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

Percentage Accurate: 85.1% → 89.4%

Time: 50.9s

Alternatives: 24

Speedup: 0.9×

• 50.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% 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: 89.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(c, b, 18 \cdot \left(y \cdot \left(\left(x \cdot z\right) \cdot t\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), c \cdot b\right)\right)\right)\\ \end{array} \end{array} \]

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 (<= x -8e+142)
   (fma
    j
    (* k -27.0)
    (fma x (* i -4.0) (fma c b (* 18.0 (* y (* (* x z) t))))))
   (fma
    j
    (* k -27.0)
    (fma x (* i -4.0) (fma t (fma x (* 18.0 (* y z)) (* -4.0 a)) (* c b))))))

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 <= -8e+142) {
		tmp = fma(j, (k * -27.0), fma(x, (i * -4.0), fma(c, b, (18.0 * (y * ((x * z) * t))))));
	} else {
		tmp = fma(j, (k * -27.0), fma(x, (i * -4.0), fma(t, fma(x, (18.0 * (y * z)), (-4.0 * a)), (c * b))));
	}
	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 <= -8e+142)
		tmp = fma(j, Float64(k * -27.0), fma(x, Float64(i * -4.0), fma(c, b, Float64(18.0 * Float64(y * Float64(Float64(x * z) * t))))));
	else
		tmp = fma(j, Float64(k * -27.0), fma(x, Float64(i * -4.0), fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(-4.0 * a)), Float64(c * b))));
	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, -8e+142], N[(j * N[(k * -27.0), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision] + N[(c * b + N[(18.0 * N[(y * N[(N[(x * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision] + N[(t * N[(x * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.00000000000000041e142

   1. Initial program 69.6%

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

      1. sub-neg 69.6%

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

      2. +-commutative 69.6%

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

      3. associate-*l* 69.6%

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

      4. distribute-rgt-neg-in 69.6%

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

      5. fma-def 72.2%

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

      6. *-commutative 72.2%

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

      7. distribute-rgt-neg-in 72.2%

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

      8. metadata-eval 72.2%

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

      9. sub-neg 72.2%

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

      10. +-commutative 72.2%

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

      11. associate-*l* 72.2%

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

      12. distribute-rgt-neg-in 72.2%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in a around 0 79.7%

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

      1. fma-def 82.2%

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

      2. *-commutative 82.2%

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

   6. Simplified 82.2%

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

   if -8.00000000000000041e142 < x

   1. Initial program 88.4%

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

      1. sub-neg 88.4%

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

      2. +-commutative 88.4%

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

      3. associate-*l* 88.5%

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

      4. distribute-rgt-neg-in 88.5%

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

      5. fma-def 89.8%

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

      6. *-commutative 89.8%

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

      7. distribute-rgt-neg-in 89.8%

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

      8. metadata-eval 89.8%

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

      9. sub-neg 89.8%

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

      10. +-commutative 89.8%

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

      11. associate-*l* 89.8%

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

      12. distribute-rgt-neg-in 89.8%

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

   3. Simplified 91.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(c, b, 18 \cdot \left(y \cdot \left(\left(x \cdot z\right) \cdot t\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), -4 \cdot a\right), c \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 2: 91.6% accurate, 0.1× speedup

Math

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

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
         (-
          (-
           (+ (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))) (* c b))
           (* i (* x 4.0)))
          (* k (* j 27.0)))))
   (if (<= t_1 INFINITY)
     t_1
     (fma
      j
      (* k -27.0)
      (fma x (* i -4.0) (fma c b (* 18.0 (* y (* (* x z) t)))))))))

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 * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (c * b)) - (i * (x * 4.0))) - (k * (j * 27.0));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(j, (k * -27.0), fma(x, (i * -4.0), fma(c, b, (18.0 * (y * ((x * z) * t))))));
	}
	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(Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0))) + Float64(c * b)) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(j, Float64(k * -27.0), fma(x, Float64(i * -4.0), fma(c, b, Float64(18.0 * Float64(y * Float64(Float64(x * z) * t))))));
	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_] := Block[{t$95$1 = N[(N[(N[(N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(j * N[(k * -27.0), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision] + N[(c * b + N[(18.0 * N[(y * N[(N[(x * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.9%

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

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

   1. Initial program 0.0%

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

      1. sub-neg 0.0%

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

      2. +-commutative 0.0%

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

      3. associate-*l* 0.0%

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

      4. distribute-rgt-neg-in 0.0%

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

      5. fma-def 13.3%

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

      6. *-commutative 13.3%

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

      7. distribute-rgt-neg-in 13.3%

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

      8. metadata-eval 13.3%

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

      9. sub-neg 13.3%

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

      10. +-commutative 13.3%

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

      11. associate-*l* 13.3%

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

      12. distribute-rgt-neg-in 13.3%

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

   3. Simplified 46.7%

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

   4. Taylor expanded in a around 0 46.7%

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

      1. fma-def 50.0%

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

      2. *-commutative 50.0%

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

   6. Simplified 50.0%

      \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \color{blue}{\mathsf{fma}\left(c, b, 18 \cdot \left(y \cdot \left(\left(z \cdot x\right) \cdot t\right)\right)\right)}\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.4%

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

Alternative 3: 90.8% accurate, 0.5× speedup

Math

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

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
         (-
          (-
           (+ (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))) (* c b))
           (* i (* x 4.0)))
          (* k (* j 27.0)))))
   (if (<= t_1 INFINITY) t_1 (* t (- (* 18.0 (* y (* x z))) (* a 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 = ((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (c * b)) - (i * (x * 4.0))) - (k * (j * 27.0));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	}
	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 t_1 = ((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (c * b)) - (i * (x * 4.0))) - (k * (j * 27.0));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 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 = ((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (c * b)) - (i * (x * 4.0))) - (k * (j * 27.0))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 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(Float64(Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0))) + Float64(c * b)) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 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 = ((((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0))) + (c * b)) - (i * (x * 4.0))) - (k * (j * 27.0));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = t * ((18.0 * (y * (x * z))) - (a * 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[(N[(N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.9%

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

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

   1. Initial program 0.0%

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

      1. sub-neg 0.0%

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

      2. associate-+l- 0.0%

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

      3. sub-neg 0.0%

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

      4. sub-neg 0.0%

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

      5. distribute-rgt-out-- 13.3%

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

      6. associate-*l* 10.0%

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

      7. distribute-lft-neg-in 10.0%

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

      8. cancel-sign-sub 10.0%

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

      9. associate-*l* 10.0%

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

      10. associate-*l* 10.0%

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

   3. Simplified 10.0%

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

   4. Taylor expanded in t around inf 56.8%

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

4. Final simplification 92.2%

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

Alternative 4: 68.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot 27\right)\\ t_3 := \left(c \cdot b - t_1\right) - t_2\\ t_4 := c \cdot b - \left(t_1 + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+149}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-162}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+103}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

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 (* 4.0 (* x i)))
        (t_2 (* k (* j 27.0)))
        (t_3 (- (- (* c b) t_1) t_2))
        (t_4 (- (* c b) (+ t_1 (* 4.0 (* t a))))))
   (if (<= t_2 -5e+149)
     t_3
     (if (<= t_2 -1e-162)
       t_4
       (if (<= t_2 -5e-290)
         (* x (- (* 18.0 (* y (* z t))) (* i 4.0)))
         (if (<= t_2 5e+103) t_4 t_3))))))

