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

Percentage Accurate: 86.3% → 87.4%

Time: 28.5s

Alternatives: 29

Speedup: 0.5×

• 48.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.3% 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: 87.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+198}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right) - \mathsf{fma}\left(x, i \cdot 4, j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), b \cdot c\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (<= x -2.2e+116)
   (* x (- (* i (- 4.0)) (* -18.0 (* (* t y) z))))
   (if (<= x 5.5e+198)
     (-
      (fma t (fma x (* 18.0 (* y z)) (* a -4.0)) (* b c))
      (fma x (* i 4.0) (* j (* 27.0 k))))
     (-
      (fma x (fma 18.0 (* t (* y z)) (* i -4.0)) (* b c))
      (* k (* j 27.0))))))

C

assert(y < z);
assert(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 <= -2.2e+116) {
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)));
	} else if (x <= 5.5e+198) {
		tmp = fma(t, fma(x, (18.0 * (y * z)), (a * -4.0)), (b * c)) - fma(x, (i * 4.0), (j * (27.0 * k)));
	} else {
		tmp = fma(x, fma(18.0, (t * (y * z)), (i * -4.0)), (b * c)) - (k * (j * 27.0));
	}
	return tmp;
}

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -2.2e+116)
		tmp = Float64(x * Float64(Float64(i * Float64(-4.0)) - Float64(-18.0 * Float64(Float64(t * y) * z))));
	elseif (x <= 5.5e+198)
		tmp = Float64(fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(a * -4.0)), Float64(b * c)) - fma(x, Float64(i * 4.0), Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(fma(x, fma(18.0, Float64(t * Float64(y * z)), Float64(i * -4.0)), Float64(b * c)) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[x, -2.2e+116], N[(x * N[(N[(i * (-4.0)), $MachinePrecision] - N[(-18.0 * N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e+198], N[(N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(x * N[(i * 4.0), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2e116

   1. Initial program 68.0%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in x around inf 68.1%

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

      1. *-commutative 68.1%

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

      2. associate-*l* 77.9%

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

      3. associate-*l* 79.9%

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

   6. Simplified 79.9%

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

   7. Taylor expanded in x around -inf 83.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 83.1%

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

      2. cancel-sign-sub-inv 83.1%

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

      3. associate-*r* 87.8%

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

      4. metadata-eval 87.8%

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

      5. *-commutative 87.8%

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

   9. Simplified 87.8%

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

   if -2.2e116 < x < 5.5000000000000004e198

   1. Initial program 91.0%

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

      1. associate--l- 91.0%

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

      2. associate-+l- 91.0%

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

   3. Simplified 93.1%

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

   if 5.5000000000000004e198 < x

   1. Initial program 71.0%

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

   2. Taylor expanded in a around 0 78.2%

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

      1. sub-neg 78.2%

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

      2. +-commutative 78.2%

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

      3. associate-+l+ 78.2%

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

      4. associate-*r* 78.2%

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

      5. *-commutative 78.2%

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

      6. associate-*r* 92.5%

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

      7. associate-*r* 92.5%

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

      8. distribute-lft-neg-in 92.5%

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

      9. metadata-eval 92.5%

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

      10. associate-*r* 92.5%

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

      11. distribute-rgt-in 99.9%

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

      12. metadata-eval 99.9%

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

      13. cancel-sign-sub-inv 99.9%

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

      14. +-commutative 99.9%

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

      15. fma-def 99.9%

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

   4. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(18, \left(y \cdot z\right) \cdot t, -4 \cdot i\right), b \cdot c\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+198}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right) - \mathsf{fma}\left(x, i \cdot 4, j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(18, t \cdot \left(y \cdot z\right), i \cdot -4\right), b \cdot c\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 2: 91.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision] + N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(i * (-4.0)), $MachinePrecision] - N[(-18.0 * N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.9%

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

   3. Simplified 92.9%

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

   if +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 14.3%

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

   4. Taylor expanded in x around inf 28.6%

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

      1. *-commutative 28.6%

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

      2. associate-*l* 33.3%

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

      3. associate-*l* 33.3%

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

   6. Simplified 33.3%

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

   7. Taylor expanded in x around -inf 62.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 62.1%

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

      2. cancel-sign-sub-inv 62.1%

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

      3. associate-*r* 71.6%

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

      4. metadata-eval 71.6%

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

      5. *-commutative 71.6%

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

   9. Simplified 71.6%

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

4. Final simplification 91.1%

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

Alternative 3: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ t_2 := b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_3 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_3 \leq -1 \cdot 10^{+167}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - t_3\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 4 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (- (* 18.0 (* t (* y z))) (* i 4.0))))
        (t_2 (- (* b c) (* 4.0 (+ (* t a) (* x i)))))
        (t_3 (* k (* j 27.0))))
   (if (<= t_3 -1e+167)
     (- (* t (* a -4.0)) t_3)
     (if (<= t_3 -5e-196)
       t_2
       (if (<= t_3 1e-235)
         t_1
         (if (<= t_3 2e-72)
           t_2
           (if (<= t_3 4e+170)
             t_1
             (- (* b c) (+ (* 27.0 (* j k)) (* 4.0 (* x i)))))))))))

C

assert(y < z);
assert(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 * ((18.0 * (t * (y * z))) - (i * 4.0));
	double t_2 = (b * c) - (4.0 * ((t * a) + (x * i)));
	double t_3 = k * (j * 27.0);
	double tmp;
	if (t_3 <= -1e+167) {
		tmp = (t * (a * -4.0)) - t_3;
	} else if (t_3 <= -5e-196) {
		tmp = t_2;
	} else if (t_3 <= 1e-235) {
		tmp = t_1;
	} else if (t_3 <= 2e-72) {
		tmp = t_2;
	} else if (t_3 <= 4e+170) {
		tmp = t_1;
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) :: t_3
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    t_2 = (b * c) - (4.0d0 * ((t * a) + (x * i)))
    t_3 = k * (j * 27.0d0)
    if (t_3 <= (-1d+167)) then
        tmp = (t * (a * (-4.0d0))) - t_3
    else if (t_3 <= (-5d-196)) then
        tmp = t_2
    else if (t_3 <= 1d-235) then
        tmp = t_1
    else if (t_3 <= 2d-72) then
        tmp = t_2
    else if (t_3 <= 4d+170) then
        tmp = t_1
    else
        tmp = (b * c) - ((27.0d0 * (j * k)) + (4.0d0 * (x * i)))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 * ((18.0 * (t * (y * z))) - (i * 4.0));
	double t_2 = (b * c) - (4.0 * ((t * a) + (x * i)));
	double t_3 = k * (j * 27.0);
	double tmp;
	if (t_3 <= -1e+167) {
		tmp = (t * (a * -4.0)) - t_3;
	} else if (t_3 <= -5e-196) {
		tmp = t_2;
	} else if (t_3 <= 1e-235) {
		tmp = t_1;
	} else if (t_3 <= 2e-72) {
		tmp = t_2;
	} else if (t_3 <= 4e+170) {
		tmp = t_1;
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	t_2 = (b * c) - (4.0 * ((t * a) + (x * i)))
	t_3 = k * (j * 27.0)
	tmp = 0
	if t_3 <= -1e+167:
		tmp = (t * (a * -4.0)) - t_3
	elif t_3 <= -5e-196:
		tmp = t_2
	elif t_3 <= 1e-235:
		tmp = t_1
	elif t_3 <= 2e-72:
		tmp = t_2
	elif t_3 <= 4e+170:
		tmp = t_1
	else:
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)))
	t_2 = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i))))
	t_3 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_3 <= -1e+167)
		tmp = Float64(Float64(t * Float64(a * -4.0)) - t_3);
	elseif (t_3 <= -5e-196)
		tmp = t_2;
	elseif (t_3 <= 1e-235)
		tmp = t_1;
	elseif (t_3 <= 2e-72)
		tmp = t_2;
	elseif (t_3 <= 4e+170)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + Float64(4.0 * Float64(x * i))));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	t_2 = (b * c) - (4.0 * ((t * a) + (x * i)));
	t_3 = k * (j * 27.0);
	tmp = 0.0;
	if (t_3 <= -1e+167)
		tmp = (t * (a * -4.0)) - t_3;
	elseif (t_3 <= -5e-196)
		tmp = t_2;
	elseif (t_3 <= 1e-235)
		tmp = t_1;
	elseif (t_3 <= 2e-72)
		tmp = t_2;
	elseif (t_3 <= 4e+170)
		tmp = t_1;
	else
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+167], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[t$95$3, -5e-196], t$95$2, If[LessEqual[t$95$3, 1e-235], t$95$1, If[LessEqual[t$95$3, 2e-72], t$95$2, If[LessEqual[t$95$3, 4e+170], t$95$1, N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j 27) k) < -1e167

   1. Initial program 82.0%

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

   2. Taylor expanded in t around -inf 83.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 83.4%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)} - \left(j \cdot 27\right) \cdot k \]

      2. neg-mul-1 83.4%

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

      3. cancel-sign-sub-inv 83.4%

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

      4. *-commutative 83.4%

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

      5. metadata-eval 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in x around 0 80.9%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. associate-*r* 80.9%

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

   7. Simplified 80.9%

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

   if -1e167 < (*.f64 (*.f64 j 27) k) < -5.0000000000000005e-196 or 9.9999999999999996e-236 < (*.f64 (*.f64 j 27) k) < 1.9999999999999999e-72

   1. Initial program 84.8%

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

   2. Taylor expanded in y around 0 82.6%

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

      1. distribute-lft-out 82.6%

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

      2. *-commutative 82.6%

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

      3. *-commutative 82.6%

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

   4. Simplified 82.6%

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

   5. Taylor expanded in j around 0 77.6%

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

   if -5.0000000000000005e-196 < (*.f64 (*.f64 j 27) k) < 9.9999999999999996e-236 or 1.9999999999999999e-72 < (*.f64 (*.f64 j 27) k) < 4.00000000000000014e170

   1. Initial program 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around inf 68.4%

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

   if 4.00000000000000014e170 < (*.f64 (*.f64 j 27) k)

   1. Initial program 93.0%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in t around 0 93.0%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+167}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{-196}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{-235}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{-72}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 4 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]

Alternative 4: 60.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ t_2 := b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_3 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_3 \leq -1 \cdot 10^{+167}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - t_3\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 4 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (- (* 18.0 (* t (* y z))) (* i 4.0))))
        (t_2 (- (* b c) (* 4.0 (+ (* t a) (* x i)))))
        (t_3 (* k (* j 27.0))))
   (if (<= t_3 -1e+167)
     (- (* t (* a -4.0)) t_3)
     (if (<= t_3 -5e-196)
       t_2
       (if (<= t_3 1e-235)
         t_1
         (if (<= t_3 2e-72)
           t_2
           (if (<= t_3 4e+170) t_1 (- (* b c) (* 27.0 (* j k))))))))))

C

assert(y < z);
assert(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 * ((18.0 * (t * (y * z))) - (i * 4.0));
	double t_2 = (b * c) - (4.0 * ((t * a) + (x * i)));
	double t_3 = k * (j * 27.0);
	double tmp;
	if (t_3 <= -1e+167) {
		tmp = (t * (a * -4.0)) - t_3;
	} else if (t_3 <= -5e-196) {
		tmp = t_2;
	} else if (t_3 <= 1e-235) {
		tmp = t_1;
	} else if (t_3 <= 2e-72) {
		tmp = t_2;
	} else if (t_3 <= 4e+170) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) :: t_3
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    t_2 = (b * c) - (4.0d0 * ((t * a) + (x * i)))
    t_3 = k * (j * 27.0d0)
    if (t_3 <= (-1d+167)) then
        tmp = (t * (a * (-4.0d0))) - t_3
    else if (t_3 <= (-5d-196)) then
        tmp = t_2
    else if (t_3 <= 1d-235) then
        tmp = t_1
    else if (t_3 <= 2d-72) then
        tmp = t_2
    else if (t_3 <= 4d+170) then
        tmp = t_1
    else
        tmp = (b * c) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 * ((18.0 * (t * (y * z))) - (i * 4.0));
	double t_2 = (b * c) - (4.0 * ((t * a) + (x * i)));
	double t_3 = k * (j * 27.0);
	double tmp;
	if (t_3 <= -1e+167) {
		tmp = (t * (a * -4.0)) - t_3;
	} else if (t_3 <= -5e-196) {
		tmp = t_2;
	} else if (t_3 <= 1e-235) {
		tmp = t_1;
	} else if (t_3 <= 2e-72) {
		tmp = t_2;
	} else if (t_3 <= 4e+170) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	t_2 = (b * c) - (4.0 * ((t * a) + (x * i)))
	t_3 = k * (j * 27.0)
	tmp = 0
	if t_3 <= -1e+167:
		tmp = (t * (a * -4.0)) - t_3
	elif t_3 <= -5e-196:
		tmp = t_2
	elif t_3 <= 1e-235:
		tmp = t_1
	elif t_3 <= 2e-72:
		tmp = t_2
	elif t_3 <= 4e+170:
		tmp = t_1
	else:
		tmp = (b * c) - (27.0 * (j * k))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)))
	t_2 = Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i))))
	t_3 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t_3 <= -1e+167)
		tmp = Float64(Float64(t * Float64(a * -4.0)) - t_3);
	elseif (t_3 <= -5e-196)
		tmp = t_2;
	elseif (t_3 <= 1e-235)
		tmp = t_1;
	elseif (t_3 <= 2e-72)
		tmp = t_2;
	elseif (t_3 <= 4e+170)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	t_2 = (b * c) - (4.0 * ((t * a) + (x * i)));
	t_3 = k * (j * 27.0);
	tmp = 0.0;
	if (t_3 <= -1e+167)
		tmp = (t * (a * -4.0)) - t_3;
	elseif (t_3 <= -5e-196)
		tmp = t_2;
	elseif (t_3 <= 1e-235)
		tmp = t_1;
	elseif (t_3 <= 2e-72)
		tmp = t_2;
	elseif (t_3 <= 4e+170)
		tmp = t_1;
	else
		tmp = (b * c) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+167], N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[t$95$3, -5e-196], t$95$2, If[LessEqual[t$95$3, 1e-235], t$95$1, If[LessEqual[t$95$3, 2e-72], t$95$2, If[LessEqual[t$95$3, 4e+170], t$95$1, N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 j 27) k) < -1e167

   1. Initial program 82.0%

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

   2. Taylor expanded in t around -inf 83.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 83.4%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)} - \left(j \cdot 27\right) \cdot k \]

      2. neg-mul-1 83.4%

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

      3. cancel-sign-sub-inv 83.4%

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

      4. *-commutative 83.4%

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

      5. metadata-eval 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in x around 0 80.9%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. associate-*r* 80.9%

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

   7. Simplified 80.9%

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

   if -1e167 < (*.f64 (*.f64 j 27) k) < -5.0000000000000005e-196 or 9.9999999999999996e-236 < (*.f64 (*.f64 j 27) k) < 1.9999999999999999e-72

   1. Initial program 84.8%

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

   2. Taylor expanded in y around 0 82.6%

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

      1. distribute-lft-out 82.6%

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

      2. *-commutative 82.6%

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

      3. *-commutative 82.6%

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

   4. Simplified 82.6%

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

   5. Taylor expanded in j around 0 77.6%

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

   if -5.0000000000000005e-196 < (*.f64 (*.f64 j 27) k) < 9.9999999999999996e-236 or 1.9999999999999999e-72 < (*.f64 (*.f64 j 27) k) < 4.00000000000000014e170

   1. Initial program 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around inf 68.4%

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

   if 4.00000000000000014e170 < (*.f64 (*.f64 j 27) k)

