg-rr 85.0%

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

   6. Taylor expanded in j around inf 35.4%

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

      1. *-commutative 35.4%

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

      2. *-commutative 35.4%

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

      3. associate-*r* 35.4%

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

   8. Simplified 35.4%

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

   if -1.89999999999999997e-33 < k < 7.99999999999999993e239

   1. Initial program 84.0%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in t around 0 61.0%

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

   6. Taylor expanded in j around 0 50.2%

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

   if 7.99999999999999993e239 < k

   1. Initial program 93.6%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in j around inf 56.9%

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

      1. metadata-eval 56.9%

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

      2. distribute-lft-neg-in 56.9%

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

      3. associate-*r* 56.9%

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

      4. *-commutative 56.9%

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

      5. associate-*r* 56.9%

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

      6. distribute-rgt-neg-in 56.9%

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

      7. *-commutative 56.9%

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

      8. distribute-rgt-neg-in 56.9%

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

      9. metadata-eval 56.9%

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

   7. Simplified 56.9%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.9 \cdot 10^{-33}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 8 \cdot 10^{+239}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 31.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{-42} \lor \neg \left(c \leq 1.26 \cdot 10^{+118}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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 (<= c -8.5e-42) (not (<= c 1.26e+118))) (* b c) (* i (* x -4.0))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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 ((c <= -8.5e-42) || !(c <= 1.26e+118)) {
		tmp = b * c;
	} else {
		tmp = i * (x * -4.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k 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 ((c <= (-8.5d-42)) .or. (.not. (c <= 1.26d+118))) then
        tmp = b * c
    else
        tmp = i * (x * (-4.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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 ((c <= -8.5e-42) || !(c <= 1.26e+118)) {
		tmp = b * c;
	} else {
		tmp = i * (x * -4.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (c <= -8.5e-42) or not (c <= 1.26e+118):
		tmp = b * c
	else:
		tmp = i * (x * -4.0)
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((c <= -8.5e-42) || !(c <= 1.26e+118))
		tmp = Float64(b * c);
	else
		tmp = Float64(i * Float64(x * -4.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((c <= -8.5e-42) || ~((c <= 1.26e+118)))
		tmp = b * c;
	else
		tmp = i * (x * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[c, -8.5e-42], N[Not[LessEqual[c, 1.26e+118]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -8.4999999999999996e-42 or 1.25999999999999996e118 < c

   1. Initial program 82.5%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in b around inf 42.7%

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

   if -8.4999999999999996e-42 < c < 1.25999999999999996e118

   1. Initial program 85.2%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in i around inf 29.0%

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

      1. *-commutative 29.0%

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

      2. associate-*r* 29.0%

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

   7. Simplified 29.0%

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

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{-42} \lor \neg \left(c \leq 1.26 \cdot 10^{+118}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 23.9% accurate, 10.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ b \cdot c \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k 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(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
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: x, y, z, t, a, b, c, i, j, and k 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 x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
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

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = b * c;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k 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 84.1%

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

3. Simplified 84.6%

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

5. Taylor expanded in b around inf 24.2%

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

6. Final simplification 24.2%

   \[\leadsto b \cdot c \]
7. Add Preprocessing

Developer target: 89.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024034 
(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)))