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 = 4.0 * (x * i);
	double t_2 = k * (j * 27.0);
	double t_3 = ((c * b) - t_1) - t_2;
	double t_4 = (c * b) - (t_1 + (4.0 * (t * a)));
	double tmp;
	if (t_2 <= -5e+149) {
		tmp = t_3;
	} else if (t_2 <= -1e-162) {
		tmp = t_4;
	} else if (t_2 <= -5e-290) {
		tmp = x * ((18.0 * (y * (z * t))) - (i * 4.0));
	} else if (t_2 <= 5e+103) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = k * (j * 27.0d0)
    t_3 = ((c * b) - t_1) - t_2
    t_4 = (c * b) - (t_1 + (4.0d0 * (t * a)))
    if (t_2 <= (-5d+149)) then
        tmp = t_3
    else if (t_2 <= (-1d-162)) then
        tmp = t_4
    else if (t_2 <= (-5d-290)) then
        tmp = x * ((18.0d0 * (y * (z * t))) - (i * 4.0d0))
    else if (t_2 <= 5d+103) then
        tmp = t_4
    else
        tmp = t_3
    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 = 4.0 * (x * i);
	double t_2 = k * (j * 27.0);
	double t_3 = ((c * b) - t_1) - t_2;
	double t_4 = (c * b) - (t_1 + (4.0 * (t * a)));
	double tmp;
	if (t_2 <= -5e+149) {
		tmp = t_3;
	} else if (t_2 <= -1e-162) {
		tmp = t_4;
	} else if (t_2 <= -5e-290) {
		tmp = x * ((18.0 * (y * (z * t))) - (i * 4.0));
	} else if (t_2 <= 5e+103) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	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 = 4.0 * (x * i)
	t_2 = k * (j * 27.0)
	t_3 = ((c * b) - t_1) - t_2
	t_4 = (c * b) - (t_1 + (4.0 * (t * a)))
	tmp = 0
	if t_2 <= -5e+149:
		tmp = t_3
	elif t_2 <= -1e-162:
		tmp = t_4
	elif t_2 <= -5e-290:
		tmp = x * ((18.0 * (y * (z * t))) - (i * 4.0))
	elif t_2 <= 5e+103:
		tmp = t_4
	else:
		tmp = t_3
	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(4.0 * Float64(x * i))
	t_2 = Float64(k * Float64(j * 27.0))
	t_3 = Float64(Float64(Float64(c * b) - t_1) - t_2)
	t_4 = Float64(Float64(c * b) - Float64(t_1 + Float64(4.0 * Float64(t * a))))
	tmp = 0.0
	if (t_2 <= -5e+149)
		tmp = t_3;
	elseif (t_2 <= -1e-162)
		tmp = t_4;
	elseif (t_2 <= -5e-290)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(i * 4.0)));
	elseif (t_2 <= 5e+103)
		tmp = t_4;
	else
		tmp = t_3;
	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 = 4.0 * (x * i);
	t_2 = k * (j * 27.0);
	t_3 = ((c * b) - t_1) - t_2;
	t_4 = (c * b) - (t_1 + (4.0 * (t * a)));
	tmp = 0.0;
	if (t_2 <= -5e+149)
		tmp = t_3;
	elseif (t_2 <= -1e-162)
		tmp = t_4;
	elseif (t_2 <= -5e-290)
		tmp = x * ((18.0 * (y * (z * t))) - (i * 4.0));
	elseif (t_2 <= 5e+103)
		tmp = t_4;
	else
		tmp = t_3;
	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[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(c * b), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c * b), $MachinePrecision] - N[(t$95$1 + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+149], t$95$3, If[LessEqual[t$95$2, -1e-162], t$95$4, If[LessEqual[t$95$2, -5e-290], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+103], t$95$4, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -4.9999999999999999e149 or 5e103 < (*.f64 (*.f64 j 27) k)

   1. Initial program 81.2%

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

   2. Taylor expanded in t around 0 80.4%

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

   if -4.9999999999999999e149 < (*.f64 (*.f64 j 27) k) < -9.99999999999999954e-163 or -5.0000000000000001e-290 < (*.f64 (*.f64 j 27) k) < 5e103

   1. Initial program 88.1%

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

   2. Taylor expanded in y around 0 80.0%

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

   3. Taylor expanded in j around 0 76.3%

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

   if -9.99999999999999954e-163 < (*.f64 (*.f64 j 27) k) < -5.0000000000000001e-290

   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. Step-by-step derivation

      1. sub-neg 83.5%

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

      2. associate-+l- 83.5%

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

      3. sub-neg 83.5%

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

      4. sub-neg 83.5%

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

      5. distribute-rgt-out-- 83.5%

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

      6. associate-*l* 75.6%

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

      7. distribute-lft-neg-in 75.6%

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

      8. cancel-sign-sub 75.6%

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

      9. associate-*l* 75.6%

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

      10. associate-*l* 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in x around inf 84.2%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{+149}:\\ \;\;\;\;\left(c \cdot b - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -1 \cdot 10^{-162}:\\ \;\;\;\;c \cdot b - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;k \cdot \left(j \cdot 27\right) \leq 5 \cdot 10^{+103}:\\ \;\;\;\;c \cdot b - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot b - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 5: 87.6% accurate, 0.9× speedup

Math

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

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 (<= (* k (* j 27.0)) (- INFINITY))
   (* -27.0 (* j k))
   (-
    (+ (* t (- (* (* y z) (* x 18.0)) (* a 4.0))) (* c b))
    (+ (* x (* i 4.0)) (* j (* k 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 * (j * 27.0)) <= -((double) INFINITY)) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (c * b)) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	}
	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 ((k * (j * 27.0)) <= -Double.POSITIVE_INFINITY) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (c * b)) - ((x * (i * 4.0)) + (j * (k * 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 * (j * 27.0)) <= -math.inf:
		tmp = -27.0 * (j * k)
	else:
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (c * b)) - ((x * (i * 4.0)) + (j * (k * 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 (Float64(k * Float64(j * 27.0)) <= Float64(-Inf))
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(Float64(Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0))) + Float64(c * b)) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 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 * (j * 27.0)) <= -Inf)
		tmp = -27.0 * (j * k);
	else
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (c * b)) - ((x * (i * 4.0)) + (j * (k * 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[N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision], (-Infinity)], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j 27) k) < -inf.0

   1. Initial program 44.4%

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

      1. sub-neg 44.4%

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

      2. +-commutative 44.4%

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

      3. associate-*l* 44.4%

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

      4. distribute-rgt-neg-in 44.4%

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

      5. fma-def 61.1%

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

      6. *-commutative 61.1%

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

      7. distribute-rgt-neg-in 61.1%

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

      8. metadata-eval 61.1%

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

      9. sub-neg 61.1%

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

      10. +-commutative 61.1%

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

      11. associate-*l* 61.1%

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

      12. distribute-rgt-neg-in 61.1%

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

   3. Simplified 61.1%

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

   4. Taylor expanded in j around inf 72.2%

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

   if -inf.0 < (*.f64 (*.f64 j 27) k)

   1. Initial program 88.7%

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

      1. sub-neg 88.7%

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

      2. associate-+l- 88.7%

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

      3. sub-neg 88.7%

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

      4. sub-neg 88.7%

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

      5. distribute-rgt-out-- 90.4%

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

      6. associate-*l* 88.7%

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

      7. distribute-lft-neg-in 88.7%

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

      8. cancel-sign-sub 88.7%

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

      9. associate-*l* 88.7%

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

      10. associate-*l* 88.7%

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

   3. Simplified 88.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.6%

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

Alternative 6: 59.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - i \cdot 4\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ t_3 := t_2 + a \cdot \left(-4 \cdot t\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+48}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-292}:\\ \;\;\;\;c \cdot b + t_2\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-270}:\\ \;\;\;\;c \cdot b + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-103}:\\ \;\;\;\;c \cdot b - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-42} \lor \neg \left(x \leq 8200000000000\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

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 (* y (* z t))) (* i 4.0))))
        (t_2 (* k (* j -27.0)))
        (t_3 (+ t_2 (* a (* -4.0 t)))))
   (if (<= x -1.2e+116)
     t_1
     (if (<= x -8e+48)
       t_3
       (if (<= x -2.7e+14)
         t_1
         (if (<= x 6e-292)
           (+ (* c b) t_2)
           (if (<= x 6e-270)
             (+ (* c b) (* -4.0 (* t a)))
             (if (<= x 7.5e-103)
               (- (* c b) (* 27.0 (* j k)))
               (if (or (<= x 2.2e-42) (not (<= x 8200000000000.0)))
                 t_1
                 t_3)))))))))