   1. Initial program 93.0%

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

   2. Taylor expanded in a around 0 86.6%

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

      1. sub-neg 86.6%

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

      2. +-commutative 86.6%

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

      3. associate-+l+ 86.6%

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

      4. associate-*r* 86.6%

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

      5. *-commutative 86.6%

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

      6. associate-*r* 89.8%

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

      7. associate-*r* 89.8%

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

      8. distribute-lft-neg-in 89.8%

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

      9. metadata-eval 89.8%

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

      10. associate-*r* 89.8%

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

      11. distribute-rgt-in 89.8%

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

      12. metadata-eval 89.8%

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

      13. cancel-sign-sub-inv 89.8%

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

      14. +-commutative 89.8%

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

      15. fma-def 93.3%

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

   4. Simplified 93.3%

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

   5. Taylor expanded in x around 0 89.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+167}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{-196}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 10^{-235}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 2 \cdot 10^{-72}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 4 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 5: 52.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := t \cdot \left(a \cdot -4\right) - t_2\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-75}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (- (* 18.0 (* t (* y z))) (* i 4.0))))
        (t_2 (* k (* j 27.0)))
        (t_3 (- (* t (* a -4.0)) t_2)))
   (if (<= t_2 -1e+111)
     t_3
     (if (<= t_2 -2e-39)
       t_1
       (if (<= t_2 -2e-75)
         t_3
         (if (<= t_2 4e+170) t_1 (- (* b c) (* 27.0 (* j k)))))))))

C

assert(y < z);
assert(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 * ((18.0 * (t * (y * z))) - (i * 4.0));
	double t_2 = k * (j * 27.0);
	double t_3 = (t * (a * -4.0)) - t_2;
	double tmp;
	if (t_2 <= -1e+111) {
		tmp = t_3;
	} else if (t_2 <= -2e-39) {
		tmp = t_1;
	} else if (t_2 <= -2e-75) {
		tmp = t_3;
	} else if (t_2 <= 4e+170) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) :: t_3
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    t_2 = k * (j * 27.0d0)
    t_3 = (t * (a * (-4.0d0))) - t_2
    if (t_2 <= (-1d+111)) then
        tmp = t_3
    else if (t_2 <= (-2d-39)) then
        tmp = t_1
    else if (t_2 <= (-2d-75)) then
        tmp = t_3
    else if (t_2 <= 4d+170) then
        tmp = t_1
    else
        tmp = (b * c) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 * ((18.0 * (t * (y * z))) - (i * 4.0));
	double t_2 = k * (j * 27.0);
	double t_3 = (t * (a * -4.0)) - t_2;
	double tmp;
	if (t_2 <= -1e+111) {
		tmp = t_3;
	} else if (t_2 <= -2e-39) {
		tmp = t_1;
	} else if (t_2 <= -2e-75) {
		tmp = t_3;
	} else if (t_2 <= 4e+170) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	t_2 = k * (j * 27.0)
	t_3 = (t * (a * -4.0)) - t_2
	tmp = 0
	if t_2 <= -1e+111:
		tmp = t_3
	elif t_2 <= -2e-39:
		tmp = t_1
	elif t_2 <= -2e-75:
		tmp = t_3
	elif t_2 <= 4e+170:
		tmp = t_1
	else:
		tmp = (b * c) - (27.0 * (j * k))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)))
	t_2 = Float64(k * Float64(j * 27.0))
	t_3 = Float64(Float64(t * Float64(a * -4.0)) - t_2)
	tmp = 0.0
	if (t_2 <= -1e+111)
		tmp = t_3;
	elseif (t_2 <= -2e-39)
		tmp = t_1;
	elseif (t_2 <= -2e-75)
		tmp = t_3;
	elseif (t_2 <= 4e+170)
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	t_2 = k * (j * 27.0);
	t_3 = (t * (a * -4.0)) - t_2;
	tmp = 0.0;
	if (t_2 <= -1e+111)
		tmp = t_3;
	elseif (t_2 <= -2e-39)
		tmp = t_1;
	elseif (t_2 <= -2e-75)
		tmp = t_3;
	elseif (t_2 <= 4e+170)
		tmp = t_1;
	else
		tmp = (b * c) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+111], t$95$3, If[LessEqual[t$95$2, -2e-39], t$95$1, If[LessEqual[t$95$2, -2e-75], t$95$3, If[LessEqual[t$95$2, 4e+170], t$95$1, N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -9.99999999999999957e110 or -1.99999999999999986e-39 < (*.f64 (*.f64 j 27) k) < -1.9999999999999999e-75

   1. Initial program 84.8%

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

   2. Taylor expanded in t around -inf 77.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 77.4%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)} - \left(j \cdot 27\right) \cdot k \]

      2. neg-mul-1 77.4%

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

      3. cancel-sign-sub-inv 77.4%

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

      4. *-commutative 77.4%

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

      5. metadata-eval 77.4%

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

   4. Simplified 77.4%

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

   5. Taylor expanded in x around 0 74.1%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. associate-*r* 74.1%

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

   7. Simplified 74.1%

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

   if -9.99999999999999957e110 < (*.f64 (*.f64 j 27) k) < -1.99999999999999986e-39 or -1.9999999999999999e-75 < (*.f64 (*.f64 j 27) k) < 4.00000000000000014e170

   1. Initial program 84.2%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in x around inf 61.4%

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

   if 4.00000000000000014e170 < (*.f64 (*.f64 j 27) k)

   1. Initial program 93.0%

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

   2. Taylor expanded in a around 0 86.6%

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

      1. sub-neg 86.6%

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

      2. +-commutative 86.6%

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

      3. associate-+l+ 86.6%

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

      4. associate-*r* 86.6%

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

      5. *-commutative 86.6%

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

      6. associate-*r* 89.8%

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

      7. associate-*r* 89.8%

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

      8. distribute-lft-neg-in 89.8%

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

      9. metadata-eval 89.8%

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

      10. associate-*r* 89.8%

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

      11. distribute-rgt-in 89.8%

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

      12. metadata-eval 89.8%

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

      13. cancel-sign-sub-inv 89.8%

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

      14. +-commutative 89.8%

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

      15. fma-def 93.3%

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

   4. Simplified 93.3%

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

   5. Taylor expanded in x around 0 89.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -2 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -2 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 4 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 6: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-210}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-18}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(x \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) (* t (- (* 18.0 (* x (* y z))) (* 4.0 a))))
          (* 27.0 (* j k)))))
   (if (<= t -2.25e+42)
     t_1
     (if (<= t -1.45e-210)
       (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) (* k (* j 27.0)))
       (if (<= t 5.5e-18)
         (-
          (+ (* b c) (* 18.0 (* x (* y (* t z)))))
          (+ (* j (* 27.0 k)) (* x (* i 4.0))))
         t_1)))))

C

assert(y < z);
assert(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) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - (27.0 * (j * k));
	double tmp;
	if (t <= -2.25e+42) {
		tmp = t_1;
	} else if (t <= -1.45e-210) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (k * (j * 27.0));
	} else if (t <= 5.5e-18) {
		tmp = ((b * c) + (18.0 * (x * (y * (t * z))))) - ((j * (27.0 * k)) + (x * (i * 4.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) + (t * ((18.0d0 * (x * (y * z))) - (4.0d0 * a)))) - (27.0d0 * (j * k))
    if (t <= (-2.25d+42)) then
        tmp = t_1
    else if (t <= (-1.45d-210)) then
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - (k * (j * 27.0d0))
    else if (t <= 5.5d-18) then
        tmp = ((b * c) + (18.0d0 * (x * (y * (t * z))))) - ((j * (27.0d0 * k)) + (x * (i * 4.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z;
assert 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) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - (27.0 * (j * k));
	double tmp;
	if (t <= -2.25e+42) {
		tmp = t_1;
	} else if (t <= -1.45e-210) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (k * (j * 27.0));
	} else if (t <= 5.5e-18) {
		tmp = ((b * c) + (18.0 * (x * (y * (t * z))))) - ((j * (27.0 * k)) + (x * (i * 4.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - (27.0 * (j * k))
	tmp = 0
	if t <= -2.25e+42:
		tmp = t_1
	elif t <= -1.45e-210:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (k * (j * 27.0))
	elif t <= 5.5e-18:
		tmp = ((b * c) + (18.0 * (x * (y * (t * z))))) - ((j * (27.0 * k)) + (x * (i * 4.0)))
	else:
		tmp = t_1
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(4.0 * a)))) - Float64(27.0 * Float64(j * k)))
	tmp = 0.0
	if (t <= -2.25e+42)
		tmp = t_1;
	elseif (t <= -1.45e-210)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - Float64(k * Float64(j * 27.0)));
	elseif (t <= 5.5e-18)
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(x * Float64(y * Float64(t * z))))) - Float64(Float64(j * Float64(27.0 * k)) + Float64(x * Float64(i * 4.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - (27.0 * (j * k));
	tmp = 0.0;
	if (t <= -2.25e+42)
		tmp = t_1;
	elseif (t <= -1.45e-210)
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (k * (j * 27.0));
	elseif (t <= 5.5e-18)
		tmp = ((b * c) + (18.0 * (x * (y * (t * z))))) - ((j * (27.0 * k)) + (x * (i * 4.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.25e+42], t$95$1, If[LessEqual[t, -1.45e-210], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-18], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(x * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision] + N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.25000000000000006e42 or 5.5e-18 < t

   1. Initial program 86.5%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in i around 0 87.7%

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

   if -2.25000000000000006e42 < t < -1.45000000000000003e-210

   1. Initial program 91.9%

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

   2. Taylor expanded in y around 0 94.0%

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

      1. distribute-lft-out 94.0%

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

      2. *-commutative 94.0%

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

      3. *-commutative 94.0%

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

   4. Simplified 94.0%

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

   if -1.45000000000000003e-210 < t < 5.5e-18

   1. Initial program 79.6%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in x around inf 77.1%

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

      1. *-commutative 77.1%

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

      2. associate-*l* 86.8%

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

      3. associate-*l* 92.6%

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

   6. Simplified 92.6%

      \[\leadsto \left(\color{blue}{18 \cdot \left(x \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+42}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-210}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-18}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(x \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 7: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+38}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot t_1 - 4 \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-216}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t_2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(x \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(t \cdot t_1\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (* y z))) (t_2 (* k (* j 27.0))))
   (if (<= t -6e+38)
     (- (+ (* b c) (* t (- (* 18.0 t_1) (* 4.0 a)))) (* 27.0 (* j k)))
     (if (<= t -1.25e-216)
       (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) t_2)
       (if (<= t 5e-16)
         (-
          (+ (* b c) (* 18.0 (* x (* y (* t z)))))
          (+ (* j (* 27.0 k)) (* x (* i 4.0))))
         (- (- (+ (* b c) (* 18.0 (* t t_1))) (* 4.0 (* t a))) t_2))))))

C

assert(y < z);
assert(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 * (y * z);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t <= -6e+38) {
		tmp = ((b * c) + (t * ((18.0 * t_1) - (4.0 * a)))) - (27.0 * (j * k));
	} else if (t <= -1.25e-216) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_2;
	} else if (t <= 5e-16) {
		tmp = ((b * c) + (18.0 * (x * (y * (t * z))))) - ((j * (27.0 * k)) + (x * (i * 4.0)));
	} else {
		tmp = (((b * c) + (18.0 * (t * t_1))) - (4.0 * (t * a))) - t_2;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 * (y * z)
    t_2 = k * (j * 27.0d0)
    if (t <= (-6d+38)) then
        tmp = ((b * c) + (t * ((18.0d0 * t_1) - (4.0d0 * a)))) - (27.0d0 * (j * k))
    else if (t <= (-1.25d-216)) then
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - t_2
    else if (t <= 5d-16) then
        tmp = ((b * c) + (18.0d0 * (x * (y * (t * z))))) - ((j * (27.0d0 * k)) + (x * (i * 4.0d0)))
    else
        tmp = (((b * c) + (18.0d0 * (t * t_1))) - (4.0d0 * (t * a))) - t_2
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 * (y * z);
	double t_2 = k * (j * 27.0);
	double tmp;
	if (t <= -6e+38) {
		tmp = ((b * c) + (t * ((18.0 * t_1) - (4.0 * a)))) - (27.0 * (j * k));
	} else if (t <= -1.25e-216) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_2;
	} else if (t <= 5e-16) {
		tmp = ((b * c) + (18.0 * (x * (y * (t * z))))) - ((j * (27.0 * k)) + (x * (i * 4.0)));
	} else {
		tmp = (((b * c) + (18.0 * (t * t_1))) - (4.0 * (t * a))) - t_2;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (y * z)
	t_2 = k * (j * 27.0)
	tmp = 0
	if t <= -6e+38:
		tmp = ((b * c) + (t * ((18.0 * t_1) - (4.0 * a)))) - (27.0 * (j * k))
	elif t <= -1.25e-216:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_2
	elif t <= 5e-16:
		tmp = ((b * c) + (18.0 * (x * (y * (t * z))))) - ((j * (27.0 * k)) + (x * (i * 4.0)))
	else:
		tmp = (((b * c) + (18.0 * (t * t_1))) - (4.0 * (t * a))) - t_2
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t <= -6e+38)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * t_1) - Float64(4.0 * a)))) - Float64(27.0 * Float64(j * k)));
	elseif (t <= -1.25e-216)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - t_2);
	elseif (t <= 5e-16)
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(x * Float64(y * Float64(t * z))))) - Float64(Float64(j * Float64(27.0 * k)) + Float64(x * Float64(i * 4.0))));
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * t_1))) - Float64(4.0 * Float64(t * a))) - t_2);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (y * z);
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t <= -6e+38)
		tmp = ((b * c) + (t * ((18.0 * t_1) - (4.0 * a)))) - (27.0 * (j * k));
	elseif (t <= -1.25e-216)
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_2;
	elseif (t <= 5e-16)
		tmp = ((b * c) + (18.0 * (x * (y * (t * z))))) - ((j * (27.0 * k)) + (x * (i * 4.0)));
	else
		tmp = (((b * c) + (18.0 * (t * t_1))) - (4.0 * (t * a))) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+38], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * t$95$1), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.25e-216], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t, 5e-16], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(x * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision] + N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.0000000000000002e38

   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 91.4%

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

   4. Taylor expanded in i around 0 88.6%

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

   if -6.0000000000000002e38 < t < -1.25000000000000005e-216

   1. Initial program 91.9%

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

   2. Taylor expanded in y around 0 94.0%

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

      1. distribute-lft-out 94.0%

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

      2. *-commutative 94.0%

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

      3. *-commutative 94.0%

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

   4. Simplified 94.0%

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

   if -1.25000000000000005e-216 < t < 5.0000000000000004e-16

   1. Initial program 79.6%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in x around inf 77.1%

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

      1. *-commutative 77.1%

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

      2. associate-*l* 86.8%

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

      3. associate-*l* 92.6%

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

   6. Simplified 92.6%

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

   if 5.0000000000000004e-16 < t

   1. Initial program 88.2%

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

   2. Taylor expanded in i around 0 86.9%

      \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+38}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-216}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(x \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 8: 84.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+36} \lor \neg \left(t \leq 3.4 \cdot 10^{+31}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (<= t -4e+36) (not (<= t 3.4e+31)))
   (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* 4.0 a)))) (* 27.0 (* j k)))
   (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) (* k (* j 27.0)))))

C

assert(y < z);
assert(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 ((t <= -4e+36) || !(t <= 3.4e+31)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (k * (j * 27.0));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 ((t <= (-4d+36)) .or. (.not. (t <= 3.4d+31))) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (4.0d0 * a)))) - (27.0d0 * (j * k))
    else
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - (k * (j * 27.0d0))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 ((t <= -4e+36) || !(t <= 3.4e+31)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (k * (j * 27.0));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -4e+36) or not (t <= 3.4e+31):
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - (27.0 * (j * k))
	else:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (k * (j * 27.0))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -4e+36) || !(t <= 3.4e+31))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(4.0 * a)))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -4e+36) || ~((t <= 3.4e+31)))
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (4.0 * a)))) - (27.0 * (j * k));
	else
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[t, -4e+36], N[Not[LessEqual[t, 3.4e+31]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.00000000000000017e36 or 3.3999999999999998e31 < t