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 * (y * (z * t))) - (i * 4.0));
	double t_2 = k * (j * -27.0);
	double t_3 = t_2 + (a * (-4.0 * t));
	double tmp;
	if (x <= -1.2e+116) {
		tmp = t_1;
	} else if (x <= -8e+48) {
		tmp = t_3;
	} else if (x <= -2.7e+14) {
		tmp = t_1;
	} else if (x <= 6e-292) {
		tmp = (c * b) + t_2;
	} else if (x <= 6e-270) {
		tmp = (c * b) + (-4.0 * (t * a));
	} else if (x <= 7.5e-103) {
		tmp = (c * b) - (27.0 * (j * k));
	} else if ((x <= 2.2e-42) || !(x <= 8200000000000.0)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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 * (y * (z * t))) - (i * 4.0d0))
    t_2 = k * (j * (-27.0d0))
    t_3 = t_2 + (a * ((-4.0d0) * t))
    if (x <= (-1.2d+116)) then
        tmp = t_1
    else if (x <= (-8d+48)) then
        tmp = t_3
    else if (x <= (-2.7d+14)) then
        tmp = t_1
    else if (x <= 6d-292) then
        tmp = (c * b) + t_2
    else if (x <= 6d-270) then
        tmp = (c * b) + ((-4.0d0) * (t * a))
    else if (x <= 7.5d-103) then
        tmp = (c * b) - (27.0d0 * (j * k))
    else if ((x <= 2.2d-42) .or. (.not. (x <= 8200000000000.0d0))) then
        tmp = t_1
    else
        tmp = t_3
    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 * (y * (z * t))) - (i * 4.0));
	double t_2 = k * (j * -27.0);
	double t_3 = t_2 + (a * (-4.0 * t));
	double tmp;
	if (x <= -1.2e+116) {
		tmp = t_1;
	} else if (x <= -8e+48) {
		tmp = t_3;
	} else if (x <= -2.7e+14) {
		tmp = t_1;
	} else if (x <= 6e-292) {
		tmp = (c * b) + t_2;
	} else if (x <= 6e-270) {
		tmp = (c * b) + (-4.0 * (t * a));
	} else if (x <= 7.5e-103) {
		tmp = (c * b) - (27.0 * (j * k));
	} else if ((x <= 2.2e-42) || !(x <= 8200000000000.0)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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 * (y * (z * t))) - (i * 4.0))
	t_2 = k * (j * -27.0)
	t_3 = t_2 + (a * (-4.0 * t))
	tmp = 0
	if x <= -1.2e+116:
		tmp = t_1
	elif x <= -8e+48:
		tmp = t_3
	elif x <= -2.7e+14:
		tmp = t_1
	elif x <= 6e-292:
		tmp = (c * b) + t_2
	elif x <= 6e-270:
		tmp = (c * b) + (-4.0 * (t * a))
	elif x <= 7.5e-103:
		tmp = (c * b) - (27.0 * (j * k))
	elif (x <= 2.2e-42) or not (x <= 8200000000000.0):
		tmp = t_1
	else:
		tmp = t_3
	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(y * Float64(z * t))) - Float64(i * 4.0)))
	t_2 = Float64(k * Float64(j * -27.0))
	t_3 = Float64(t_2 + Float64(a * Float64(-4.0 * t)))
	tmp = 0.0
	if (x <= -1.2e+116)
		tmp = t_1;
	elseif (x <= -8e+48)
		tmp = t_3;
	elseif (x <= -2.7e+14)
		tmp = t_1;
	elseif (x <= 6e-292)
		tmp = Float64(Float64(c * b) + t_2);
	elseif (x <= 6e-270)
		tmp = Float64(Float64(c * b) + Float64(-4.0 * Float64(t * a)));
	elseif (x <= 7.5e-103)
		tmp = Float64(Float64(c * b) - Float64(27.0 * Float64(j * k)));
	elseif ((x <= 2.2e-42) || !(x <= 8200000000000.0))
		tmp = t_1;
	else
		tmp = t_3;
	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 * (y * (z * t))) - (i * 4.0));
	t_2 = k * (j * -27.0);
	t_3 = t_2 + (a * (-4.0 * t));
	tmp = 0.0;
	if (x <= -1.2e+116)
		tmp = t_1;
	elseif (x <= -8e+48)
		tmp = t_3;
	elseif (x <= -2.7e+14)
		tmp = t_1;
	elseif (x <= 6e-292)
		tmp = (c * b) + t_2;
	elseif (x <= 6e-270)
		tmp = (c * b) + (-4.0 * (t * a));
	elseif (x <= 7.5e-103)
		tmp = (c * b) - (27.0 * (j * k));
	elseif ((x <= 2.2e-42) || ~((x <= 8200000000000.0)))
		tmp = t_1;
	else
		tmp = t_3;
	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[(y * N[(z * t), $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[(t$95$2 + N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+116], t$95$1, If[LessEqual[x, -8e+48], t$95$3, If[LessEqual[x, -2.7e+14], t$95$1, If[LessEqual[x, 6e-292], N[(N[(c * b), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[x, 6e-270], N[(N[(c * b), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-103], N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 2.2e-42], N[Not[LessEqual[x, 8200000000000.0]], $MachinePrecision]], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.2e116 or -8.00000000000000035e48 < x < -2.7e14 or 7.5e-103 < x < 2.20000000000000005e-42 or 8.2e12 < x

   1. Initial program 76.8%

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

      1. sub-neg 76.8%

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

      2. associate-+l- 76.8%

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

      3. sub-neg 76.8%

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

      4. sub-neg 76.8%

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

      5. distribute-rgt-out-- 78.5%

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

      6. associate-*l* 81.0%

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

      7. distribute-lft-neg-in 81.0%

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

      8. cancel-sign-sub 81.0%

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

      9. associate-*l* 81.0%

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

      10. associate-*l* 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in x around inf 68.5%

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

   if -1.2e116 < x < -8.00000000000000035e48 or 2.20000000000000005e-42 < x < 8.2e12

   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. Step-by-step derivation

      1. sub-neg 86.2%

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

      2. *-commutative 86.2%

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

      3. distribute-rgt-neg-in 86.2%

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

   3. Simplified 90.8%

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

      1. fma-udef 90.8%

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

   5. Applied egg-rr 90.8%

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

   6. Taylor expanded in a around inf 64.4%

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

      1. associate-*r* 64.4%

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

      2. *-commutative 64.4%

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

      3. associate-*l* 64.4%

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

   8. Simplified 64.4%

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

   if -2.7e14 < x < 6.00000000000000031e-292

   1. Initial program 92.4%

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

      1. sub-neg 92.4%

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

      2. *-commutative 92.4%

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

      3. distribute-rgt-neg-in 92.4%

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

   3. Simplified 89.5%

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

      1. fma-udef 89.5%

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

   5. Applied egg-rr 89.5%

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

   6. Taylor expanded in b around inf 66.7%

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

   if 6.00000000000000031e-292 < x < 6.00000000000000025e-270

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. associate-+l- 100.0%

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

      3. sub-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. distribute-rgt-out-- 100.0%

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

      6. associate-*l* 89.3%

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

      7. distribute-lft-neg-in 89.3%

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

      8. cancel-sign-sub 89.3%

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

      9. associate-*l* 89.3%

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

      10. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around 0 89.1%

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

   5. Taylor expanded in k around 0 89.1%

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

   if 6.00000000000000025e-270 < x < 7.5e-103

   1. Initial program 95.4%

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

      1. sub-neg 95.4%

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

      2. associate-+l- 95.4%

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

      3. sub-neg 95.4%

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

      4. sub-neg 95.4%

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

      5. distribute-rgt-out-- 95.4%

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

      6. associate-*l* 88.7%

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

      7. distribute-lft-neg-in 88.7%

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

      8. cancel-sign-sub 88.7%

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

      9. associate-*l* 88.7%

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

      10. associate-*l* 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in x around 0 83.8%

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

   5. Taylor expanded in a around 0 72.1%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+48}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + a \cdot \left(-4 \cdot t\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-292}:\\ \;\;\;\;c \cdot b + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-270}:\\ \;\;\;\;c \cdot b + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-103}:\\ \;\;\;\;c \cdot b - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-42} \lor \neg \left(x \leq 8200000000000\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + a \cdot \left(-4 \cdot t\right)\\ \end{array} \]

Alternative 7: 80.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right) + 18 \cdot \left(y \cdot \left(\left(x \cdot z\right) \cdot t\right)\right)\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+221}:\\ \;\;\;\;c \cdot b + t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-113}:\\ \;\;\;\;\left(c \cdot b - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b + \left(t_1 + -4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \end{array} \]