   1. Initial program 85.6%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in i around 0 88.5%

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

   if -4.00000000000000017e36 < t < 3.3999999999999998e31

   1. Initial program 85.1%

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

   2. Taylor expanded in y around 0 89.1%

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

      1. distribute-lft-out 89.1%

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

      2. *-commutative 89.1%

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

      3. *-commutative 89.1%

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

   4. Simplified 89.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+36} \lor \neg \left(t \leq 3.4 \cdot 10^{+31}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 9: 71.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-168}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+83}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (<= x -7.5e+72)
   (* x (- (* i (- 4.0)) (* -18.0 (* (* t y) z))))
   (if (<= x 2.7e-168)
     (- (+ (* b c) (* -4.0 (* t a))) (* 27.0 (* j k)))
     (if (<= x 3.2e+83)
       (- (+ (* b c) (* 18.0 (* t (* x (* y z))))) (* k (* j 27.0)))
       (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))))))

C

assert(y < z);
assert(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 <= -7.5e+72) {
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)));
	} else if (x <= 2.7e-168) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	} else if (x <= 3.2e+83) {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (k * (j * 27.0));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 <= (-7.5d+72)) then
        tmp = x * ((i * -4.0d0) - ((-18.0d0) * ((t * y) * z)))
    else if (x <= 2.7d-168) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (27.0d0 * (j * k))
    else if (x <= 3.2d+83) then
        tmp = ((b * c) + (18.0d0 * (t * (x * (y * z))))) - (k * (j * 27.0d0))
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 <= -7.5e+72) {
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)));
	} else if (x <= 2.7e-168) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	} else if (x <= 3.2e+83) {
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (k * (j * 27.0));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -7.5e+72:
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)))
	elif x <= 2.7e-168:
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k))
	elif x <= 3.2e+83:
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (k * (j * 27.0))
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -7.5e+72)
		tmp = Float64(x * Float64(Float64(i * Float64(-4.0)) - Float64(-18.0 * Float64(Float64(t * y) * z))));
	elseif (x <= 2.7e-168)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(27.0 * Float64(j * k)));
	elseif (x <= 3.2e+83)
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -7.5e+72)
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)));
	elseif (x <= 2.7e-168)
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	elseif (x <= 3.2e+83)
		tmp = ((b * c) + (18.0 * (t * (x * (y * z))))) - (k * (j * 27.0));
	else
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[x, -7.5e+72], N[(x * N[(N[(i * (-4.0)), $MachinePrecision] - N[(-18.0 * N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e-168], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+83], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.50000000000000027e72

   1. Initial program 71.5%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in x around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. associate-*l* 76.3%

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

      3. associate-*l* 78.1%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in x around -inf 80.9%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 80.9%

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

      2. cancel-sign-sub-inv 80.9%

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

      3. associate-*r* 85.0%

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

      4. metadata-eval 85.0%

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

      5. *-commutative 85.0%

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

   9. Simplified 85.0%

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

   if -7.50000000000000027e72 < x < 2.70000000000000016e-168

   1. Initial program 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in x around 0 77.9%

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

   if 2.70000000000000016e-168 < x < 3.1999999999999999e83

   1. Initial program 94.1%

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

   2. Taylor expanded in a around 0 86.3%

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

      1. sub-neg 86.3%

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

      2. +-commutative 86.3%

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

      3. associate-+l+ 86.3%

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

      4. associate-*r* 86.3%

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

      5. *-commutative 86.3%

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

      6. associate-*r* 84.4%

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

      7. associate-*r* 84.4%

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

      8. distribute-lft-neg-in 84.4%

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

      9. metadata-eval 84.4%

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

      10. associate-*r* 84.5%

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

      11. distribute-rgt-in 84.5%

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

      12. metadata-eval 84.5%

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

      13. cancel-sign-sub-inv 84.5%

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

      14. +-commutative 84.5%

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

      15. fma-def 84.5%

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

   4. Simplified 84.5%

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

   5. Taylor expanded in i around 0 73.8%

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

   if 3.1999999999999999e83 < x

   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 82.5%

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

   4. Taylor expanded in x around inf 70.7%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-168}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+83}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]

Alternative 10: 79.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right) - 4 \cdot a\right) - t_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+29}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(t \cdot a\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (* k (* j 27.0))))
   (if (<= t -2.4e+85)
     (- (* t (- (* -18.0 (* x (* y (- z)))) (* 4.0 a))) t_1)
     (if (<= t 8.8e+29)
       (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) t_1)
       (- (+ (* 18.0 (* t (* x (* y z)))) (* -4.0 (* t a))) t_1)))))

C

assert(y < z);
assert(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 = k * (j * 27.0);
	double tmp;
	if (t <= -2.4e+85) {
		tmp = (t * ((-18.0 * (x * (y * -z))) - (4.0 * a))) - t_1;
	} else if (t <= 8.8e+29) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	} else {
		tmp = ((18.0 * (t * (x * (y * z)))) + (-4.0 * (t * a))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 = k * (j * 27.0d0)
    if (t <= (-2.4d+85)) then
        tmp = (t * (((-18.0d0) * (x * (y * -z))) - (4.0d0 * a))) - t_1
    else if (t <= 8.8d+29) then
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - t_1
    else
        tmp = ((18.0d0 * (t * (x * (y * z)))) + ((-4.0d0) * (t * a))) - t_1
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 = k * (j * 27.0);
	double tmp;
	if (t <= -2.4e+85) {
		tmp = (t * ((-18.0 * (x * (y * -z))) - (4.0 * a))) - t_1;
	} else if (t <= 8.8e+29) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	} else {
		tmp = ((18.0 * (t * (x * (y * z)))) + (-4.0 * (t * a))) - t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if t <= -2.4e+85:
		tmp = (t * ((-18.0 * (x * (y * -z))) - (4.0 * a))) - t_1
	elif t <= 8.8e+29:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1
	else:
		tmp = ((18.0 * (t * (x * (y * z)))) + (-4.0 * (t * a))) - t_1
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t <= -2.4e+85)
		tmp = Float64(Float64(t * Float64(Float64(-18.0 * Float64(x * Float64(y * Float64(-z)))) - Float64(4.0 * a))) - t_1);
	elseif (t <= 8.8e+29)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - t_1);
	else
		tmp = Float64(Float64(Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))) + Float64(-4.0 * Float64(t * a))) - t_1);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (t <= -2.4e+85)
		tmp = (t * ((-18.0 * (x * (y * -z))) - (4.0 * a))) - t_1;
	elseif (t <= 8.8e+29)
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	else
		tmp = ((18.0 * (t * (x * (y * z)))) + (-4.0 * (t * a))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e+85], N[(N[(t * N[(N[(-18.0 * N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 8.8e+29], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.39999999999999997e85

   1. Initial program 83.5%

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

   2. Taylor expanded in t around -inf 84.3%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 84.3%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)} - \left(j \cdot 27\right) \cdot k \]

      2. neg-mul-1 84.3%

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

      3. cancel-sign-sub-inv 84.3%

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

      4. *-commutative 84.3%

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

      5. metadata-eval 84.3%

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

   4. Simplified 84.3%

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

   if -2.39999999999999997e85 < t < 8.8000000000000005e29

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0 88.5%

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

      1. distribute-lft-out 88.5%

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

      2. *-commutative 88.5%

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

      3. *-commutative 88.5%

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

   4. Simplified 88.5%

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

   if 8.8000000000000005e29 < t

   1. Initial program 86.6%

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

   2. Taylor expanded in t around -inf 83.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 83.6%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)} - \left(j \cdot 27\right) \cdot k \]

      2. neg-mul-1 83.6%

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

      3. cancel-sign-sub-inv 83.6%

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

      4. *-commutative 83.6%

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

      5. metadata-eval 83.6%

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

   4. Simplified 83.6%

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

   5. Taylor expanded in x around 0 83.7%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right) - 4 \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+29}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 11: 79.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right) - 4 \cdot a\right) - t_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+29}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(t \cdot a\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (* k (* j 27.0))))
   (if (<= t -3.4e+85)
     (- (* t (- (* -18.0 (* x (* y (- z)))) (* 4.0 a))) t_1)
     (if (<= t 1.3e+29)
       (- (+ (* b c) (* t (* a -4.0))) (+ (* j (* 27.0 k)) (* x (* i 4.0))))
       (- (+ (* 18.0 (* t (* x (* y z)))) (* -4.0 (* t a))) t_1)))))

C

assert(y < z);
assert(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 = k * (j * 27.0);
	double tmp;
	if (t <= -3.4e+85) {
		tmp = (t * ((-18.0 * (x * (y * -z))) - (4.0 * a))) - t_1;
	} else if (t <= 1.3e+29) {
		tmp = ((b * c) + (t * (a * -4.0))) - ((j * (27.0 * k)) + (x * (i * 4.0)));
	} else {
		tmp = ((18.0 * (t * (x * (y * z)))) + (-4.0 * (t * a))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 = k * (j * 27.0d0)
    if (t <= (-3.4d+85)) then
        tmp = (t * (((-18.0d0) * (x * (y * -z))) - (4.0d0 * a))) - t_1
    else if (t <= 1.3d+29) then
        tmp = ((b * c) + (t * (a * (-4.0d0)))) - ((j * (27.0d0 * k)) + (x * (i * 4.0d0)))
    else
        tmp = ((18.0d0 * (t * (x * (y * z)))) + ((-4.0d0) * (t * a))) - t_1
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 = k * (j * 27.0);
	double tmp;
	if (t <= -3.4e+85) {
		tmp = (t * ((-18.0 * (x * (y * -z))) - (4.0 * a))) - t_1;
	} else if (t <= 1.3e+29) {
		tmp = ((b * c) + (t * (a * -4.0))) - ((j * (27.0 * k)) + (x * (i * 4.0)));
	} else {
		tmp = ((18.0 * (t * (x * (y * z)))) + (-4.0 * (t * a))) - t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if t <= -3.4e+85:
		tmp = (t * ((-18.0 * (x * (y * -z))) - (4.0 * a))) - t_1
	elif t <= 1.3e+29:
		tmp = ((b * c) + (t * (a * -4.0))) - ((j * (27.0 * k)) + (x * (i * 4.0)))
	else:
		tmp = ((18.0 * (t * (x * (y * z)))) + (-4.0 * (t * a))) - t_1
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t <= -3.4e+85)
		tmp = Float64(Float64(t * Float64(Float64(-18.0 * Float64(x * Float64(y * Float64(-z)))) - Float64(4.0 * a))) - t_1);
	elseif (t <= 1.3e+29)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(a * -4.0))) - Float64(Float64(j * Float64(27.0 * k)) + Float64(x * Float64(i * 4.0))));
	else
		tmp = Float64(Float64(Float64(18.0 * Float64(t * Float64(x * Float64(y * z)))) + Float64(-4.0 * Float64(t * a))) - t_1);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if (t <= -3.4e+85)
		tmp = (t * ((-18.0 * (x * (y * -z))) - (4.0 * a))) - t_1;
	elseif (t <= 1.3e+29)
		tmp = ((b * c) + (t * (a * -4.0))) - ((j * (27.0 * k)) + (x * (i * 4.0)));
	else
		tmp = ((18.0 * (t * (x * (y * z)))) + (-4.0 * (t * a))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+85], N[(N[(t * N[(N[(-18.0 * N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 1.3e+29], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision] + N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.4000000000000003e85

   1. Initial program 83.5%

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

   2. Taylor expanded in t around -inf 84.3%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 84.3%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)} - \left(j \cdot 27\right) \cdot k \]

      2. neg-mul-1 84.3%

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

      3. cancel-sign-sub-inv 84.3%

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

      4. *-commutative 84.3%

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

      5. metadata-eval 84.3%

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

   4. Simplified 84.3%

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

   if -3.4000000000000003e85 < t < 1.3e29

   1. Initial program 85.4%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in x around 0 88.5%

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

      1. *-commutative 88.5%

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

      2. *-commutative 88.5%

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

      3. associate-*r* 88.5%

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

   6. Simplified 88.5%

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

   if 1.3e29 < t

   1. Initial program 86.6%

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

   2. Taylor expanded in t around -inf 83.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 83.6%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)} - \left(j \cdot 27\right) \cdot k \]

      2. neg-mul-1 83.6%

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

      3. cancel-sign-sub-inv 83.6%

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

      4. *-commutative 83.6%

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

      5. metadata-eval 83.6%

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

   4. Simplified 83.6%

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

   5. Taylor expanded in x around 0 83.7%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right) - 4 \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+29}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) - \left(j \cdot \left(27 \cdot k\right) + x \cdot \left(i \cdot 4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + -4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 12: 80.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t \leq -2.95 \cdot 10^{+85} \lor \neg \left(t \leq 1.12 \cdot 10^{+33}\right):\\ \;\;\;\;t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right) - 4 \cdot a\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (* k (* j 27.0))))
   (if (or (<= t -2.95e+85) (not (<= t 1.12e+33)))
     (- (* t (- (* -18.0 (* x (* y (- z)))) (* 4.0 a))) t_1)
     (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) t_1))))

C

assert(y < z);
assert(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 = k * (j * 27.0);
	double tmp;
	if ((t <= -2.95e+85) || !(t <= 1.12e+33)) {
		tmp = (t * ((-18.0 * (x * (y * -z))) - (4.0 * a))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 = k * (j * 27.0d0)
    if ((t <= (-2.95d+85)) .or. (.not. (t <= 1.12d+33))) then
        tmp = (t * (((-18.0d0) * (x * (y * -z))) - (4.0d0 * a))) - t_1
    else
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - t_1
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 = k * (j * 27.0);
	double tmp;
	if ((t <= -2.95e+85) || !(t <= 1.12e+33)) {
		tmp = (t * ((-18.0 * (x * (y * -z))) - (4.0 * a))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * 27.0)
	tmp = 0
	if (t <= -2.95e+85) or not (t <= 1.12e+33):
		tmp = (t * ((-18.0 * (x * (y * -z))) - (4.0 * a))) - t_1
	else:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if ((t <= -2.95e+85) || !(t <= 1.12e+33))
		tmp = Float64(Float64(t * Float64(Float64(-18.0 * Float64(x * Float64(y * Float64(-z)))) - Float64(4.0 * a))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - t_1);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = k * (j * 27.0);
	tmp = 0.0;
	if ((t <= -2.95e+85) || ~((t <= 1.12e+33)))
		tmp = (t * ((-18.0 * (x * (y * -z))) - (4.0 * a))) - t_1;
	else
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -2.95e+85], N[Not[LessEqual[t, 1.12e+33]], $MachinePrecision]], N[(N[(t * N[(N[(-18.0 * N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.95e85 or 1.12e33 < t

   1. Initial program 85.2%

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

   2. Taylor expanded in t around -inf 83.9%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 83.9%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)} - \left(j \cdot 27\right) \cdot k \]

      2. neg-mul-1 83.9%

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

      3. cancel-sign-sub-inv 83.9%

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

      4. *-commutative 83.9%

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

      5. metadata-eval 83.9%

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

   4. Simplified 83.9%

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

   if -2.95e85 < t < 1.12e33

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0 88.5%

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

      1. distribute-lft-out 88.5%

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

      2. *-commutative 88.5%

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

      3. *-commutative 88.5%

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

   4. Simplified 88.5%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{+85} \lor \neg \left(t \leq 1.12 \cdot 10^{+33}\right):\\ \;\;\;\;t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot \left(-z\right)\right)\right) - 4 \cdot a\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 13: 45.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(z \cdot \left(t \cdot \left(-18 \cdot \left(-y\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-32}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(y \cdot \left(-18 \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+200}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+242}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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))) (t_2 (- (* b c) (* 27.0 (* j k)))))
   (if (<= x -1.15e+68)
     (* x (* z (* t (* -18.0 (- y)))))
     (if (<= x 5.2e-64)
       t_2
       (if (<= x 2.35e-32)
         (* (* t z) (* y (* -18.0 (- x))))
         (if (<= x 2.9e+102)
           t_2
           (if (<= x 1.16e+181)
             t_1
             (if (<= x 1.12e+200)
               (* j (* k -27.0))
               (if (<= x 6.2e+242) (* x (* (* y z) (* t 18.0))) t_1)))))))))

C

assert(y < z);
assert(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);
	double t_2 = (b * c) - (27.0 * (j * k));
	double tmp;
	if (x <= -1.15e+68) {
		tmp = x * (z * (t * (-18.0 * -y)));
	} else if (x <= 5.2e-64) {
		tmp = t_2;
	} else if (x <= 2.35e-32) {
		tmp = (t * z) * (y * (-18.0 * -x));
	} else if (x <= 2.9e+102) {
		tmp = t_2;
	} else if (x <= 1.16e+181) {
		tmp = t_1;
	} else if (x <= 1.12e+200) {
		tmp = j * (k * -27.0);
	} else if (x <= 6.2e+242) {
		tmp = x * ((y * z) * (t * 18.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 * (i * (-4.0d0))
    t_2 = (b * c) - (27.0d0 * (j * k))
    if (x <= (-1.15d+68)) then
        tmp = x * (z * (t * ((-18.0d0) * -y)))
    else if (x <= 5.2d-64) then
        tmp = t_2
    else if (x <= 2.35d-32) then
        tmp = (t * z) * (y * ((-18.0d0) * -x))
    else if (x <= 2.9d+102) then
        tmp = t_2
    else if (x <= 1.16d+181) then
        tmp = t_1
    else if (x <= 1.12d+200) then
        tmp = j * (k * (-27.0d0))
    else if (x <= 6.2d+242) then
        tmp = x * ((y * z) * (t * 18.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z;
assert 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);
	double t_2 = (b * c) - (27.0 * (j * k));
	double tmp;
	if (x <= -1.15e+68) {
		tmp = x * (z * (t * (-18.0 * -y)));
	} else if (x <= 5.2e-64) {
		tmp = t_2;
	} else if (x <= 2.35e-32) {
		tmp = (t * z) * (y * (-18.0 * -x));
	} else if (x <= 2.9e+102) {
		tmp = t_2;
	} else if (x <= 1.16e+181) {
		tmp = t_1;
	} else if (x <= 1.12e+200) {
		tmp = j * (k * -27.0);
	} else if (x <= 6.2e+242) {
		tmp = x * ((y * z) * (t * 18.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (i * -4.0)
	t_2 = (b * c) - (27.0 * (j * k))
	tmp = 0
	if x <= -1.15e+68:
		tmp = x * (z * (t * (-18.0 * -y)))
	elif x <= 5.2e-64:
		tmp = t_2
	elif x <= 2.35e-32:
		tmp = (t * z) * (y * (-18.0 * -x))
	elif x <= 2.9e+102:
		tmp = t_2
	elif x <= 1.16e+181:
		tmp = t_1
	elif x <= 1.12e+200:
		tmp = j * (k * -27.0)
	elif x <= 6.2e+242:
		tmp = x * ((y * z) * (t * 18.0))
	else:
		tmp = t_1
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(i * -4.0))
	t_2 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	tmp = 0.0
	if (x <= -1.15e+68)
		tmp = Float64(x * Float64(z * Float64(t * Float64(-18.0 * Float64(-y)))));
	elseif (x <= 5.2e-64)
		tmp = t_2;
	elseif (x <= 2.35e-32)
		tmp = Float64(Float64(t * z) * Float64(y * Float64(-18.0 * Float64(-x))));
	elseif (x <= 2.9e+102)
		tmp = t_2;
	elseif (x <= 1.16e+181)
		tmp = t_1;
	elseif (x <= 1.12e+200)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (x <= 6.2e+242)
		tmp = Float64(x * Float64(Float64(y * z) * Float64(t * 18.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (i * -4.0);
	t_2 = (b * c) - (27.0 * (j * k));
	tmp = 0.0;
	if (x <= -1.15e+68)
		tmp = x * (z * (t * (-18.0 * -y)));
	elseif (x <= 5.2e-64)
		tmp = t_2;
	elseif (x <= 2.35e-32)
		tmp = (t * z) * (y * (-18.0 * -x));
	elseif (x <= 2.9e+102)
		tmp = t_2;
	elseif (x <= 1.16e+181)
		tmp = t_1;
	elseif (x <= 1.12e+200)
		tmp = j * (k * -27.0);
	elseif (x <= 6.2e+242)
		tmp = x * ((y * z) * (t * 18.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+68], N[(x * N[(z * N[(t * N[(-18.0 * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e-64], t$95$2, If[LessEqual[x, 2.35e-32], N[(N[(t * z), $MachinePrecision] * N[(y * N[(-18.0 * (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e+102], t$95$2, If[LessEqual[x, 1.16e+181], t$95$1, If[LessEqual[x, 1.12e+200], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+242], N[(x * N[(N[(y * z), $MachinePrecision] * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.15e68

   1. Initial program 70.2%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in x around inf 66.2%

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

      1. *-commutative 66.2%

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

      2. associate-*l* 74.7%

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

      3. associate-*l* 76.5%

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

   6. Simplified 76.5%

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

   7. Taylor expanded in x around -inf 79.3%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 79.3%

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

      2. cancel-sign-sub-inv 79.3%

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

      3. associate-*r* 83.3%

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

      4. metadata-eval 83.3%

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

      5. *-commutative 83.3%

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

   9. Simplified 83.3%

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

   10. Taylor expanded in t around inf 53.8%

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

       1. *-commutative 53.8%

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

       2. associate-*r* 51.7%

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

       3. associate-*l* 51.7%

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

       4. associate-*r* 53.7%

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

       5. *-commutative 53.7%

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

       6. associate-*r* 55.8%

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

       7. associate-*l* 55.8%

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

       8. associate-*r* 55.4%

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

       9. *-commutative 55.4%

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

       10. *-commutative 55.4%

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

       11. *-commutative 55.4%

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

       12. associate-*l* 55.4%

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

       13. *-commutative 55.4%

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

       14. associate-*l* 55.5%

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

   12. Simplified 55.5%

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

   if -1.15e68 < x < 5.2e-64 or 2.3500000000000001e-32 < x < 2.9000000000000002e102

   1. Initial program 92.7%

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

   2. Taylor expanded in a around 0 74.7%

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

      1. sub-neg 74.7%

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

      2. +-commutative 74.7%

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

      3. associate-+l+ 74.7%

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

      4. associate-*r* 74.1%

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

      5. *-commutative 74.1%

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

      6. associate-*r* 74.1%

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

      7. associate-*r* 74.8%

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

      8. distribute-lft-neg-in 74.8%

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

      9. metadata-eval 74.8%

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

      10. associate-*r* 75.5%

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

      11. distribute-rgt-in 75.5%

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

      12. metadata-eval 75.5%

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

      13. cancel-sign-sub-inv 75.5%

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

      14. +-commutative 75.5%

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

      15. fma-def 76.1%

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

   4. Simplified 76.1%

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

   5. Taylor expanded in x around 0 56.0%

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

   if 5.2e-64 < x < 2.3500000000000001e-32

   1. Initial program 71.1%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in x around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. associate-*l* 51.6%

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

      3. associate-*l* 70.4%

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

   6. Simplified 70.4%

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

   7. Taylor expanded in x around -inf 52.4%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 52.4%

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

      2. cancel-sign-sub-inv 52.4%

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

      3. associate-*r* 61.9%

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

      4. metadata-eval 61.9%

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

      5. *-commutative 61.9%

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

   9. Simplified 61.9%

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

   10. Taylor expanded in t around inf 51.8%

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

       1. associate-*r* 51.8%

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

       2. *-commutative 51.8%

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

       3. associate-*r* 51.8%

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

       4. associate-*r* 51.8%

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

       5. associate-*r* 51.9%

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

       6. associate-*l* 52.0%

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

       7. associate-*r* 70.7%

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

       8. *-commutative 70.7%

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

       9. *-commutative 70.7%

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

       10. associate-*l* 70.7%

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

       11. *-commutative 70.7%

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

       12. *-commutative 70.7%

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

   12. Simplified 70.7%

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

   if 2.9000000000000002e102 < x < 1.16000000000000003e181 or 6.2000000000000002e242 < x

   1. Initial program 81.9%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in i around inf 60.9%

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

      1. associate-*r* 60.9%

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

      2. *-commutative 60.9%

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

   6. Simplified 60.9%

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

   if 1.16000000000000003e181 < x < 1.12000000000000004e200

   1. Initial program 50.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in j around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. associate-*l* 50.2%

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

   6. Simplified 50.2%

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

   if 1.12000000000000004e200 < x < 6.2000000000000002e242

   1. Initial program 81.1%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in x around inf 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-*l* 99.8%

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

      3. associate-*l* 99.8%

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

   6. Simplified 99.8%

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

      1. fma-def 99.7%

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

      2. associate-*r* 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*r* 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in y around inf 42.0%

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

       1. *-commutative 42.0%

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

       2. associate-*r* 51.3%

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

       3. *-commutative 51.3%

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

       4. associate-*r* 51.3%

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

       5. associate-*r* 51.5%

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

       6. *-commutative 51.5%

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

       7. associate-*r* 51.3%

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

       8. associate-*l* 51.3%

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

   11. Simplified 51.3%

       \[\leadsto \color{blue}{\left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right) \cdot x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(z \cdot \left(t \cdot \left(-18 \cdot \left(-y\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-64}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-32}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(y \cdot \left(-18 \cdot \left(-x\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+102}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+181}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+200}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+242}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \]

Alternative 14: 71.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-168}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-55}:\\ \;\;\;\;b \cdot c - \left(t_1 + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (* 27.0 (* j k))) (t_2 (- (+ (* b c) (* -4.0 (* t a))) t_1)))
   (if (<= x -4.2e+74)
     (* x (- (* i (- 4.0)) (* -18.0 (* (* t y) z))))
     (if (<= x 4.3e-168)
       t_2
       (if (<= x 1.6e-55)
         (- (* b c) (+ t_1 (* 4.0 (* x i))))
         (if (<= x 2.4e+47)
           t_2
           (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))))))))

C

assert(y < z);
assert(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 = 27.0 * (j * k);
	double t_2 = ((b * c) + (-4.0 * (t * a))) - t_1;
	double tmp;
	if (x <= -4.2e+74) {
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)));
	} else if (x <= 4.3e-168) {
		tmp = t_2;
	} else if (x <= 1.6e-55) {
		tmp = (b * c) - (t_1 + (4.0 * (x * i)));
	} else if (x <= 2.4e+47) {
		tmp = t_2;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 = 27.0d0 * (j * k)
    t_2 = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    if (x <= (-4.2d+74)) then
        tmp = x * ((i * -4.0d0) - ((-18.0d0) * ((t * y) * z)))
    else if (x <= 4.3d-168) then
        tmp = t_2
    else if (x <= 1.6d-55) then
        tmp = (b * c) - (t_1 + (4.0d0 * (x * i)))
    else if (x <= 2.4d+47) then
        tmp = t_2
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 = 27.0 * (j * k);
	double t_2 = ((b * c) + (-4.0 * (t * a))) - t_1;
	double tmp;
	if (x <= -4.2e+74) {
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)));
	} else if (x <= 4.3e-168) {
		tmp = t_2;
	} else if (x <= 1.6e-55) {
		tmp = (b * c) - (t_1 + (4.0 * (x * i)));
	} else if (x <= 2.4e+47) {
		tmp = t_2;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	t_2 = ((b * c) + (-4.0 * (t * a))) - t_1
	tmp = 0
	if x <= -4.2e+74:
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)))
	elif x <= 4.3e-168:
		tmp = t_2
	elif x <= 1.6e-55:
		tmp = (b * c) - (t_1 + (4.0 * (x * i)))
	elif x <= 2.4e+47:
		tmp = t_2
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	t_2 = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1)
	tmp = 0.0
	if (x <= -4.2e+74)
		tmp = Float64(x * Float64(Float64(i * Float64(-4.0)) - Float64(-18.0 * Float64(Float64(t * y) * z))));
	elseif (x <= 4.3e-168)
		tmp = t_2;
	elseif (x <= 1.6e-55)
		tmp = Float64(Float64(b * c) - Float64(t_1 + Float64(4.0 * Float64(x * i))));
	elseif (x <= 2.4e+47)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 27.0 * (j * k);
	t_2 = ((b * c) + (-4.0 * (t * a))) - t_1;
	tmp = 0.0;
	if (x <= -4.2e+74)
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)));
	elseif (x <= 4.3e-168)
		tmp = t_2;
	elseif (x <= 1.6e-55)
		tmp = (b * c) - (t_1 + (4.0 * (x * i)));
	elseif (x <= 2.4e+47)
		tmp = t_2;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[x, -4.2e+74], N[(x * N[(N[(i * (-4.0)), $MachinePrecision] - N[(-18.0 * N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.3e-168], t$95$2, If[LessEqual[x, 1.6e-55], N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+47], t$95$2, N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.1999999999999998e74

   1. Initial program 71.5%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in x around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. associate-*l* 76.3%

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

      3. associate-*l* 78.1%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in x around -inf 80.9%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 80.9%

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

      2. cancel-sign-sub-inv 80.9%

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

      3. associate-*r* 85.0%

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

      4. metadata-eval 85.0%

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

      5. *-commutative 85.0%

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

   9. Simplified 85.0%

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

   if -4.1999999999999998e74 < x < 4.29999999999999995e-168 or 1.6000000000000001e-55 < x < 2.40000000000000019e47

   1. Initial program 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in x around 0 75.4%

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

   if 4.29999999999999995e-168 < x < 1.6000000000000001e-55

   1. Initial program 99.8%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 79.0%

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

   if 2.40000000000000019e47 < x

   1. Initial program 80.6%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in x around inf 70.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-168}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-55}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]

Alternative 15: 71.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-169}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-77}:\\ \;\;\;\;b \cdot c - \left(t_1 + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+46}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (* 27.0 (* j k))))
   (if (<= x -1.9e+73)
     (* x (- (* i (- 4.0)) (* -18.0 (* (* t y) z))))
     (if (<= x 9.6e-169)
       (- (+ (* b c) (* -4.0 (* t a))) t_1)
       (if (<= x 2.35e-77)
         (- (* b c) (+ t_1 (* 4.0 (* x i))))
         (if (<= x 1.8e+46)
           (- (- (* b c) (* 4.0 (* t a))) (* k (* j 27.0)))
           (* x (- (* 18.0 (* t (* y z))) (* i 4.0)))))))))

C

assert(y < z);
assert(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 = 27.0 * (j * k);
	double tmp;
	if (x <= -1.9e+73) {
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)));
	} else if (x <= 9.6e-169) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (x <= 2.35e-77) {
		tmp = (b * c) - (t_1 + (4.0 * (x * i)));
	} else if (x <= 1.8e+46) {
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 = 27.0d0 * (j * k)
    if (x <= (-1.9d+73)) then
        tmp = x * ((i * -4.0d0) - ((-18.0d0) * ((t * y) * z)))
    else if (x <= 9.6d-169) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    else if (x <= 2.35d-77) then
        tmp = (b * c) - (t_1 + (4.0d0 * (x * i)))
    else if (x <= 1.8d+46) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - (k * (j * 27.0d0))
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (i * 4.0d0))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 = 27.0 * (j * k);
	double tmp;
	if (x <= -1.9e+73) {
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)));
	} else if (x <= 9.6e-169) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (x <= 2.35e-77) {
		tmp = (b * c) - (t_1 + (4.0 * (x * i)));
	} else if (x <= 1.8e+46) {
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	tmp = 0
	if x <= -1.9e+73:
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)))
	elif x <= 9.6e-169:
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1
	elif x <= 2.35e-77:
		tmp = (b * c) - (t_1 + (4.0 * (x * i)))
	elif x <= 1.8e+46:
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0))
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	tmp = 0.0
	if (x <= -1.9e+73)
		tmp = Float64(x * Float64(Float64(i * Float64(-4.0)) - Float64(-18.0 * Float64(Float64(t * y) * z))));
	elseif (x <= 9.6e-169)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1);
	elseif (x <= 2.35e-77)
		tmp = Float64(Float64(b * c) - Float64(t_1 + Float64(4.0 * Float64(x * i))));
	elseif (x <= 1.8e+46)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(i * 4.0)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 27.0 * (j * k);
	tmp = 0.0;
	if (x <= -1.9e+73)
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)));
	elseif (x <= 9.6e-169)
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	elseif (x <= 2.35e-77)
		tmp = (b * c) - (t_1 + (4.0 * (x * i)));
	elseif (x <= 1.8e+46)
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	else
		tmp = x * ((18.0 * (t * (y * z))) - (i * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.9e+73], N[(x * N[(N[(i * (-4.0)), $MachinePrecision] - N[(-18.0 * N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.6e-169], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 2.35e-77], N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e+46], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.90000000000000011e73