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 (+ (* -27.0 (* j k)) (* 18.0 (* y (* (* x z) t))))))
   (if (<= y -1.65e+221)
     (+ (* c b) t_1)
     (if (<= y 3e-113)
       (- (- (* c b) (+ (* 4.0 (* x i)) (* 4.0 (* t a)))) (* k (* j 27.0)))
       (+ (* c b) (+ t_1 (* -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 = (-27.0 * (j * k)) + (18.0 * (y * ((x * z) * t)));
	double tmp;
	if (y <= -1.65e+221) {
		tmp = (c * b) + t_1;
	} else if (y <= 3e-113) {
		tmp = ((c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)))) - (k * (j * 27.0));
	} else {
		tmp = (c * b) + (t_1 + (-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) :: tmp
    t_1 = ((-27.0d0) * (j * k)) + (18.0d0 * (y * ((x * z) * t)))
    if (y <= (-1.65d+221)) then
        tmp = (c * b) + t_1
    else if (y <= 3d-113) then
        tmp = ((c * b) - ((4.0d0 * (x * i)) + (4.0d0 * (t * a)))) - (k * (j * 27.0d0))
    else
        tmp = (c * b) + (t_1 + ((-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 = (-27.0 * (j * k)) + (18.0 * (y * ((x * z) * t)));
	double tmp;
	if (y <= -1.65e+221) {
		tmp = (c * b) + t_1;
	} else if (y <= 3e-113) {
		tmp = ((c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)))) - (k * (j * 27.0));
	} else {
		tmp = (c * b) + (t_1 + (-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 = (-27.0 * (j * k)) + (18.0 * (y * ((x * z) * t)))
	tmp = 0
	if y <= -1.65e+221:
		tmp = (c * b) + t_1
	elif y <= 3e-113:
		tmp = ((c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)))) - (k * (j * 27.0))
	else:
		tmp = (c * b) + (t_1 + (-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(Float64(-27.0 * Float64(j * k)) + Float64(18.0 * Float64(y * Float64(Float64(x * z) * t))))
	tmp = 0.0
	if (y <= -1.65e+221)
		tmp = Float64(Float64(c * b) + t_1);
	elseif (y <= 3e-113)
		tmp = Float64(Float64(Float64(c * b) - Float64(Float64(4.0 * Float64(x * i)) + Float64(4.0 * Float64(t * a)))) - Float64(k * Float64(j * 27.0)));
	else
		tmp = Float64(Float64(c * b) + Float64(t_1 + 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 = (-27.0 * (j * k)) + (18.0 * (y * ((x * z) * t)));
	tmp = 0.0;
	if (y <= -1.65e+221)
		tmp = (c * b) + t_1;
	elseif (y <= 3e-113)
		tmp = ((c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)))) - (k * (j * 27.0));
	else
		tmp = (c * b) + (t_1 + (-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[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(y * N[(N[(x * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+221], N[(N[(c * b), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[y, 3e-113], N[(N[(N[(c * b), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * b), $MachinePrecision] + N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.64999999999999996e221

   1. Initial program 85.3%

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

      1. sub-neg 85.3%

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

      2. *-commutative 85.3%

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

      3. distribute-rgt-neg-in 85.3%

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

   3. Simplified 79.0%

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

      1. fma-udef 79.0%

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

   5. Applied egg-rr 79.0%

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

   6. Taylor expanded in a around 0 64.8%

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

      1. fma-def 64.8%

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

      2. fma-def 64.8%

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

      3. *-commutative 64.8%

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

      4. associate-*r* 64.7%

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

      5. *-commutative 64.7%

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

   8. Simplified 64.7%

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

   9. Taylor expanded in i around 0 65.2%

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

   if -1.64999999999999996e221 < y < 3.0000000000000001e-113

   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 y around 0 85.2%

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

   if 3.0000000000000001e-113 < y

   1. Initial program 82.5%

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

      1. sub-neg 82.5%

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

      2. +-commutative 82.5%

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

      3. associate-*l* 82.6%

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

      4. distribute-rgt-neg-in 82.6%

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

      5. fma-def 83.7%

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

      6. *-commutative 83.7%

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

      7. distribute-rgt-neg-in 83.7%

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

      8. metadata-eval 83.7%

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

      9. sub-neg 83.7%

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

      10. +-commutative 83.7%

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

      11. associate-*l* 83.7%

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

      12. distribute-rgt-neg-in 83.7%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in a around 0 77.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+221}:\\ \;\;\;\;c \cdot b + \left(-27 \cdot \left(j \cdot k\right) + 18 \cdot \left(y \cdot \left(\left(x \cdot z\right) \cdot t\right)\right)\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-113}:\\ \;\;\;\;\left(c \cdot b - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b + \left(\left(-27 \cdot \left(j \cdot k\right) + 18 \cdot \left(y \cdot \left(\left(x \cdot z\right) \cdot t\right)\right)\right) + -4 \cdot \left(x \cdot i\right)\right)\\ \end{array} \]

Alternative 8: 82.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right)\\ t_2 := c \cdot b - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{if}\;i \leq -5.8 \cdot 10^{+39}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{+86}:\\ \;\;\;\;\left(t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right) + c \cdot b\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 - k \cdot \left(j \cdot 27\right)\\ \end{array} \end{array} \]

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 (* j (* k 27.0)))
        (t_2 (- (* c b) (+ (* 4.0 (* x i)) (* 4.0 (* t a))))))
   (if (<= i -5.8e+39)
     (- t_2 t_1)
     (if (<= i 1.9e+86)
       (- (+ (* t (- (* (* y z) (* x 18.0)) (* a 4.0))) (* c b)) t_1)
       (- t_2 (* 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 = j * (k * 27.0);
	double t_2 = (c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)));
	double tmp;
	if (i <= -5.8e+39) {
		tmp = t_2 - t_1;
	} else if (i <= 1.9e+86) {
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (c * b)) - t_1;
	} else {
		tmp = t_2 - (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) :: t_2
    real(8) :: tmp
    t_1 = j * (k * 27.0d0)
    t_2 = (c * b) - ((4.0d0 * (x * i)) + (4.0d0 * (t * a)))
    if (i <= (-5.8d+39)) then
        tmp = t_2 - t_1
    else if (i <= 1.9d+86) then
        tmp = ((t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0))) + (c * b)) - t_1
    else
        tmp = t_2 - (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 = j * (k * 27.0);
	double t_2 = (c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)));
	double tmp;
	if (i <= -5.8e+39) {
		tmp = t_2 - t_1;
	} else if (i <= 1.9e+86) {
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (c * b)) - t_1;
	} else {
		tmp = t_2 - (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 = j * (k * 27.0)
	t_2 = (c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)))
	tmp = 0
	if i <= -5.8e+39:
		tmp = t_2 - t_1
	elif i <= 1.9e+86:
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (c * b)) - t_1
	else:
		tmp = t_2 - (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(j * Float64(k * 27.0))
	t_2 = Float64(Float64(c * b) - Float64(Float64(4.0 * Float64(x * i)) + Float64(4.0 * Float64(t * a))))
	tmp = 0.0
	if (i <= -5.8e+39)
		tmp = Float64(t_2 - t_1);
	elseif (i <= 1.9e+86)
		tmp = Float64(Float64(Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0))) + Float64(c * b)) - t_1);
	else
		tmp = Float64(t_2 - 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 = j * (k * 27.0);
	t_2 = (c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)));
	tmp = 0.0;
	if (i <= -5.8e+39)
		tmp = t_2 - t_1;
	elseif (i <= 1.9e+86)
		tmp = ((t * (((y * z) * (x * 18.0)) - (a * 4.0))) + (c * b)) - t_1;
	else
		tmp = t_2 - (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[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * b), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.8e+39], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[i, 1.9e+86], N[(N[(N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(t$95$2 - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -5.80000000000000059e39

   1. Initial program 92.5%

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

   2. Taylor expanded in y around 0 87.9%

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

   3. Taylor expanded in j around 0 87.9%

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

      1. *-commutative 87.9%

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

      2. associate-*r* 87.9%

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

      3. *-commutative 87.9%

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

      4. associate-*l* 87.9%

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

   5. Simplified 87.9%

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

   if -5.80000000000000059e39 < i < 1.89999999999999989e86

   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. Step-by-step derivation

      1. sub-neg 86.6%

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

      2. associate-+l- 86.6%

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

      3. sub-neg 86.6%

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

      4. sub-neg 86.6%

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

      5. distribute-rgt-out-- 88.5%

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

      6. associate-*l* 87.2%

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

      7. distribute-lft-neg-in 87.2%

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

      8. cancel-sign-sub 87.2%

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

      9. associate-*l* 87.2%

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

      10. associate-*l* 87.2%

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

   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 x around 0 86.0%

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

      1. associate-*r* 86.1%

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

   6. Simplified 86.1%

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

   if 1.89999999999999989e86 < i

   1. Initial program 74.4%

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

   2. Taylor expanded in y around 0 78.9%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.8 \cdot 10^{+39}:\\ \;\;\;\;\left(c \cdot b - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{+86}:\\ \;\;\;\;\left(t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right) + c \cdot b\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot b - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\right) - k \cdot \left(j \cdot 27\right)\\ \end{array} \]