   1. Initial program 71.5%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in x around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. associate-*l* 76.3%

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

      3. associate-*l* 78.1%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in x around -inf 80.9%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 80.9%

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

      2. cancel-sign-sub-inv 80.9%

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

      3. associate-*r* 85.0%

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

      4. metadata-eval 85.0%

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

      5. *-commutative 85.0%

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

   9. Simplified 85.0%

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

   if -1.90000000000000011e73 < x < 9.60000000000000043e-169

   1. Initial program 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in x around 0 77.9%

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

   if 9.60000000000000043e-169 < x < 2.3499999999999999e-77

   1. Initial program 99.8%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 83.7%

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

   if 2.3499999999999999e-77 < x < 1.7999999999999999e46

   1. Initial program 86.2%

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

   2. Taylor expanded in y around 0 63.1%

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

      1. distribute-lft-out 63.1%

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

      2. *-commutative 63.1%

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

      3. *-commutative 63.1%

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

   4. Simplified 63.1%

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

   5. Taylor expanded in t around inf 58.1%

      \[\leadsto \left(b \cdot c - 4 \cdot \color{blue}{\left(a \cdot t\right)}\right) - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. *-commutative 58.1%

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

   7. Simplified 58.1%

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

   if 1.7999999999999999e46 < x

   1. Initial program 80.6%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in x around inf 70.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-169}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-77}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+46}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]

Alternative 16: 36.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.08 \cdot 10^{+148}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -7.2 \cdot 10^{-224}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-314}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+78}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (<= (* b c) -1.08e+148)
   (* b c)
   (if (<= (* b c) -7.2e-224)
     (* k (* j -27.0))
     (if (<= (* b c) -5e-314)
       (* t (* a -4.0))
       (if (<= (* b c) 2e+78) (* j (* k -27.0)) (* b c))))))

C

assert(y < z);
assert(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) <= -1.08e+148) {
		tmp = b * c;
	} else if ((b * c) <= -7.2e-224) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= -5e-314) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 2e+78) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) <= (-1.08d+148)) then
        tmp = b * c
    else if ((b * c) <= (-7.2d-224)) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= (-5d-314)) then
        tmp = t * (a * (-4.0d0))
    else if ((b * c) <= 2d+78) then
        tmp = j * (k * (-27.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert y < z;
assert 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) <= -1.08e+148) {
		tmp = b * c;
	} else if ((b * c) <= -7.2e-224) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= -5e-314) {
		tmp = t * (a * -4.0);
	} else if ((b * c) <= 2e+78) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1.08e+148:
		tmp = b * c
	elif (b * c) <= -7.2e-224:
		tmp = k * (j * -27.0)
	elif (b * c) <= -5e-314:
		tmp = t * (a * -4.0)
	elif (b * c) <= 2e+78:
		tmp = j * (k * -27.0)
	else:
		tmp = b * c
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1.08e+148)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -7.2e-224)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= -5e-314)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (Float64(b * c) <= 2e+78)
		tmp = Float64(j * Float64(k * -27.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1.08e+148)
		tmp = b * c;
	elseif ((b * c) <= -7.2e-224)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= -5e-314)
		tmp = t * (a * -4.0);
	elseif ((b * c) <= 2e+78)
		tmp = j * (k * -27.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[N[(b * c), $MachinePrecision], -1.08e+148], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -7.2e-224], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5e-314], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+78], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.07999999999999999e148 or 2.00000000000000002e78 < (*.f64 b c)

   1. Initial program 80.6%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in b around inf 55.5%

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

   if -1.07999999999999999e148 < (*.f64 b c) < -7.1999999999999999e-224

   1. Initial program 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in j around inf 34.1%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   5. 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-*l* 34.1%

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

   6. Simplified 34.1%

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

   if -7.1999999999999999e-224 < (*.f64 b c) < -4.99999999982e-314

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 91.6%

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

      1. distribute-lft-out 91.6%

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

      2. *-commutative 91.6%

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

      3. *-commutative 91.6%

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

   4. Simplified 91.6%

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

   5. Taylor expanded in t around inf 62.0%

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

      1. associate-*r* 62.0%

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

      2. *-commutative 62.0%

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

   7. Simplified 62.0%

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

   if -4.99999999982e-314 < (*.f64 b c) < 2.00000000000000002e78

   1. Initial program 86.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in j around inf 24.7%

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

      1. *-commutative 24.7%

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

      2. associate-*l* 24.8%

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

   6. Simplified 24.8%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.08 \cdot 10^{+148}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -7.2 \cdot 10^{-224}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -5 \cdot 10^{-314}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+78}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 17: 77.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (<= x -2e+79)
   (* x (- (* i (- 4.0)) (* -18.0 (* (* t y) z))))
   (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) (* k (* j 27.0)))))

C

assert(y < z);
assert(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 <= -2e+79) {
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)));
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (k * (j * 27.0));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 <= (-2d+79)) then
        tmp = x * ((i * -4.0d0) - ((-18.0d0) * ((t * y) * z)))
    else
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - (k * (j * 27.0d0))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 <= -2e+79) {
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)));
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (k * (j * 27.0));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -2e+79:
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)))
	else:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (k * (j * 27.0))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -2e+79)
		tmp = Float64(x * Float64(Float64(i * Float64(-4.0)) - Float64(-18.0 * Float64(Float64(t * y) * z))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - Float64(k * Float64(j * 27.0)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -2e+79)
		tmp = x * ((i * -4.0) - (-18.0 * ((t * y) * z)));
	else
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - (k * (j * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[x, -2e+79], N[(x * N[(N[(i * (-4.0)), $MachinePrecision] - N[(-18.0 * N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.99999999999999993e79

   1. Initial program 70.9%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in x around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-*l* 75.7%

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

      3. associate-*l* 77.6%

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

   6. Simplified 77.6%

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

   7. Taylor expanded in x around -inf 80.5%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 80.5%

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

      2. cancel-sign-sub-inv 80.5%

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

      3. associate-*r* 84.6%

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

      4. metadata-eval 84.6%

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

      5. *-commutative 84.6%

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

   9. Simplified 84.6%

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

   if -1.99999999999999993e79 < x

   1. Initial program 88.3%

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

   2. Taylor expanded in y around 0 79.8%

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

      1. distribute-lft-out 79.8%

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

      2. *-commutative 79.8%

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

      3. *-commutative 79.8%

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

   4. Simplified 79.8%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(i \cdot \left(-4\right) - -18 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 18: 47.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+105}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -185000:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1050:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - t_2\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+174}:\\ \;\;\;\;t_1 - t_2\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+288}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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))) (t_2 (* k (* j 27.0))))
   (if (<= t -1.05e+105)
     (* 18.0 (* t (* x (* y z))))
     (if (<= t -185000.0)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= t 1050.0)
         (- (* x (* i -4.0)) t_2)
         (if (<= t 6.6e+174)
           (- t_1 t_2)
           (if (<= t 1.95e+288) (* x (* (* y z) (* t 18.0))) t_1)))))))

C

assert(y < z);
assert(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 t_2 = k * (j * 27.0);
	double tmp;
	if (t <= -1.05e+105) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t <= -185000.0) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 1050.0) {
		tmp = (x * (i * -4.0)) - t_2;
	} else if (t <= 6.6e+174) {
		tmp = t_1 - t_2;
	} else if (t <= 1.95e+288) {
		tmp = x * ((y * z) * (t * 18.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 = t * (a * (-4.0d0))
    t_2 = k * (j * 27.0d0)
    if (t <= (-1.05d+105)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (t <= (-185000.0d0)) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (t <= 1050.0d0) then
        tmp = (x * (i * (-4.0d0))) - t_2
    else if (t <= 6.6d+174) then
        tmp = t_1 - t_2
    else if (t <= 1.95d+288) then
        tmp = x * ((y * z) * (t * 18.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 t_2 = k * (j * 27.0);
	double tmp;
	if (t <= -1.05e+105) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t <= -185000.0) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 1050.0) {
		tmp = (x * (i * -4.0)) - t_2;
	} else if (t <= 6.6e+174) {
		tmp = t_1 - t_2;
	} else if (t <= 1.95e+288) {
		tmp = x * ((y * z) * (t * 18.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	t_2 = k * (j * 27.0)
	tmp = 0
	if t <= -1.05e+105:
		tmp = 18.0 * (t * (x * (y * z)))
	elif t <= -185000.0:
		tmp = (b * c) - (27.0 * (j * k))
	elif t <= 1050.0:
		tmp = (x * (i * -4.0)) - t_2
	elif t <= 6.6e+174:
		tmp = t_1 - t_2
	elif t <= 1.95e+288:
		tmp = x * ((y * z) * (t * 18.0))
	else:
		tmp = t_1
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	t_2 = Float64(k * Float64(j * 27.0))
	tmp = 0.0
	if (t <= -1.05e+105)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (t <= -185000.0)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 1050.0)
		tmp = Float64(Float64(x * Float64(i * -4.0)) - t_2);
	elseif (t <= 6.6e+174)
		tmp = Float64(t_1 - t_2);
	elseif (t <= 1.95e+288)
		tmp = Float64(x * Float64(Float64(y * z) * Float64(t * 18.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	t_2 = k * (j * 27.0);
	tmp = 0.0;
	if (t <= -1.05e+105)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (t <= -185000.0)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (t <= 1050.0)
		tmp = (x * (i * -4.0)) - t_2;
	elseif (t <= 6.6e+174)
		tmp = t_1 - t_2;
	elseif (t <= 1.95e+288)
		tmp = x * ((y * z) * (t * 18.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+105], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -185000.0], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1050.0], N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t, 6.6e+174], N[(t$95$1 - t$95$2), $MachinePrecision], If[LessEqual[t, 1.95e+288], N[(x * N[(N[(y * z), $MachinePrecision] * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.05000000000000005e105

   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 91.2%

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

   4. Taylor expanded in x around inf 73.1%

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

      1. *-commutative 73.1%

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

      2. associate-*l* 71.1%

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

      3. associate-*l* 64.7%

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

   6. Simplified 64.7%

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

      1. fma-def 64.8%

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

      2. associate-*r* 71.1%

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

      3. *-commutative 71.1%

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

      4. associate-*r* 64.8%

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

   8. Applied egg-rr 64.8%

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

   9. Taylor expanded in y around inf 59.4%

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

   if -1.05000000000000005e105 < t < -185000

   1. Initial program 87.4%

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

   2. Taylor expanded in a around 0 87.7%

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

      1. sub-neg 87.7%

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

      2. +-commutative 87.7%

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

      3. associate-+l+ 87.7%

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

      4. associate-*r* 87.7%

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

      5. *-commutative 87.7%

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

      6. associate-*r* 87.7%

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

      7. associate-*r* 87.7%

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

      8. distribute-lft-neg-in 87.7%

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

      9. metadata-eval 87.7%

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

      10. associate-*r* 87.7%

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

      11. distribute-rgt-in 87.7%

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

      12. metadata-eval 87.7%

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

      13. cancel-sign-sub-inv 87.7%

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

      14. +-commutative 87.7%

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

      15. fma-def 87.7%

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

   4. Simplified 87.7%

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

   5. Taylor expanded in x around 0 69.5%

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

   if -185000 < t < 1050

   1. Initial program 84.1%

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

   2. Taylor expanded in a around 0 77.4%

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

      1. sub-neg 77.4%

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

      2. +-commutative 77.4%

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

      3. associate-+l+ 77.4%

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

      4. associate-*r* 77.4%

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

      5. *-commutative 77.4%

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

      6. associate-*r* 84.2%

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

      7. associate-*r* 84.2%

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

      8. distribute-lft-neg-in 84.2%

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

      9. metadata-eval 84.2%

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

      10. associate-*r* 84.2%

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

      11. distribute-rgt-in 84.2%

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

      12. metadata-eval 84.2%

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

      13. cancel-sign-sub-inv 84.2%

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

      14. +-commutative 84.2%

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

      15. fma-def 84.2%

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

   4. Simplified 84.2%

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

   5. Taylor expanded in i around inf 61.4%

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

      1. associate-*r* 61.5%

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

      2. *-commutative 61.5%

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

   7. Simplified 61.5%

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

   if 1050 < t < 6.6000000000000001e174

   1. Initial program 93.7%

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

   2. Taylor expanded in t around -inf 79.7%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. associate-*r* 79.7%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(-18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - -4 \cdot a\right)} - \left(j \cdot 27\right) \cdot k \]

      2. neg-mul-1 79.7%

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

      3. cancel-sign-sub-inv 79.7%

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

      4. *-commutative 79.7%

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

      5. metadata-eval 79.7%

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

   4. Simplified 79.7%

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

   5. Taylor expanded in x around 0 52.5%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. associate-*r* 52.5%

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

   7. Simplified 52.5%

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

   if 6.6000000000000001e174 < t < 1.94999999999999989e288

   1. Initial program 81.3%

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

   3. Simplified 81.4%

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

   4. Taylor expanded in x around inf 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-*l* 78.3%

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

      3. associate-*l* 70.8%

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

   6. Simplified 70.8%

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

      1. fma-def 70.8%

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

      2. associate-*r* 78.3%

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

      3. *-commutative 78.3%

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

      4. associate-*r* 70.8%

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

   8. Applied egg-rr 70.8%

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

   9. Taylor expanded in y around inf 59.1%

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

       1. *-commutative 59.1%

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

       2. associate-*r* 63.7%

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

       3. *-commutative 63.7%

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

       4. associate-*r* 63.7%

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

       5. associate-*r* 63.7%

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

       6. *-commutative 63.7%

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

       7. associate-*r* 63.7%

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

       8. associate-*l* 63.7%

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

   11. Simplified 63.7%

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

   if 1.94999999999999989e288 < t

   1. Initial program 83.3%

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

   2. Taylor expanded in y around 0 74.3%

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

      1. distribute-lft-out 74.3%

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

      2. *-commutative 74.3%

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

      3. *-commutative 74.3%

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

   4. Simplified 74.3%

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

   5. Taylor expanded in t around inf 74.2%

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

      1. associate-*r* 74.2%

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

      2. *-commutative 74.2%

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

   7. Simplified 74.2%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+105}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -185000:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1050:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+174}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+288}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]

Alternative 19: 64.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+100} \lor \neg \left(t \leq 1.92 \cdot 10^{+31}\right):\\ \;\;\;\;\left(t \cdot 18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (<= t -4.2e+100) (not (<= t 1.92e+31)))
   (- (* (* t 18.0) (* z (* x y))) (* k (* j 27.0)))
   (- (* b c) (+ (* 27.0 (* j k)) (* 4.0 (* x i))))))

C

assert(y < z);
assert(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 ((t <= -4.2e+100) || !(t <= 1.92e+31)) {
		tmp = ((t * 18.0) * (z * (x * y))) - (k * (j * 27.0));
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 ((t <= (-4.2d+100)) .or. (.not. (t <= 1.92d+31))) then
        tmp = ((t * 18.0d0) * (z * (x * y))) - (k * (j * 27.0d0))
    else
        tmp = (b * c) - ((27.0d0 * (j * k)) + (4.0d0 * (x * i)))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 ((t <= -4.2e+100) || !(t <= 1.92e+31)) {
		tmp = ((t * 18.0) * (z * (x * y))) - (k * (j * 27.0));
	} else {
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -4.2e+100) or not (t <= 1.92e+31):
		tmp = ((t * 18.0) * (z * (x * y))) - (k * (j * 27.0))
	else:
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -4.2e+100) || !(t <= 1.92e+31))
		tmp = Float64(Float64(Float64(t * 18.0) * Float64(z * Float64(x * y))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(27.0 * Float64(j * k)) + Float64(4.0 * Float64(x * i))));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -4.2e+100) || ~((t <= 1.92e+31)))
		tmp = ((t * 18.0) * (z * (x * y))) - (k * (j * 27.0));
	else
		tmp = (b * c) - ((27.0 * (j * k)) + (4.0 * (x * i)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[t, -4.2e+100], N[Not[LessEqual[t, 1.92e+31]], $MachinePrecision]], N[(N[(N[(t * 18.0), $MachinePrecision] * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.1999999999999997e100 or 1.9199999999999999e31 < t