Alternative 9: 66.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := c \cdot b + \left(-27 \cdot \left(j \cdot k\right) + 18 \cdot \left(y \cdot \left(\left(x \cdot z\right) \cdot t\right)\right)\right)\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{+220}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-81}:\\ \;\;\;\;c \cdot b - \left(t_1 + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 1.58 \cdot 10^{-133}:\\ \;\;\;\;\left(c \cdot b - t_1\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* 4.0 (* x i)))
        (t_2 (+ (* c b) (+ (* -27.0 (* j k)) (* 18.0 (* y (* (* x z) t)))))))
   (if (<= y -7.4e+220)
     t_2
     (if (<= y -1.26e-81)
       (- (* c b) (+ t_1 (* 4.0 (* t a))))
       (if (<= y 1.58e-133) (- (- (* c b) t_1) (* k (* j 27.0))) 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 = 4.0 * (x * i);
	double t_2 = (c * b) + ((-27.0 * (j * k)) + (18.0 * (y * ((x * z) * t))));
	double tmp;
	if (y <= -7.4e+220) {
		tmp = t_2;
	} else if (y <= -1.26e-81) {
		tmp = (c * b) - (t_1 + (4.0 * (t * a)));
	} else if (y <= 1.58e-133) {
		tmp = ((c * b) - t_1) - (k * (j * 27.0));
	} else {
		tmp = 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 = 4.0d0 * (x * i)
    t_2 = (c * b) + (((-27.0d0) * (j * k)) + (18.0d0 * (y * ((x * z) * t))))
    if (y <= (-7.4d+220)) then
        tmp = t_2
    else if (y <= (-1.26d-81)) then
        tmp = (c * b) - (t_1 + (4.0d0 * (t * a)))
    else if (y <= 1.58d-133) then
        tmp = ((c * b) - t_1) - (k * (j * 27.0d0))
    else
        tmp = 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 = 4.0 * (x * i);
	double t_2 = (c * b) + ((-27.0 * (j * k)) + (18.0 * (y * ((x * z) * t))));
	double tmp;
	if (y <= -7.4e+220) {
		tmp = t_2;
	} else if (y <= -1.26e-81) {
		tmp = (c * b) - (t_1 + (4.0 * (t * a)));
	} else if (y <= 1.58e-133) {
		tmp = ((c * b) - t_1) - (k * (j * 27.0));
	} else {
		tmp = 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 = 4.0 * (x * i)
	t_2 = (c * b) + ((-27.0 * (j * k)) + (18.0 * (y * ((x * z) * t))))
	tmp = 0
	if y <= -7.4e+220:
		tmp = t_2
	elif y <= -1.26e-81:
		tmp = (c * b) - (t_1 + (4.0 * (t * a)))
	elif y <= 1.58e-133:
		tmp = ((c * b) - t_1) - (k * (j * 27.0))
	else:
		tmp = 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(4.0 * Float64(x * i))
	t_2 = Float64(Float64(c * b) + Float64(Float64(-27.0 * Float64(j * k)) + Float64(18.0 * Float64(y * Float64(Float64(x * z) * t)))))
	tmp = 0.0
	if (y <= -7.4e+220)
		tmp = t_2;
	elseif (y <= -1.26e-81)
		tmp = Float64(Float64(c * b) - Float64(t_1 + Float64(4.0 * Float64(t * a))));
	elseif (y <= 1.58e-133)
		tmp = Float64(Float64(Float64(c * b) - t_1) - Float64(k * Float64(j * 27.0)));
	else
		tmp = 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 = 4.0 * (x * i);
	t_2 = (c * b) + ((-27.0 * (j * k)) + (18.0 * (y * ((x * z) * t))));
	tmp = 0.0;
	if (y <= -7.4e+220)
		tmp = t_2;
	elseif (y <= -1.26e-81)
		tmp = (c * b) - (t_1 + (4.0 * (t * a)));
	elseif (y <= 1.58e-133)
		tmp = ((c * b) - t_1) - (k * (j * 27.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
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[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * b), $MachinePrecision] + N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(y * N[(N[(x * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.4e+220], t$95$2, If[LessEqual[y, -1.26e-81], N[(N[(c * b), $MachinePrecision] - N[(t$95$1 + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.58e-133], N[(N[(N[(c * b), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.4e220 or 1.58e-133 < y

   1. Initial program 83.4%

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

      1. sub-neg 83.4%

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

      2. *-commutative 83.4%

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

      3. distribute-rgt-neg-in 83.4%

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

   3. Simplified 82.5%

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

      1. fma-udef 82.5%

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

   5. Applied egg-rr 82.5%

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

   6. Taylor expanded in a around 0 75.7%

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

      1. fma-def 75.7%

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

      2. fma-def 75.7%

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

      3. *-commutative 75.7%

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

      4. associate-*r* 74.7%

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

      5. *-commutative 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in i around 0 67.7%

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

   if -7.4e220 < y < -1.2599999999999999e-81

   1. Initial program 81.3%

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

   2. Taylor expanded in y around 0 77.9%

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

   3. Taylor expanded in j around 0 66.5%

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

   if -1.2599999999999999e-81 < y < 1.58e-133

   1. Initial program 92.3%

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

   2. Taylor expanded in t around 0 84.7%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+220}:\\ \;\;\;\;c \cdot b + \left(-27 \cdot \left(j \cdot k\right) + 18 \cdot \left(y \cdot \left(\left(x \cdot z\right) \cdot t\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-81}:\\ \;\;\;\;c \cdot b - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 1.58 \cdot 10^{-133}:\\ \;\;\;\;\left(c \cdot b - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b + \left(-27 \cdot \left(j \cdot k\right) + 18 \cdot \left(y \cdot \left(\left(x \cdot z\right) \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 10: 80.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+221}:\\ \;\;\;\;c \cdot b + \left(-27 \cdot \left(j \cdot k\right) + 18 \cdot \left(y \cdot \left(\left(x \cdot z\right) \cdot t\right)\right)\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-84}:\\ \;\;\;\;\left(c \cdot b - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

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 (<= y -3.3e+221)
   (+ (* c b) (+ (* -27.0 (* j k)) (* 18.0 (* y (* (* x z) t)))))
   (if (<= y 7e-84)
     (- (- (* c b) (+ (* 4.0 (* x i)) (* 4.0 (* t a)))) (* j (* k 27.0)))
     (+ (* x (+ (* 18.0 (* y (* z t))) (* 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 (y <= -3.3e+221) {
		tmp = (c * b) + ((-27.0 * (j * k)) + (18.0 * (y * ((x * z) * t))));
	} else if (y <= 7e-84) {
		tmp = ((c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)))) - (j * (k * 27.0));
	} else {
		tmp = (x * ((18.0 * (y * (z * t))) + (i * -4.0))) + (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 (y <= (-3.3d+221)) then
        tmp = (c * b) + (((-27.0d0) * (j * k)) + (18.0d0 * (y * ((x * z) * t))))
    else if (y <= 7d-84) then
        tmp = ((c * b) - ((4.0d0 * (x * i)) + (4.0d0 * (t * a)))) - (j * (k * 27.0d0))
    else
        tmp = (x * ((18.0d0 * (y * (z * t))) + (i * (-4.0d0)))) + (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 (y <= -3.3e+221) {
		tmp = (c * b) + ((-27.0 * (j * k)) + (18.0 * (y * ((x * z) * t))));
	} else if (y <= 7e-84) {
		tmp = ((c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)))) - (j * (k * 27.0));
	} else {
		tmp = (x * ((18.0 * (y * (z * t))) + (i * -4.0))) + (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 y <= -3.3e+221:
		tmp = (c * b) + ((-27.0 * (j * k)) + (18.0 * (y * ((x * z) * t))))
	elif y <= 7e-84:
		tmp = ((c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)))) - (j * (k * 27.0))
	else:
		tmp = (x * ((18.0 * (y * (z * t))) + (i * -4.0))) + (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 (y <= -3.3e+221)
		tmp = Float64(Float64(c * b) + Float64(Float64(-27.0 * Float64(j * k)) + Float64(18.0 * Float64(y * Float64(Float64(x * z) * t)))));
	elseif (y <= 7e-84)
		tmp = Float64(Float64(Float64(c * b) - Float64(Float64(4.0 * Float64(x * i)) + Float64(4.0 * Float64(t * a)))) - Float64(j * Float64(k * 27.0)));
	else
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) + Float64(i * -4.0))) + 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 (y <= -3.3e+221)
		tmp = (c * b) + ((-27.0 * (j * k)) + (18.0 * (y * ((x * z) * t))));
	elseif (y <= 7e-84)
		tmp = ((c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)))) - (j * (k * 27.0));
	else
		tmp = (x * ((18.0 * (y * (z * t))) + (i * -4.0))) + (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[y, -3.3e+221], N[(N[(c * b), $MachinePrecision] + N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(y * N[(N[(x * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-84], N[(N[(N[(c * b), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.29999999999999991e221