   1. Initial program 85.8%

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

   2. Taylor expanded in a around 0 68.1%

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

      1. sub-neg 68.1%

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

      2. +-commutative 68.1%

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

      3. associate-+l+ 68.1%

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

      4. associate-*r* 67.1%

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

      5. *-commutative 67.1%

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

      6. associate-*r* 66.3%

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

      7. associate-*r* 67.2%

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

      8. distribute-lft-neg-in 67.2%

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

      9. metadata-eval 67.2%

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

      10. associate-*r* 68.2%

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

      11. distribute-rgt-in 72.9%

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

      12. metadata-eval 72.9%

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

      13. cancel-sign-sub-inv 72.9%

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

      14. +-commutative 72.9%

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

      15. fma-def 73.8%

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

   4. Simplified 73.8%

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

   5. Taylor expanded in y around inf 62.2%

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

      1. associate-*r* 62.3%

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

      2. associate-*r* 62.3%

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

   7. Simplified 62.3%

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

   if -4.1999999999999997e100 < t < 1.9199999999999999e31

   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 85.0%

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

   4. Taylor expanded in t around 0 79.1%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+100} \lor \neg \left(t \leq 1.92 \cdot 10^{+31}\right):\\ \;\;\;\;\left(t \cdot 18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(27 \cdot \left(j \cdot k\right) + 4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]

Alternative 20: 33.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;k \leq -2.1 \cdot 10^{+24}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.9 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.35 \cdot 10^{-233}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 4.4 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (* x (* y z))))))
   (if (<= k -2.1e+24)
     (* j (* k -27.0))
     (if (<= k 1.9e-280)
       t_1
       (if (<= k 3.35e-233)
         (* b c)
         (if (<= k 4.4e-138)
           t_1
           (if (<= k 2.9e+128) (* x (* i -4.0)) (* k (* j -27.0)))))))))

C

assert(y < z);
assert(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 * (x * (y * z)));
	double tmp;
	if (k <= -2.1e+24) {
		tmp = j * (k * -27.0);
	} else if (k <= 1.9e-280) {
		tmp = t_1;
	} else if (k <= 3.35e-233) {
		tmp = b * c;
	} else if (k <= 4.4e-138) {
		tmp = t_1;
	} else if (k <= 2.9e+128) {
		tmp = x * (i * -4.0);
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 * (x * (y * z)))
    if (k <= (-2.1d+24)) then
        tmp = j * (k * (-27.0d0))
    else if (k <= 1.9d-280) then
        tmp = t_1
    else if (k <= 3.35d-233) then
        tmp = b * c
    else if (k <= 4.4d-138) then
        tmp = t_1
    else if (k <= 2.9d+128) then
        tmp = x * (i * (-4.0d0))
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 * (x * (y * z)));
	double tmp;
	if (k <= -2.1e+24) {
		tmp = j * (k * -27.0);
	} else if (k <= 1.9e-280) {
		tmp = t_1;
	} else if (k <= 3.35e-233) {
		tmp = b * c;
	} else if (k <= 4.4e-138) {
		tmp = t_1;
	} else if (k <= 2.9e+128) {
		tmp = x * (i * -4.0);
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (x * (y * z)))
	tmp = 0
	if k <= -2.1e+24:
		tmp = j * (k * -27.0)
	elif k <= 1.9e-280:
		tmp = t_1
	elif k <= 3.35e-233:
		tmp = b * c
	elif k <= 4.4e-138:
		tmp = t_1
	elif k <= 2.9e+128:
		tmp = x * (i * -4.0)
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	tmp = 0.0
	if (k <= -2.1e+24)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (k <= 1.9e-280)
		tmp = t_1;
	elseif (k <= 3.35e-233)
		tmp = Float64(b * c);
	elseif (k <= 4.4e-138)
		tmp = t_1;
	elseif (k <= 2.9e+128)
		tmp = Float64(x * Float64(i * -4.0));
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (t * (x * (y * z)));
	tmp = 0.0;
	if (k <= -2.1e+24)
		tmp = j * (k * -27.0);
	elseif (k <= 1.9e-280)
		tmp = t_1;
	elseif (k <= 3.35e-233)
		tmp = b * c;
	elseif (k <= 4.4e-138)
		tmp = t_1;
	elseif (k <= 2.9e+128)
		tmp = x * (i * -4.0);
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.1e+24], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.9e-280], t$95$1, If[LessEqual[k, 3.35e-233], N[(b * c), $MachinePrecision], If[LessEqual[k, 4.4e-138], t$95$1, If[LessEqual[k, 2.9e+128], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -2.1000000000000001e24

   1. Initial program 87.2%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in j around inf 39.5%

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

      1. *-commutative 39.5%

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

      2. associate-*l* 39.5%

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

   6. Simplified 39.5%

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

   if -2.1000000000000001e24 < k < 1.9000000000000001e-280 or 3.35000000000000011e-233 < k < 4.3999999999999998e-138

   1. Initial program 86.3%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in x around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*l* 79.7%

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

      3. associate-*l* 78.3%

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

   6. Simplified 78.3%

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

      1. fma-def 78.3%

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

      2. associate-*r* 79.7%

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

      3. *-commutative 79.7%

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

      4. associate-*r* 78.3%

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

   8. Applied egg-rr 78.3%

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

   9. Taylor expanded in y around inf 33.3%

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

   if 1.9000000000000001e-280 < k < 3.35000000000000011e-233

   1. Initial program 88.7%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in b around inf 30.8%

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

   if 4.3999999999999998e-138 < k < 2.9e128

   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 84.6%

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

   4. Taylor expanded in i around inf 30.3%

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

      1. associate-*r* 30.3%

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

      2. *-commutative 30.3%

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

   6. Simplified 30.3%

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

   if 2.9e128 < k

   1. Initial program 87.3%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in j around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. *-commutative 50.2%

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

      3. associate-*l* 50.2%

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

   6. Simplified 50.2%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.1 \cdot 10^{+24}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.9 \cdot 10^{-280}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 3.35 \cdot 10^{-233}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 4.4 \cdot 10^{-138}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 21: 33.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;k \leq -7 \cdot 10^{+18}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 2.5 \cdot 10^{-281}:\\ \;\;\;\;t \cdot \left(18 \cdot t_1\right)\\ \mathbf{elif}\;k \leq 7.1 \cdot 10^{-230}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.85 \cdot 10^{-137}:\\ \;\;\;\;18 \cdot \left(t \cdot t_1\right)\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (* y z))))
   (if (<= k -7e+18)
     (* j (* k -27.0))
     (if (<= k 2.5e-281)
       (* t (* 18.0 t_1))
       (if (<= k 7.1e-230)
         (* b c)
         (if (<= k 1.85e-137)
           (* 18.0 (* t t_1))
           (if (<= k 3.6e+125) (* x (* i -4.0)) (* k (* j -27.0)))))))))

C

assert(y < z);
assert(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 * (y * z);
	double tmp;
	if (k <= -7e+18) {
		tmp = j * (k * -27.0);
	} else if (k <= 2.5e-281) {
		tmp = t * (18.0 * t_1);
	} else if (k <= 7.1e-230) {
		tmp = b * c;
	} else if (k <= 1.85e-137) {
		tmp = 18.0 * (t * t_1);
	} else if (k <= 3.6e+125) {
		tmp = x * (i * -4.0);
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 * (y * z)
    if (k <= (-7d+18)) then
        tmp = j * (k * (-27.0d0))
    else if (k <= 2.5d-281) then
        tmp = t * (18.0d0 * t_1)
    else if (k <= 7.1d-230) then
        tmp = b * c
    else if (k <= 1.85d-137) then
        tmp = 18.0d0 * (t * t_1)
    else if (k <= 3.6d+125) then
        tmp = x * (i * (-4.0d0))
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 * (y * z);
	double tmp;
	if (k <= -7e+18) {
		tmp = j * (k * -27.0);
	} else if (k <= 2.5e-281) {
		tmp = t * (18.0 * t_1);
	} else if (k <= 7.1e-230) {
		tmp = b * c;
	} else if (k <= 1.85e-137) {
		tmp = 18.0 * (t * t_1);
	} else if (k <= 3.6e+125) {
		tmp = x * (i * -4.0);
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (y * z)
	tmp = 0
	if k <= -7e+18:
		tmp = j * (k * -27.0)
	elif k <= 2.5e-281:
		tmp = t * (18.0 * t_1)
	elif k <= 7.1e-230:
		tmp = b * c
	elif k <= 1.85e-137:
		tmp = 18.0 * (t * t_1)
	elif k <= 3.6e+125:
		tmp = x * (i * -4.0)
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (k <= -7e+18)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (k <= 2.5e-281)
		tmp = Float64(t * Float64(18.0 * t_1));
	elseif (k <= 7.1e-230)
		tmp = Float64(b * c);
	elseif (k <= 1.85e-137)
		tmp = Float64(18.0 * Float64(t * t_1));
	elseif (k <= 3.6e+125)
		tmp = Float64(x * Float64(i * -4.0));
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (k <= -7e+18)
		tmp = j * (k * -27.0);
	elseif (k <= 2.5e-281)
		tmp = t * (18.0 * t_1);
	elseif (k <= 7.1e-230)
		tmp = b * c;
	elseif (k <= 1.85e-137)
		tmp = 18.0 * (t * t_1);
	elseif (k <= 3.6e+125)
		tmp = x * (i * -4.0);
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -7e+18], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.5e-281], N[(t * N[(18.0 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7.1e-230], N[(b * c), $MachinePrecision], If[LessEqual[k, 1.85e-137], N[(18.0 * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.6e+125], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -7e18

   1. Initial program 87.2%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in j around inf 39.5%

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

      1. *-commutative 39.5%

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

      2. associate-*l* 39.5%

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

   6. Simplified 39.5%

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

   if -7e18 < k < 2.4999999999999999e-281

   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 87.8%

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

   4. Taylor expanded in x around inf 77.0%

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

      1. *-commutative 77.0%

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

      2. associate-*l* 78.5%

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

      3. associate-*l* 78.2%

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

   6. Simplified 78.2%

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

      1. fma-def 78.2%

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

      2. associate-*r* 78.5%

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

      3. *-commutative 78.5%

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

      4. associate-*r* 78.2%

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

   8. Applied egg-rr 78.2%

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

   9. Taylor expanded in y around inf 32.6%

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

       1. *-commutative 32.6%

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

       2. associate-*r* 31.3%

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

       3. associate-*l* 31.3%

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

       4. associate-*r* 32.6%

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

   11. Simplified 32.6%

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

   if 2.4999999999999999e-281 < k < 7.10000000000000018e-230

   1. Initial program 89.3%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in b around inf 29.3%

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

   if 7.10000000000000018e-230 < k < 1.85e-137

   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%

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

   4. Taylor expanded in x around inf 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-*l* 85.0%

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

      3. associate-*l* 77.2%

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

   6. Simplified 77.2%

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

      1. fma-def 77.2%

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

      2. associate-*r* 85.0%

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

      3. *-commutative 85.0%

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

      4. associate-*r* 77.2%

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

   8. Applied egg-rr 77.2%

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

   9. Taylor expanded in y around inf 32.1%

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

   if 1.85e-137 < k < 3.6000000000000003e125

   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 84.6%

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

   4. Taylor expanded in i around inf 30.3%

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

      1. associate-*r* 30.3%

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

      2. *-commutative 30.3%

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

   6. Simplified 30.3%

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

   if 3.6000000000000003e125 < k

   1. Initial program 87.3%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in j around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. *-commutative 50.2%

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

      3. associate-*l* 50.2%

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

   6. Simplified 50.2%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -7 \cdot 10^{+18}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 2.5 \cdot 10^{-281}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 7.1 \cdot 10^{-230}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.85 \cdot 10^{-137}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 22: 32.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -3.65 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{-282}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \mathbf{elif}\;k \leq 6.9 \cdot 10^{-227}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{-139}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 4 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 -3.65e+25)
   (* j (* k -27.0))
   (if (<= k 6.2e-282)
     (* x (* (* y z) (* t 18.0)))
     (if (<= k 6.9e-227)
       (* b c)
       (if (<= k 8.2e-139)
         (* 18.0 (* t (* x (* y z))))
         (if (<= k 4e+126) (* x (* i -4.0)) (* k (* j -27.0))))))))

C

assert(y < z);
assert(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 <= -3.65e+25) {
		tmp = j * (k * -27.0);
	} else if (k <= 6.2e-282) {
		tmp = x * ((y * z) * (t * 18.0));
	} else if (k <= 6.9e-227) {
		tmp = b * c;
	} else if (k <= 8.2e-139) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (k <= 4e+126) {
		tmp = x * (i * -4.0);
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 <= (-3.65d+25)) then
        tmp = j * (k * (-27.0d0))
    else if (k <= 6.2d-282) then
        tmp = x * ((y * z) * (t * 18.0d0))
    else if (k <= 6.9d-227) then
        tmp = b * c
    else if (k <= 8.2d-139) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (k <= 4d+126) then
        tmp = x * (i * (-4.0d0))
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 <= -3.65e+25) {
		tmp = j * (k * -27.0);
	} else if (k <= 6.2e-282) {
		tmp = x * ((y * z) * (t * 18.0));
	} else if (k <= 6.9e-227) {
		tmp = b * c;
	} else if (k <= 8.2e-139) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (k <= 4e+126) {
		tmp = x * (i * -4.0);
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -3.65e+25:
		tmp = j * (k * -27.0)
	elif k <= 6.2e-282:
		tmp = x * ((y * z) * (t * 18.0))
	elif k <= 6.9e-227:
		tmp = b * c
	elif k <= 8.2e-139:
		tmp = 18.0 * (t * (x * (y * z)))
	elif k <= 4e+126:
		tmp = x * (i * -4.0)
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -3.65e+25)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (k <= 6.2e-282)
		tmp = Float64(x * Float64(Float64(y * z) * Float64(t * 18.0)));
	elseif (k <= 6.9e-227)
		tmp = Float64(b * c);
	elseif (k <= 8.2e-139)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (k <= 4e+126)
		tmp = Float64(x * Float64(i * -4.0));
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -3.65e+25)
		tmp = j * (k * -27.0);
	elseif (k <= 6.2e-282)
		tmp = x * ((y * z) * (t * 18.0));
	elseif (k <= 6.9e-227)
		tmp = b * c;
	elseif (k <= 8.2e-139)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (k <= 4e+126)
		tmp = x * (i * -4.0);
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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, -3.65e+25], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6.2e-282], N[(x * N[(N[(y * z), $MachinePrecision] * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 6.9e-227], N[(b * c), $MachinePrecision], If[LessEqual[k, 8.2e-139], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4e+126], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -3.6499999999999998e25

   1. Initial program 86.8%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in j around inf 39.1%

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

      1. *-commutative 39.1%

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

      2. associate-*l* 39.1%

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

   6. Simplified 39.1%

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

   if -3.6499999999999998e25 < k < 6.20000000000000027e-282

   1. Initial program 85.4%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in x around inf 76.3%

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

      1. *-commutative 76.3%

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

      2. associate-*l* 77.7%

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

      3. associate-*l* 78.8%

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

   6. Simplified 78.8%

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

      1. fma-def 78.8%

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

      2. associate-*r* 77.7%

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

      3. *-commutative 77.7%

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

      4. associate-*r* 78.8%

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

   8. Applied egg-rr 78.8%

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

   9. Taylor expanded in y around inf 31.8%

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

       1. *-commutative 31.8%

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

       2. associate-*r* 32.2%

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

       3. *-commutative 32.2%

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

       4. associate-*r* 32.0%

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

       5. associate-*r* 32.0%

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

       6. *-commutative 32.0%

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

       7. associate-*r* 32.2%

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

       8. associate-*l* 32.2%

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

   11. Simplified 32.2%

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

   if 6.20000000000000027e-282 < k < 6.89999999999999989e-227

   1. Initial program 89.3%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in b around inf 29.3%

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

   if 6.89999999999999989e-227 < k < 8.20000000000000028e-139

   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%

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

   4. Taylor expanded in x around inf 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-*l* 85.0%

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

      3. associate-*l* 77.2%

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

   6. Simplified 77.2%

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

      1. fma-def 77.2%

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

      2. associate-*r* 85.0%

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

      3. *-commutative 85.0%

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

      4. associate-*r* 77.2%

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

   8. Applied egg-rr 77.2%

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

   9. Taylor expanded in y around inf 32.1%

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

   if 8.20000000000000028e-139 < k < 3.9999999999999997e126

   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 84.6%

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

   4. Taylor expanded in i around inf 30.3%

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

      1. associate-*r* 30.3%

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

      2. *-commutative 30.3%

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

   6. Simplified 30.3%

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

   if 3.9999999999999997e126 < k

   1. Initial program 87.3%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in j around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. *-commutative 50.2%