   1. Initial program 85.3%

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

      1. sub-neg 85.3%

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

      2. *-commutative 85.3%

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

      3. distribute-rgt-neg-in 85.3%

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

   3. Simplified 79.0%

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

      1. fma-udef 79.0%

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

   5. Applied egg-rr 79.0%

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

   6. Taylor expanded in a around 0 64.8%

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

      1. fma-def 64.8%

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

      2. fma-def 64.8%

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

      3. *-commutative 64.8%

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

      4. associate-*r* 64.7%

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

      5. *-commutative 64.7%

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

   8. Simplified 64.7%

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

   9. Taylor expanded in i around 0 65.2%

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

   if -3.29999999999999991e221 < y < 7.0000000000000002e-84

   1. Initial program 87.6%

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

   2. Taylor expanded in y around 0 84.9%

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

   3. Taylor expanded in j around 0 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-*r* 84.9%

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

      3. *-commutative 84.9%

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

      4. associate-*l* 84.9%

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

   5. Simplified 84.9%

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

   if 7.0000000000000002e-84 < y

   1. Initial program 81.7%

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

      1. sub-neg 81.7%

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

      2. *-commutative 81.7%

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

      3. distribute-rgt-neg-in 81.7%

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

   3. Simplified 81.6%

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

      1. fma-udef 81.6%

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

   5. Applied egg-rr 81.6%

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

   6. Taylor expanded in x around inf 65.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+221}:\\ \;\;\;\;c \cdot b + \left(-27 \cdot \left(j \cdot k\right) + 18 \cdot \left(y \cdot \left(\left(x \cdot z\right) \cdot t\right)\right)\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-84}:\\ \;\;\;\;\left(c \cdot b - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 11: 31.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;i \leq -8 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-223}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+18}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+188}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(\left(x \cdot z\right) \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* j (* k -27.0))) (t_2 (* -4.0 (* x i))))
   (if (<= i -8e+36)
     t_2
     (if (<= i -1.7e-202)
       t_1
       (if (<= i 2.5e-223)
         (* c b)
         (if (<= i 3.3e-106)
           (* x (* (* 18.0 y) (* z t)))
           (if (<= i 3.2e+18)
             (* c b)
             (if (<= i 3.2e+71)
               t_1
               (if (<= i 1.1e+188) (* 18.0 (* y (* (* x z) t))) 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 = j * (k * -27.0);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if (i <= -8e+36) {
		tmp = t_2;
	} else if (i <= -1.7e-202) {
		tmp = t_1;
	} else if (i <= 2.5e-223) {
		tmp = c * b;
	} else if (i <= 3.3e-106) {
		tmp = x * ((18.0 * y) * (z * t));
	} else if (i <= 3.2e+18) {
		tmp = c * b;
	} else if (i <= 3.2e+71) {
		tmp = t_1;
	} else if (i <= 1.1e+188) {
		tmp = 18.0 * (y * ((x * z) * t));
	} else {
		tmp = 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 = j * (k * (-27.0d0))
    t_2 = (-4.0d0) * (x * i)
    if (i <= (-8d+36)) then
        tmp = t_2
    else if (i <= (-1.7d-202)) then
        tmp = t_1
    else if (i <= 2.5d-223) then
        tmp = c * b
    else if (i <= 3.3d-106) then
        tmp = x * ((18.0d0 * y) * (z * t))
    else if (i <= 3.2d+18) then
        tmp = c * b
    else if (i <= 3.2d+71) then
        tmp = t_1
    else if (i <= 1.1d+188) then
        tmp = 18.0d0 * (y * ((x * z) * t))
    else
        tmp = 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 = j * (k * -27.0);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if (i <= -8e+36) {
		tmp = t_2;
	} else if (i <= -1.7e-202) {
		tmp = t_1;
	} else if (i <= 2.5e-223) {
		tmp = c * b;
	} else if (i <= 3.3e-106) {
		tmp = x * ((18.0 * y) * (z * t));
	} else if (i <= 3.2e+18) {
		tmp = c * b;
	} else if (i <= 3.2e+71) {
		tmp = t_1;
	} else if (i <= 1.1e+188) {
		tmp = 18.0 * (y * ((x * z) * t));
	} else {
		tmp = 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 = j * (k * -27.0)
	t_2 = -4.0 * (x * i)
	tmp = 0
	if i <= -8e+36:
		tmp = t_2
	elif i <= -1.7e-202:
		tmp = t_1
	elif i <= 2.5e-223:
		tmp = c * b
	elif i <= 3.3e-106:
		tmp = x * ((18.0 * y) * (z * t))
	elif i <= 3.2e+18:
		tmp = c * b
	elif i <= 3.2e+71:
		tmp = t_1
	elif i <= 1.1e+188:
		tmp = 18.0 * (y * ((x * z) * t))
	else:
		tmp = 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(j * Float64(k * -27.0))
	t_2 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (i <= -8e+36)
		tmp = t_2;
	elseif (i <= -1.7e-202)
		tmp = t_1;
	elseif (i <= 2.5e-223)
		tmp = Float64(c * b);
	elseif (i <= 3.3e-106)
		tmp = Float64(x * Float64(Float64(18.0 * y) * Float64(z * t)));
	elseif (i <= 3.2e+18)
		tmp = Float64(c * b);
	elseif (i <= 3.2e+71)
		tmp = t_1;
	elseif (i <= 1.1e+188)
		tmp = Float64(18.0 * Float64(y * Float64(Float64(x * z) * t)));
	else
		tmp = 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 = j * (k * -27.0);
	t_2 = -4.0 * (x * i);
	tmp = 0.0;
	if (i <= -8e+36)
		tmp = t_2;
	elseif (i <= -1.7e-202)
		tmp = t_1;
	elseif (i <= 2.5e-223)
		tmp = c * b;
	elseif (i <= 3.3e-106)
		tmp = x * ((18.0 * y) * (z * t));
	elseif (i <= 3.2e+18)
		tmp = c * b;
	elseif (i <= 3.2e+71)
		tmp = t_1;
	elseif (i <= 1.1e+188)
		tmp = 18.0 * (y * ((x * z) * t));
	else
		tmp = 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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8e+36], t$95$2, If[LessEqual[i, -1.7e-202], t$95$1, If[LessEqual[i, 2.5e-223], N[(c * b), $MachinePrecision], If[LessEqual[i, 3.3e-106], N[(x * N[(N[(18.0 * y), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.2e+18], N[(c * b), $MachinePrecision], If[LessEqual[i, 3.2e+71], t$95$1, If[LessEqual[i, 1.1e+188], N[(18.0 * N[(y * N[(N[(x * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -8.00000000000000034e36 or 1.09999999999999999e188 < i

   1. Initial program 87.8%

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

      1. sub-neg 87.8%

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

      2. +-commutative 87.8%

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

      3. associate-*l* 87.9%

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

      4. distribute-rgt-neg-in 87.9%

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

      5. fma-def 89.1%

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

      6. *-commutative 89.1%

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

      7. distribute-rgt-neg-in 89.1%

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

      8. metadata-eval 89.1%

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

      9. sub-neg 89.1%

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

      10. +-commutative 89.1%

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

      11. associate-*l* 89.1%

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

      12. distribute-rgt-neg-in 89.1%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in i around inf 56.0%

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

      1. *-commutative 56.0%

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

   6. Simplified 56.0%

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

   if -8.00000000000000034e36 < i < -1.70000000000000006e-202 or 3.2e18 < i < 3.20000000000000023e71

   1. Initial program 83.7%

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

      1. sub-neg 83.7%

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

      2. *-commutative 83.7%

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

      3. distribute-rgt-neg-in 83.7%

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

   3. Simplified 86.8%

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

      1. fma-udef 86.8%

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

   5. Applied egg-rr 86.8%

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

   6. Taylor expanded in a around 0 73.1%

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

      1. fma-def 73.1%

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

      2. fma-def 73.1%

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

      3. *-commutative 73.1%

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

      4. associate-*r* 73.1%

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

      5. *-commutative 73.1%

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

   8. Simplified 73.1%

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

   9. Taylor expanded in k around inf 43.9%

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

       1. associate-*r* 43.9%

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

   11. Simplified 43.9%

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

   if -1.70000000000000006e-202 < i < 2.50000000000000012e-223 or 3.30000000000000016e-106 < i < 3.2e18

   1. Initial program 90.4%

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

      1. sub-neg 90.4%

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

      2. *-commutative 90.4%

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

      3. distribute-rgt-neg-in 90.4%

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

   3. Simplified 88.7%

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

      1. fma-udef 88.7%

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

   5. Applied egg-rr 88.7%

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

   6. Taylor expanded in a around 0 74.7%

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

      1. fma-def 74.7%

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

      2. fma-def 74.7%

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

      3. *-commutative 74.7%

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

      4. associate-*r* 73.1%

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

      5. *-commutative 73.1%

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

   8. Simplified 73.1%

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

   9. Taylor expanded in c around inf 44.2%

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

   if 2.50000000000000012e-223 < i < 3.30000000000000016e-106

   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. Step-by-step derivation

      1. sub-neg 85.2%

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

      2. associate-+l- 85.2%

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

      3. sub-neg 85.2%

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

      4. sub-neg 85.2%

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

      5. distribute-rgt-out-- 85.2%

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

      6. associate-*l* 85.2%

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

      7. distribute-lft-neg-in 85.2%

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

      8. cancel-sign-sub 85.2%

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

      9. associate-*l* 85.2%

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

      10. associate-*l* 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in x around inf 56.2%

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

   5. Taylor expanded in y around inf 51.4%

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

      1. associate-*r* 51.4%

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

      2. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   if 3.20000000000000023e71 < i < 1.09999999999999999e188

   1. Initial program 70.8%

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

      1. sub-neg 70.8%

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

      2. *-commutative 70.8%

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

      3. distribute-rgt-neg-in 70.8%

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

   3. Simplified 70.8%

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

      1. fma-udef 70.8%

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

   5. Applied egg-rr 70.8%

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

   6. Taylor expanded in a around 0 66.7%

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

      1. fma-def 66.7%

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

      2. fma-def 66.7%

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

      3. *-commutative 66.7%

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

      4. associate-*r* 66.7%

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

      5. *-commutative 66.7%

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

   8. Simplified 66.7%

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

      1. fma-udef 66.7%

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

      2. *-commutative 66.7%

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

      3. associate-*r* 66.7%

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

      4. *-commutative 66.7%

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

      5. associate-*r* 66.7%

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

      6. associate-*l* 66.7%

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

      7. *-commutative 66.7%

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

      8. associate-*r* 66.7%

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

   10. Applied egg-rr 66.7%

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

   11. Taylor expanded in y around inf 38.7%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8 \cdot 10^{+36}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-223}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+18}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+71}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+188}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(\left(x \cdot z\right) \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 12: 63.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := c \cdot b - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;j \leq -1.5 \cdot 10^{+203}:\\ \;\;\;\;t_2 + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot b + t_2\\ \end{array} \end{array} \]

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 (- (* c b) (+ (* 4.0 (* x i)) (* 4.0 (* t a)))))
        (t_2 (* k (* j -27.0))))
   (if (<= j -1.5e+203)
     (+ t_2 (* x (* i -4.0)))
     (if (<= j -1.6e+52)
       t_1
       (if (<= j -1.7e+35)
         (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))
         (if (<= j 1.6e-13) t_1 (+ (* c b) 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 = (c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)));
	double t_2 = k * (j * -27.0);
	double tmp;
	if (j <= -1.5e+203) {
		tmp = t_2 + (x * (i * -4.0));
	} else if (j <= -1.6e+52) {
		tmp = t_1;
	} else if (j <= -1.7e+35) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (j <= 1.6e-13) {
		tmp = t_1;
	} else {
		tmp = (c * b) + 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 = (c * b) - ((4.0d0 * (x * i)) + (4.0d0 * (t * a)))
    t_2 = k * (j * (-27.0d0))
    if (j <= (-1.5d+203)) then
        tmp = t_2 + (x * (i * (-4.0d0)))
    else if (j <= (-1.6d+52)) then
        tmp = t_1
    else if (j <= (-1.7d+35)) then
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    else if (j <= 1.6d-13) then
        tmp = t_1
    else
        tmp = (c * b) + 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 = (c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)));
	double t_2 = k * (j * -27.0);
	double tmp;
	if (j <= -1.5e+203) {
		tmp = t_2 + (x * (i * -4.0));
	} else if (j <= -1.6e+52) {
		tmp = t_1;
	} else if (j <= -1.7e+35) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else if (j <= 1.6e-13) {
		tmp = t_1;
	} else {
		tmp = (c * b) + 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 = (c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)))
	t_2 = k * (j * -27.0)
	tmp = 0
	if j <= -1.5e+203:
		tmp = t_2 + (x * (i * -4.0))
	elif j <= -1.6e+52:
		tmp = t_1
	elif j <= -1.7e+35:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	elif j <= 1.6e-13:
		tmp = t_1
	else:
		tmp = (c * b) + 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(Float64(c * b) - Float64(Float64(4.0 * Float64(x * i)) + Float64(4.0 * Float64(t * a))))
	t_2 = Float64(k * Float64(j * -27.0))
	tmp = 0.0
	if (j <= -1.5e+203)
		tmp = Float64(t_2 + Float64(x * Float64(i * -4.0)));
	elseif (j <= -1.6e+52)
		tmp = t_1;
	elseif (j <= -1.7e+35)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	elseif (j <= 1.6e-13)
		tmp = t_1;
	else
		tmp = Float64(Float64(c * b) + 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 = (c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)));
	t_2 = k * (j * -27.0);
	tmp = 0.0;
	if (j <= -1.5e+203)
		tmp = t_2 + (x * (i * -4.0));
	elseif (j <= -1.6e+52)
		tmp = t_1;
	elseif (j <= -1.7e+35)
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	elseif (j <= 1.6e-13)
		tmp = t_1;
	else
		tmp = (c * b) + 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[(N[(c * b), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.5e+203], N[(t$95$2 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.6e+52], t$95$1, If[LessEqual[j, -1.7e+35], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.6e-13], t$95$1, N[(N[(c * b), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.5e203

   1. Initial program 71.8%

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

      1. sub-neg 71.8%

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

      2. *-commutative 71.8%

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

      3. distribute-rgt-neg-in 71.8%

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

   3. Simplified 71.8%

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

      1. fma-udef 71.8%

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

   5. Applied egg-rr 71.8%

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

   6. Taylor expanded in i around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. *-commutative 75.0%

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

      3. associate-*l* 75.0%

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

      4. *-commutative 75.0%

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

   8. Simplified 75.0%

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

   if -1.5e203 < j < -1.6e52 or -1.7000000000000001e35 < j < 1.6e-13

   1. Initial program 87.9%

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

   2. Taylor expanded in y around 0 76.3%

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

   3. Taylor expanded in j around 0 66.1%

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

   if -1.6e52 < j < -1.7000000000000001e35

   1. Initial program 85.5%

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

      1. sub-neg 85.5%

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

      2. associate-+l- 85.5%

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

      3. sub-neg 85.5%

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

      4. sub-neg 85.5%

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

      5. distribute-rgt-out-- 85.5%

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

      6. associate-*l* 85.5%

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

      7. distribute-lft-neg-in 85.5%

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

      8. cancel-sign-sub 85.5%

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

      9. associate-*l* 85.5%

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

      10. associate-*l* 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in t around inf 57.9%

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

   if 1.6e-13 < j

   1. Initial program 85.5%

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

      1. sub-neg 85.5%

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

      2. *-commutative 85.5%

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

      3. distribute-rgt-neg-in 85.5%

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

   3. Simplified 85.4%

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

      1. fma-udef 85.4%

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

   5. Applied egg-rr 85.4%

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

   6. Taylor expanded in b around inf 54.4%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+203}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{+52}:\\ \;\;\;\;c \cdot b - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-13}:\\ \;\;\;\;c \cdot b - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 13: 75.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-27} \lor \neg \left(x \leq 8.6 \cdot 10^{-87}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot b + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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
 (if (or (<= x -2.9e-27) (not (<= x 8.6e-87)))
   (+ (* x (+ (* 18.0 (* y (* z t))) (* i -4.0))) (* k (* j -27.0)))
   (- (+ (* c b) (* -4.0 (* t a))) (* 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 tmp;
	if ((x <= -2.9e-27) || !(x <= 8.6e-87)) {
		tmp = (x * ((18.0 * (y * (z * t))) + (i * -4.0))) + (k * (j * -27.0));
	} else {
		tmp = ((c * b) + (-4.0 * (t * a))) - (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) :: tmp
    if ((x <= (-2.9d-27)) .or. (.not. (x <= 8.6d-87))) then
        tmp = (x * ((18.0d0 * (y * (z * t))) + (i * (-4.0d0)))) + (k * (j * (-27.0d0)))
    else
        tmp = ((c * b) + ((-4.0d0) * (t * a))) - (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 tmp;
	if ((x <= -2.9e-27) || !(x <= 8.6e-87)) {
		tmp = (x * ((18.0 * (y * (z * t))) + (i * -4.0))) + (k * (j * -27.0));
	} else {
		tmp = ((c * b) + (-4.0 * (t * a))) - (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):
	tmp = 0
	if (x <= -2.9e-27) or not (x <= 8.6e-87):
		tmp = (x * ((18.0 * (y * (z * t))) + (i * -4.0))) + (k * (j * -27.0))
	else:
		tmp = ((c * b) + (-4.0 * (t * a))) - (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)
	tmp = 0.0
	if ((x <= -2.9e-27) || !(x <= 8.6e-87))
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) + Float64(i * -4.0))) + Float64(k * Float64(j * -27.0)));
	else
		tmp = Float64(Float64(Float64(c * b) + Float64(-4.0 * Float64(t * a))) - 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)
	tmp = 0.0;
	if ((x <= -2.9e-27) || ~((x <= 8.6e-87)))
		tmp = (x * ((18.0 * (y * (z * t))) + (i * -4.0))) + (k * (j * -27.0));
	else
		tmp = ((c * b) + (-4.0 * (t * a))) - (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_] := If[Or[LessEqual[x, -2.9e-27], N[Not[LessEqual[x, 8.6e-87]], $MachinePrecision]], N[(N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(c * b), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.90000000000000004e-27 or 8.59999999999999991e-87 < x