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

      3. associate-*l* 50.2%

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

   6. Simplified 50.2%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.65 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{-282}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \mathbf{elif}\;k \leq 6.9 \cdot 10^{-227}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{-139}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;k \leq 4 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 23: 45.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_2 := x \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) (* 27.0 (* j k)))) (t_2 (* x (* (* y z) (* t 18.0)))))
   (if (<= x -3.7e+65)
     t_2
     (if (<= x 5.2e-64)
       t_1
       (if (<= x 9.6e+65) t_2 (if (<= x 3.9e+102) t_1 (* x (* i -4.0))))))))

C

assert(y < z);
assert(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) - (27.0 * (j * k));
	double t_2 = x * ((y * z) * (t * 18.0));
	double tmp;
	if (x <= -3.7e+65) {
		tmp = t_2;
	} else if (x <= 5.2e-64) {
		tmp = t_1;
	} else if (x <= 9.6e+65) {
		tmp = t_2;
	} else if (x <= 3.9e+102) {
		tmp = t_1;
	} else {
		tmp = x * (i * -4.0);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) - (27.0d0 * (j * k))
    t_2 = x * ((y * z) * (t * 18.0d0))
    if (x <= (-3.7d+65)) then
        tmp = t_2
    else if (x <= 5.2d-64) then
        tmp = t_1
    else if (x <= 9.6d+65) then
        tmp = t_2
    else if (x <= 3.9d+102) then
        tmp = t_1
    else
        tmp = x * (i * (-4.0d0))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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) - (27.0 * (j * k));
	double t_2 = x * ((y * z) * (t * 18.0));
	double tmp;
	if (x <= -3.7e+65) {
		tmp = t_2;
	} else if (x <= 5.2e-64) {
		tmp = t_1;
	} else if (x <= 9.6e+65) {
		tmp = t_2;
	} else if (x <= 3.9e+102) {
		tmp = t_1;
	} else {
		tmp = x * (i * -4.0);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (27.0 * (j * k))
	t_2 = x * ((y * z) * (t * 18.0))
	tmp = 0
	if x <= -3.7e+65:
		tmp = t_2
	elif x <= 5.2e-64:
		tmp = t_1
	elif x <= 9.6e+65:
		tmp = t_2
	elif x <= 3.9e+102:
		tmp = t_1
	else:
		tmp = x * (i * -4.0)
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_2 = Float64(x * Float64(Float64(y * z) * Float64(t * 18.0)))
	tmp = 0.0
	if (x <= -3.7e+65)
		tmp = t_2;
	elseif (x <= 5.2e-64)
		tmp = t_1;
	elseif (x <= 9.6e+65)
		tmp = t_2;
	elseif (x <= 3.9e+102)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(i * -4.0));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (27.0 * (j * k));
	t_2 = x * ((y * z) * (t * 18.0));
	tmp = 0.0;
	if (x <= -3.7e+65)
		tmp = t_2;
	elseif (x <= 5.2e-64)
		tmp = t_1;
	elseif (x <= 9.6e+65)
		tmp = t_2;
	elseif (x <= 3.9e+102)
		tmp = t_1;
	else
		tmp = x * (i * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.7e+65], t$95$2, If[LessEqual[x, 5.2e-64], t$95$1, If[LessEqual[x, 9.6e+65], t$95$2, If[LessEqual[x, 3.9e+102], t$95$1, N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.69999999999999995e65 or 5.2e-64 < x < 9.6000000000000007e65

   1. Initial program 76.2%

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

   3. Simplified 78.9%

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

   4. Taylor expanded in x around inf 68.0%

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

      1. *-commutative 68.0%

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

      2. associate-*l* 73.6%

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

      3. associate-*l* 76.2%

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

   6. Simplified 76.2%

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

      1. fma-def 76.2%

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

      2. associate-*r* 73.6%

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

      3. *-commutative 73.6%

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

      4. associate-*r* 76.2%

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

   8. Applied egg-rr 76.2%

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

   9. Taylor expanded in y around inf 50.2%

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

       1. *-commutative 50.2%

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

       2. associate-*r* 51.5%

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

       3. *-commutative 51.5%

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

       4. associate-*r* 54.1%

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

       5. associate-*r* 54.1%

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

       6. *-commutative 54.1%

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

       7. associate-*r* 51.5%

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

       8. associate-*l* 51.6%

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

   11. Simplified 51.6%

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

   if -3.69999999999999995e65 < x < 5.2e-64 or 9.6000000000000007e65 < x < 3.8999999999999998e102

   1. Initial program 92.0%

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

   2. Taylor expanded in a around 0 73.6%

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

      1. sub-neg 73.6%

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

      2. +-commutative 73.6%

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

      3. associate-+l+ 73.6%

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

      4. associate-*r* 72.9%

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

      5. *-commutative 72.9%

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

      6. associate-*r* 73.0%

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

      7. associate-*r* 73.7%

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

      8. distribute-lft-neg-in 73.7%

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

      9. metadata-eval 73.7%

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

      10. associate-*r* 74.4%

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

      11. distribute-rgt-in 74.4%

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

      12. metadata-eval 74.4%

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

      13. cancel-sign-sub-inv 74.4%

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

      14. +-commutative 74.4%

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

      15. fma-def 75.1%

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

   4. Simplified 75.1%

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

   5. Taylor expanded in x around 0 58.0%

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

   if 3.8999999999999998e102 < x

   1. Initial program 79.1%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in i around inf 47.6%

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

      1. associate-*r* 47.6%

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

      2. *-commutative 47.6%

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

   6. Simplified 47.6%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-64}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \]

Alternative 24: 45.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_2 := x \cdot \left(z \cdot \left(t \cdot \left(-18 \cdot \left(-y\right)\right)\right)\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) (* 27.0 (* j k))))
        (t_2 (* x (* z (* t (* -18.0 (- y)))))))
   (if (<= x -1.2e+72)
     t_2
     (if (<= x 1.05e-63)
       t_1
       (if (<= x 1.35e+66) t_2 (if (<= x 1.15e+103) t_1 (* x (* i -4.0))))))))

C

assert(y < z);
assert(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) - (27.0 * (j * k));
	double t_2 = x * (z * (t * (-18.0 * -y)));
	double tmp;
	if (x <= -1.2e+72) {
		tmp = t_2;
	} else if (x <= 1.05e-63) {
		tmp = t_1;
	} else if (x <= 1.35e+66) {
		tmp = t_2;
	} else if (x <= 1.15e+103) {
		tmp = t_1;
	} else {
		tmp = x * (i * -4.0);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) - (27.0d0 * (j * k))
    t_2 = x * (z * (t * ((-18.0d0) * -y)))
    if (x <= (-1.2d+72)) then
        tmp = t_2
    else if (x <= 1.05d-63) then
        tmp = t_1
    else if (x <= 1.35d+66) then
        tmp = t_2
    else if (x <= 1.15d+103) then
        tmp = t_1
    else
        tmp = x * (i * (-4.0d0))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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) - (27.0 * (j * k));
	double t_2 = x * (z * (t * (-18.0 * -y)));
	double tmp;
	if (x <= -1.2e+72) {
		tmp = t_2;
	} else if (x <= 1.05e-63) {
		tmp = t_1;
	} else if (x <= 1.35e+66) {
		tmp = t_2;
	} else if (x <= 1.15e+103) {
		tmp = t_1;
	} else {
		tmp = x * (i * -4.0);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (27.0 * (j * k))
	t_2 = x * (z * (t * (-18.0 * -y)))
	tmp = 0
	if x <= -1.2e+72:
		tmp = t_2
	elif x <= 1.05e-63:
		tmp = t_1
	elif x <= 1.35e+66:
		tmp = t_2
	elif x <= 1.15e+103:
		tmp = t_1
	else:
		tmp = x * (i * -4.0)
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_2 = Float64(x * Float64(z * Float64(t * Float64(-18.0 * Float64(-y)))))
	tmp = 0.0
	if (x <= -1.2e+72)
		tmp = t_2;
	elseif (x <= 1.05e-63)
		tmp = t_1;
	elseif (x <= 1.35e+66)
		tmp = t_2;
	elseif (x <= 1.15e+103)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(i * -4.0));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (27.0 * (j * k));
	t_2 = x * (z * (t * (-18.0 * -y)));
	tmp = 0.0;
	if (x <= -1.2e+72)
		tmp = t_2;
	elseif (x <= 1.05e-63)
		tmp = t_1;
	elseif (x <= 1.35e+66)
		tmp = t_2;
	elseif (x <= 1.15e+103)
		tmp = t_1;
	else
		tmp = x * (i * -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z * N[(t * N[(-18.0 * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+72], t$95$2, If[LessEqual[x, 1.05e-63], t$95$1, If[LessEqual[x, 1.35e+66], t$95$2, If[LessEqual[x, 1.15e+103], t$95$1, N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.20000000000000005e72 or 1.05e-63 < x < 1.35e66

   1. Initial program 76.2%

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

   3. Simplified 78.9%

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

   4. Taylor expanded in x around inf 68.0%

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

      1. *-commutative 68.0%

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

      2. associate-*l* 73.6%

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

      3. associate-*l* 76.2%

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

   6. Simplified 76.2%

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

   7. Taylor expanded in x around -inf 69.2%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 69.2%

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

      2. cancel-sign-sub-inv 69.2%

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

      3. associate-*r* 73.2%

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

      4. metadata-eval 73.2%

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

      5. *-commutative 73.2%

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

   9. Simplified 73.2%

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

   10. Taylor expanded in t around inf 50.2%

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

       1. *-commutative 50.2%

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

       2. associate-*r* 48.8%

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

       3. associate-*l* 48.8%

          \[\leadsto -\color{blue}{\left(t \cdot x\right) \cdot \left(\left(y \cdot z\right) \cdot -18\right)} \]

       4. associate-*r* 50.2%

          \[\leadsto -\color{blue}{t \cdot \left(x \cdot \left(\left(y \cdot z\right) \cdot -18\right)\right)} \]

       5. *-commutative 50.2%

          \[\leadsto -t \cdot \color{blue}{\left(\left(\left(y \cdot z\right) \cdot -18\right) \cdot x\right)} \]

       6. associate-*r* 51.6%

          \[\leadsto -\color{blue}{\left(t \cdot \left(\left(y \cdot z\right) \cdot -18\right)\right) \cdot x} \]

       7. associate-*l* 51.5%

          \[\leadsto -\color{blue}{\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot -18\right)} \cdot x \]

       8. associate-*r* 52.7%

          \[\leadsto -\left(\color{blue}{\left(\left(t \cdot y\right) \cdot z\right)} \cdot -18\right) \cdot x \]

       9. *-commutative 52.7%

          \[\leadsto -\left(\left(\color{blue}{\left(y \cdot t\right)} \cdot z\right) \cdot -18\right) \cdot x \]

       10. *-commutative 52.7%

           \[\leadsto -\left(\color{blue}{\left(z \cdot \left(y \cdot t\right)\right)} \cdot -18\right) \cdot x \]

       11. *-commutative 52.7%

           \[\leadsto -\color{blue}{x \cdot \left(\left(z \cdot \left(y \cdot t\right)\right) \cdot -18\right)} \]

       12. associate-*l* 52.7%

           \[\leadsto -x \cdot \color{blue}{\left(z \cdot \left(\left(y \cdot t\right) \cdot -18\right)\right)} \]

       13. *-commutative 52.7%

           \[\leadsto -x \cdot \left(z \cdot \left(\color{blue}{\left(t \cdot y\right)} \cdot -18\right)\right) \]

       14. associate-*l* 52.7%

           \[\leadsto -x \cdot \left(z \cdot \color{blue}{\left(t \cdot \left(y \cdot -18\right)\right)}\right) \]

   12. Simplified 52.7%

       \[\leadsto -\color{blue}{x \cdot \left(z \cdot \left(t \cdot \left(y \cdot -18\right)\right)\right)} \]

   if -1.20000000000000005e72 < x < 1.05e-63 or 1.35e66 < x < 1.15000000000000004e103

   1. Initial program 92.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in a around 0 73.6%

      \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. sub-neg 73.6%

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(-4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      2. +-commutative 73.6%

         \[\leadsto \left(\color{blue}{\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} + \left(-4 \cdot \left(i \cdot x\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate-+l+ 73.6%

         \[\leadsto \color{blue}{\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + \left(-4 \cdot \left(i \cdot x\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      4. associate-*r* 72.9%

         \[\leadsto \left(b \cdot c + \left(\color{blue}{\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)} + \left(-4 \cdot \left(i \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. *-commutative 72.9%

         \[\leadsto \left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} + \left(-4 \cdot \left(i \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. associate-*r* 73.0%

         \[\leadsto \left(b \cdot c + \left(\color{blue}{\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x} + \left(-4 \cdot \left(i \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      7. associate-*r* 73.7%

         \[\leadsto \left(b \cdot c + \left(\color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x + \left(-4 \cdot \left(i \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. distribute-lft-neg-in 73.7%

         \[\leadsto \left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \color{blue}{\left(-4\right) \cdot \left(i \cdot x\right)}\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. metadata-eval 73.7%

         \[\leadsto \left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. associate-*r* 74.4%

          \[\leadsto \left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \color{blue}{\left(-4 \cdot i\right) \cdot x}\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. distribute-rgt-in 74.4%

          \[\leadsto \left(b \cdot c + \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      12. metadata-eval 74.4%

          \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{\left(-4\right)} \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      13. cancel-sign-sub-inv 74.4%

          \[\leadsto \left(b \cdot c + x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      14. +-commutative 74.4%

          \[\leadsto \color{blue}{\left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) + b \cdot c\right)} - \left(j \cdot 27\right) \cdot k \]

      15. fma-def 75.1%

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i, b \cdot c\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Simplified 75.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(18, \left(y \cdot z\right) \cdot t, -4 \cdot i\right), b \cdot c\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in x around 0 58.0%

      \[\leadsto \color{blue}{b \cdot c - 27 \cdot \left(j \cdot k\right)} \]

   if 1.15000000000000004e103 < x

   1. Initial program 79.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in i around inf 47.6%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 47.6%

         \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]

      2. *-commutative 47.6%

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]

   6. Simplified 47.6%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(z \cdot \left(t \cdot \left(-18 \cdot \left(-y\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-63}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \left(z \cdot \left(t \cdot \left(-18 \cdot \left(-y\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+103}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \end{array} \]

Alternative 25: 46.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+102}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -95000000:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (<= t -1.05e+102)
   (* 18.0 (* t (* x (* y z))))
   (if (<= t -95000000.0)
     (- (* b c) (* 27.0 (* j k)))
     (if (<= t 6.2e+33)
       (- (* x (* i -4.0)) (* k (* j 27.0)))
       (* x (* (* y z) (* t 18.0)))))))

C

assert(y < z);
assert(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 (t <= -1.05e+102) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t <= -95000000.0) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 6.2e+33) {
		tmp = (x * (i * -4.0)) - (k * (j * 27.0));
	} else {
		tmp = x * ((y * z) * (t * 18.0));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (t <= (-1.05d+102)) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (t <= (-95000000.0d0)) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (t <= 6.2d+33) then
        tmp = (x * (i * (-4.0d0))) - (k * (j * 27.0d0))
    else
        tmp = x * ((y * z) * (t * 18.0d0))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 (t <= -1.05e+102) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (t <= -95000000.0) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 6.2e+33) {
		tmp = (x * (i * -4.0)) - (k * (j * 27.0));
	} else {
		tmp = x * ((y * z) * (t * 18.0));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -1.05e+102:
		tmp = 18.0 * (t * (x * (y * z)))
	elif t <= -95000000.0:
		tmp = (b * c) - (27.0 * (j * k))
	elif t <= 6.2e+33:
		tmp = (x * (i * -4.0)) - (k * (j * 27.0))
	else:
		tmp = x * ((y * z) * (t * 18.0))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (t <= -1.05e+102)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (t <= -95000000.0)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 6.2e+33)
		tmp = Float64(Float64(x * Float64(i * -4.0)) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(x * Float64(Float64(y * z) * Float64(t * 18.0)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (t <= -1.05e+102)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (t <= -95000000.0)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (t <= 6.2e+33)
		tmp = (x * (i * -4.0)) - (k * (j * 27.0));
	else
		tmp = x * ((y * z) * (t * 18.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[t, -1.05e+102], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -95000000.0], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+33], N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.05000000000000001e102

   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 91.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 73.1%

      \[\leadsto \left(\color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 73.1%

         \[\leadsto \left(18 \cdot \color{blue}{\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. associate-*l* 71.1%

         \[\leadsto \left(18 \cdot \color{blue}{\left(x \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 64.7%

         \[\leadsto \left(18 \cdot \left(x \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Simplified 64.7%

      \[\leadsto \left(\color{blue}{18 \cdot \left(x \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. fma-def 64.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(18, x \cdot \left(y \cdot \left(z \cdot t\right)\right), b \cdot c\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. associate-*r* 71.1%

         \[\leadsto \mathsf{fma}\left(18, x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}, b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 71.1%

         \[\leadsto \mathsf{fma}\left(18, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right) \cdot x}, b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*r* 64.8%

         \[\leadsto \mathsf{fma}\left(18, \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)} \cdot x, b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Applied egg-rr 64.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(18, \left(y \cdot \left(z \cdot t\right)\right) \cdot x, b \cdot c\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in y around inf 59.4%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

   if -1.05000000000000001e102 < t < -9.5e7

   1. Initial program 87.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in a around 0 87.7%

      \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. sub-neg 87.7%

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(-4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      2. +-commutative 87.7%

         \[\leadsto \left(\color{blue}{\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} + \left(-4 \cdot \left(i \cdot x\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate-+l+ 87.7%

         \[\leadsto \color{blue}{\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + \left(-4 \cdot \left(i \cdot x\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      4. associate-*r* 87.7%

         \[\leadsto \left(b \cdot c + \left(\color{blue}{\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)} + \left(-4 \cdot \left(i \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. *-commutative 87.7%

         \[\leadsto \left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} + \left(-4 \cdot \left(i \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. associate-*r* 87.7%

         \[\leadsto \left(b \cdot c + \left(\color{blue}{\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x} + \left(-4 \cdot \left(i \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      7. associate-*r* 87.7%

         \[\leadsto \left(b \cdot c + \left(\color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x + \left(-4 \cdot \left(i \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. distribute-lft-neg-in 87.7%

         \[\leadsto \left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \color{blue}{\left(-4\right) \cdot \left(i \cdot x\right)}\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. metadata-eval 87.7%

         \[\leadsto \left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. associate-*r* 87.7%

          \[\leadsto \left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \color{blue}{\left(-4 \cdot i\right) \cdot x}\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. distribute-rgt-in 87.7%

          \[\leadsto \left(b \cdot c + \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      12. metadata-eval 87.7%

          \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{\left(-4\right)} \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      13. cancel-sign-sub-inv 87.7%

          \[\leadsto \left(b \cdot c + x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      14. +-commutative 87.7%

          \[\leadsto \color{blue}{\left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) + b \cdot c\right)} - \left(j \cdot 27\right) \cdot k \]

      15. fma-def 87.7%

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i, b \cdot c\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Simplified 87.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(18, \left(y \cdot z\right) \cdot t, -4 \cdot i\right), b \cdot c\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in x around 0 69.5%

      \[\leadsto \color{blue}{b \cdot c - 27 \cdot \left(j \cdot k\right)} \]

   if -9.5e7 < t < 6.2e33

   1. Initial program 84.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in a around 0 76.1%

      \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]
   3. Step-by-step derivation

      1. sub-neg 76.1%

         \[\leadsto \color{blue}{\left(\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + \left(-4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      2. +-commutative 76.1%

         \[\leadsto \left(\color{blue}{\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} + \left(-4 \cdot \left(i \cdot x\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      3. associate-+l+ 76.1%

         \[\leadsto \color{blue}{\left(b \cdot c + \left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + \left(-4 \cdot \left(i \cdot x\right)\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

      4. associate-*r* 76.1%

         \[\leadsto \left(b \cdot c + \left(\color{blue}{\left(18 \cdot t\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)} + \left(-4 \cdot \left(i \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      5. *-commutative 76.1%

         \[\leadsto \left(b \cdot c + \left(\left(18 \cdot t\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} + \left(-4 \cdot \left(i \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      6. associate-*r* 82.6%

         \[\leadsto \left(b \cdot c + \left(\color{blue}{\left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right)\right) \cdot x} + \left(-4 \cdot \left(i \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      7. associate-*r* 82.6%

         \[\leadsto \left(b \cdot c + \left(\color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} \cdot x + \left(-4 \cdot \left(i \cdot x\right)\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      8. distribute-lft-neg-in 82.6%

         \[\leadsto \left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \color{blue}{\left(-4\right) \cdot \left(i \cdot x\right)}\right)\right) - \left(j \cdot 27\right) \cdot k \]

      9. metadata-eval 82.6%

         \[\leadsto \left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \color{blue}{-4} \cdot \left(i \cdot x\right)\right)\right) - \left(j \cdot 27\right) \cdot k \]

      10. associate-*r* 82.6%

          \[\leadsto \left(b \cdot c + \left(\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right) \cdot x + \color{blue}{\left(-4 \cdot i\right) \cdot x}\right)\right) - \left(j \cdot 27\right) \cdot k \]

      11. distribute-rgt-in 82.6%

          \[\leadsto \left(b \cdot c + \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + -4 \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      12. metadata-eval 82.6%

          \[\leadsto \left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{\left(-4\right)} \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k \]

      13. cancel-sign-sub-inv 82.6%

          \[\leadsto \left(b \cdot c + x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)}\right) - \left(j \cdot 27\right) \cdot k \]

      14. +-commutative 82.6%

          \[\leadsto \color{blue}{\left(x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) + b \cdot c\right)} - \left(j \cdot 27\right) \cdot k \]

      15. fma-def 82.6%

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i, b \cdot c\right)} - \left(j \cdot 27\right) \cdot k \]

   4. Simplified 82.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(18, \left(y \cdot z\right) \cdot t, -4 \cdot i\right), b \cdot c\right)} - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in i around inf 60.4%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} - \left(j \cdot 27\right) \cdot k \]
   6. Step-by-step derivation

      1. associate-*r* 60.4%

         \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative 60.4%

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

   7. Simplified 60.4%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} - \left(j \cdot 27\right) \cdot k \]

   if 6.2e33 < t

   1. Initial program 86.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 65.9%

      \[\leadsto \left(\color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 65.9%

         \[\leadsto \left(18 \cdot \color{blue}{\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. associate-*l* 65.9%

         \[\leadsto \left(18 \cdot \color{blue}{\left(x \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*l* 59.2%

         \[\leadsto \left(18 \cdot \left(x \cdot \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Simplified 59.2%

      \[\leadsto \left(\color{blue}{18 \cdot \left(x \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   7. Step-by-step derivation

      1. fma-def 59.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(18, x \cdot \left(y \cdot \left(z \cdot t\right)\right), b \cdot c\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. associate-*r* 65.9%

         \[\leadsto \mathsf{fma}\left(18, x \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot t\right)}, b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 65.9%

         \[\leadsto \mathsf{fma}\left(18, \color{blue}{\left(\left(y \cdot z\right) \cdot t\right) \cdot x}, b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*r* 59.2%

         \[\leadsto \mathsf{fma}\left(18, \color{blue}{\left(y \cdot \left(z \cdot t\right)\right)} \cdot x, b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   8. Applied egg-rr 59.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(18, \left(y \cdot \left(z \cdot t\right)\right) \cdot x, b \cdot c\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   9. Taylor expanded in y around inf 44.0%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 44.0%

          \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) \]

       2. associate-*r* 46.0%

          \[\leadsto 18 \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot x\right)} \]

       3. *-commutative 46.0%

          \[\leadsto 18 \cdot \left(\color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot x\right) \]

       4. associate-*r* 46.0%

          \[\leadsto 18 \cdot \left(\color{blue}{\left(y \cdot \left(z \cdot t\right)\right)} \cdot x\right) \]

       5. associate-*r* 46.0%

          \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) \cdot x} \]

       6. *-commutative 46.0%

          \[\leadsto \color{blue}{\left(\left(y \cdot \left(z \cdot t\right)\right) \cdot 18\right)} \cdot x \]

       7. associate-*r* 46.0%

          \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot t\right)} \cdot 18\right) \cdot x \]

       8. associate-*l* 46.0%

          \[\leadsto \color{blue}{\left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right)} \cdot x \]

   11. Simplified 46.0%

       \[\leadsto \color{blue}{\left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right) \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+102}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -95000000:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z\right) \cdot \left(t \cdot 18\right)\right)\\ \end{array} \]

Alternative 26: 36.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+148}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.15 \cdot 10^{+77}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (<= (* b c) -5e+148)
   (* b c)
   (if (<= (* b c) 1.15e+77) (* j (* k -27.0)) (* b c))))

C

assert(y < z);
assert(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) <= -5e+148) {
		tmp = b * c;
	} else if ((b * c) <= 1.15e+77) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) <= (-5d+148)) then
        tmp = b * c
    else if ((b * c) <= 1.15d+77) then
        tmp = j * (k * (-27.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert y < z;
assert 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) <= -5e+148) {
		tmp = b * c;
	} else if ((b * c) <= 1.15e+77) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -5e+148:
		tmp = b * c
	elif (b * c) <= 1.15e+77:
		tmp = j * (k * -27.0)
	else:
		tmp = b * c
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -5e+148)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 1.15e+77)
		tmp = Float64(j * Float64(k * -27.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -5e+148)
		tmp = b * c;
	elseif ((b * c) <= 1.15e+77)
		tmp = j * (k * -27.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[N[(b * c), $MachinePrecision], -5e+148], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.15e+77], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -5.00000000000000024e148 or 1.14999999999999997e77 < (*.f64 b c)

   1. Initial program 80.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in b around inf 55.5%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -5.00000000000000024e148 < (*.f64 b c) < 1.14999999999999997e77

   1. Initial program 87.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 27.5%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   5. Step-by-step derivation

      1. *-commutative 27.5%

         \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} \]

      2. associate-*l* 27.5%

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

   6. Simplified 27.5%

      \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+148}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 1.15 \cdot 10^{+77}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 27: 36.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.3 \cdot 10^{+146}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 9.8 \cdot 10^{+76}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 (<= (* b c) -1.3e+146)
   (* b c)
   (if (<= (* b c) 9.8e+76) (* k (* j -27.0)) (* b c))))

C

assert(y < z);
assert(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) <= -1.3e+146) {
		tmp = b * c;
	} else if ((b * c) <= 9.8e+76) {
		tmp = k * (j * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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) <= (-1.3d+146)) then
        tmp = b * c
    else if ((b * c) <= 9.8d+76) then
        tmp = k * (j * (-27.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert y < z;
assert 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) <= -1.3e+146) {
		tmp = b * c;
	} else if ((b * c) <= 9.8e+76) {
		tmp = k * (j * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1.3e+146:
		tmp = b * c
	elif (b * c) <= 9.8e+76:
		tmp = k * (j * -27.0)
	else:
		tmp = b * c
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1.3e+146)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 9.8e+76)
		tmp = Float64(k * Float64(j * -27.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1.3e+146)
		tmp = b * c;
	elseif ((b * c) <= 9.8e+76)
		tmp = k * (j * -27.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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[N[(b * c), $MachinePrecision], -1.3e+146], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 9.8e+76], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -1.30000000000000007e146 or 9.80000000000000053e76 < (*.f64 b c)

   1. Initial program 80.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in b around inf 55.5%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -1.30000000000000007e146 < (*.f64 b c) < 9.80000000000000053e76

   1. Initial program 87.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 88.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 27.5%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   5. Step-by-step derivation

      1. *-commutative 27.5%

         \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} \]

      2. *-commutative 27.5%

         \[\leadsto \color{blue}{\left(k \cdot j\right)} \cdot -27 \]

      3. associate-*l* 27.5%

         \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   6. Simplified 27.5%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.3 \cdot 10^{+146}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 9.8 \cdot 10^{+76}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 28: 32.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -2.5 \cdot 10^{-96}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{-168}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 -2.5e-96)
   (* j (* k -27.0))
   (if (<= k 1.8e-168)
     (* b c)
     (if (<= k 4.8e+125) (* x (* i -4.0)) (* k (* j -27.0))))))

C

assert(y < z);
assert(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 <= -2.5e-96) {
		tmp = j * (k * -27.0);
	} else if (k <= 1.8e-168) {
		tmp = b * c;
	} else if (k <= 4.8e+125) {
		tmp = x * (i * -4.0);
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 <= (-2.5d-96)) then
        tmp = j * (k * (-27.0d0))
    else if (k <= 1.8d-168) then
        tmp = b * c
    else if (k <= 4.8d+125) then
        tmp = x * (i * (-4.0d0))
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert y < z;
assert 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 <= -2.5e-96) {
		tmp = j * (k * -27.0);
	} else if (k <= 1.8e-168) {
		tmp = b * c;
	} else if (k <= 4.8e+125) {
		tmp = x * (i * -4.0);
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -2.5e-96:
		tmp = j * (k * -27.0)
	elif k <= 1.8e-168:
		tmp = b * c
	elif k <= 4.8e+125:
		tmp = x * (i * -4.0)
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -2.5e-96)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (k <= 1.8e-168)
		tmp = Float64(b * c);
	elseif (k <= 4.8e+125)
		tmp = Float64(x * Float64(i * -4.0));
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -2.5e-96)
		tmp = j * (k * -27.0);
	elseif (k <= 1.8e-168)
		tmp = b * c;
	elseif (k <= 4.8e+125)
		tmp = x * (i * -4.0);
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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, -2.5e-96], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.8e-168], N[(b * c), $MachinePrecision], If[LessEqual[k, 4.8e+125], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -2.49999999999999997e-96

   1. Initial program 87.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 34.6%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   5. Step-by-step derivation

      1. *-commutative 34.6%

         \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} \]

      2. associate-*l* 34.6%

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

   6. Simplified 34.6%

      \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

   if -2.49999999999999997e-96 < k < 1.7999999999999999e-168

   1. Initial program 87.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in b around inf 25.6%

      \[\leadsto \color{blue}{b \cdot c} \]

   if 1.7999999999999999e-168 < k < 4.7999999999999999e125

   1. Initial program 78.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 84.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in i around inf 31.5%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 31.5%

         \[\leadsto \color{blue}{\left(-4 \cdot i\right) \cdot x} \]

      2. *-commutative 31.5%

         \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]

   6. Simplified 31.5%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} \]

   if 4.7999999999999999e125 < k

   1. Initial program 87.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around inf 50.2%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   5. Step-by-step derivation

      1. *-commutative 50.2%

         \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} \]

      2. *-commutative 50.2%

         \[\leadsto \color{blue}{\left(k \cdot j\right)} \cdot -27 \]

      3. associate-*l* 50.2%

         \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   6. Simplified 50.2%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 33.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.5 \cdot 10^{-96}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{-168}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 29: 23.1% accurate, 10.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ b \cdot c \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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(y < z);
assert(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: y and z should be sorted in increasing order before calling this function.
NOTE: 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 y < z;
assert 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

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = b * c;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: 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 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 86.4%

   \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

4. Taylor expanded in b around inf 19.6%

   \[\leadsto \color{blue}{b \cdot c} \]

5. Final simplification 19.6%

   \[\leadsto b \cdot c \]

Developer target: 90.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023290 
(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)))