   1. Initial program 78.1%

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

      1. sub-neg 78.1%

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

      2. *-commutative 78.1%

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

      3. distribute-rgt-neg-in 78.1%

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

   3. Simplified 83.0%

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

      1. fma-udef 82.2%

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

   5. Applied egg-rr 82.2%

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

   6. Taylor expanded in x around inf 72.9%

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

   if -2.90000000000000004e-27 < x < 8.59999999999999991e-87

   1. Initial program 94.8%

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

      1. sub-neg 94.8%

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

      2. associate-+l- 94.8%

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

      3. sub-neg 94.8%

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

      4. sub-neg 94.8%

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

      5. distribute-rgt-out-- 95.6%

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

      6. associate-*l* 89.8%

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

      7. distribute-lft-neg-in 89.8%

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

      8. cancel-sign-sub 89.8%

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

      9. associate-*l* 89.8%

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

      10. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in x around 0 83.1%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-27} \lor \neg \left(x \leq 8.6 \cdot 10^{-87}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot b + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 14: 49.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{+161} \lor \neg \left(b \leq -1.5 \cdot 10^{+92}\right) \land \left(b \leq -1.05 \cdot 10^{+40} \lor \neg \left(b \leq 8 \cdot 10^{-153}\right)\right):\\ \;\;\;\;c \cdot b + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 + x \cdot \left(i \cdot -4\right)\\ \end{array} \end{array} \]

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 (* k (* j -27.0))))
   (if (or (<= b -1.65e+161)
           (and (not (<= b -1.5e+92))
                (or (<= b -1.05e+40) (not (<= b 8e-153)))))
     (+ (* c b) t_1)
     (+ 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 = k * (j * -27.0);
	double tmp;
	if ((b <= -1.65e+161) || (!(b <= -1.5e+92) && ((b <= -1.05e+40) || !(b <= 8e-153)))) {
		tmp = (c * b) + t_1;
	} else {
		tmp = t_1 + (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) :: tmp
    t_1 = k * (j * (-27.0d0))
    if ((b <= (-1.65d+161)) .or. (.not. (b <= (-1.5d+92))) .and. (b <= (-1.05d+40)) .or. (.not. (b <= 8d-153))) then
        tmp = (c * b) + t_1
    else
        tmp = t_1 + (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 = k * (j * -27.0);
	double tmp;
	if ((b <= -1.65e+161) || (!(b <= -1.5e+92) && ((b <= -1.05e+40) || !(b <= 8e-153)))) {
		tmp = (c * b) + t_1;
	} else {
		tmp = t_1 + (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 = k * (j * -27.0)
	tmp = 0
	if (b <= -1.65e+161) or (not (b <= -1.5e+92) and ((b <= -1.05e+40) or not (b <= 8e-153))):
		tmp = (c * b) + t_1
	else:
		tmp = t_1 + (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(k * Float64(j * -27.0))
	tmp = 0.0
	if ((b <= -1.65e+161) || (!(b <= -1.5e+92) && ((b <= -1.05e+40) || !(b <= 8e-153))))
		tmp = Float64(Float64(c * b) + t_1);
	else
		tmp = Float64(t_1 + 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 = k * (j * -27.0);
	tmp = 0.0;
	if ((b <= -1.65e+161) || (~((b <= -1.5e+92)) && ((b <= -1.05e+40) || ~((b <= 8e-153)))))
		tmp = (c * b) + t_1;
	else
		tmp = t_1 + (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[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -1.65e+161], And[N[Not[LessEqual[b, -1.5e+92]], $MachinePrecision], Or[LessEqual[b, -1.05e+40], N[Not[LessEqual[b, 8e-153]], $MachinePrecision]]]], N[(N[(c * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.64999999999999999e161 or -1.50000000000000007e92 < b < -1.05000000000000005e40 or 8.00000000000000031e-153 < b

   1. Initial program 84.0%

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

      1. sub-neg 84.0%

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

      2. *-commutative 84.0%

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

      3. distribute-rgt-neg-in 84.0%

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

   3. Simplified 84.8%

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

      1. fma-udef 84.1%

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

   5. Applied egg-rr 84.1%

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

   6. Taylor expanded in b around inf 62.5%

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

   if -1.64999999999999999e161 < b < -1.50000000000000007e92 or -1.05000000000000005e40 < b < 8.00000000000000031e-153

   1. Initial program 87.3%

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

      1. sub-neg 87.3%

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

      2. *-commutative 87.3%

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

      3. distribute-rgt-neg-in 87.3%

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

   3. Simplified 87.3%

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

      1. fma-udef 87.3%

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

   5. Applied egg-rr 87.3%

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

   6. Taylor expanded in i around inf 52.5%

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

      1. *-commutative 52.5%

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

      2. *-commutative 52.5%

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

      3. associate-*l* 52.5%

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

      4. *-commutative 52.5%

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

   8. Simplified 52.5%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+161} \lor \neg \left(b \leq -1.5 \cdot 10^{+92}\right) \land \left(b \leq -1.05 \cdot 10^{+40} \lor \neg \left(b \leq 8 \cdot 10^{-153}\right)\right):\\ \;\;\;\;c \cdot b + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \end{array} \]

Alternative 15: 51.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := t_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{-27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-102}:\\ \;\;\;\;c \cdot b + t_1\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

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 (* k (* j -27.0))) (t_2 (+ t_1 (* x (* i -4.0)))))
   (if (<= x -3.4e-27)
     t_2
     (if (<= x 2.4e-102)
       (+ (* c b) t_1)
       (if (<= x 2.2e+116) t_2 (* t (- (* 18.0 (* y (* x z))) (* a 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 = k * (j * -27.0);
	double t_2 = t_1 + (x * (i * -4.0));
	double tmp;
	if (x <= -3.4e-27) {
		tmp = t_2;
	} else if (x <= 2.4e-102) {
		tmp = (c * b) + t_1;
	} else if (x <= 2.2e+116) {
		tmp = t_2;
	} else {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 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 = k * (j * (-27.0d0))
    t_2 = t_1 + (x * (i * (-4.0d0)))
    if (x <= (-3.4d-27)) then
        tmp = t_2
    else if (x <= 2.4d-102) then
        tmp = (c * b) + t_1
    else if (x <= 2.2d+116) then
        tmp = t_2
    else
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 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 = k * (j * -27.0);
	double t_2 = t_1 + (x * (i * -4.0));
	double tmp;
	if (x <= -3.4e-27) {
		tmp = t_2;
	} else if (x <= 2.4e-102) {
		tmp = (c * b) + t_1;
	} else if (x <= 2.2e+116) {
		tmp = t_2;
	} else {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 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 = k * (j * -27.0)
	t_2 = t_1 + (x * (i * -4.0))
	tmp = 0
	if x <= -3.4e-27:
		tmp = t_2
	elif x <= 2.4e-102:
		tmp = (c * b) + t_1
	elif x <= 2.2e+116:
		tmp = t_2
	else:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 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(k * Float64(j * -27.0))
	t_2 = Float64(t_1 + Float64(x * Float64(i * -4.0)))
	tmp = 0.0
	if (x <= -3.4e-27)
		tmp = t_2;
	elseif (x <= 2.4e-102)
		tmp = Float64(Float64(c * b) + t_1);
	elseif (x <= 2.2e+116)
		tmp = t_2;
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 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 = k * (j * -27.0);
	t_2 = t_1 + (x * (i * -4.0));
	tmp = 0.0;
	if (x <= -3.4e-27)
		tmp = t_2;
	elseif (x <= 2.4e-102)
		tmp = (c * b) + t_1;
	elseif (x <= 2.2e+116)
		tmp = t_2;
	else
		tmp = t * ((18.0 * (y * (x * z))) - (a * 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[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e-27], t$95$2, If[LessEqual[x, 2.4e-102], N[(N[(c * b), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 2.2e+116], t$95$2, N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.3999999999999997e-27 or 2.4e-102 < x < 2.2e116

   1. Initial program 83.1%

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

      1. sub-neg 83.1%

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

      2. *-commutative 83.1%

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

      3. distribute-rgt-neg-in 83.1%

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

   3. Simplified 85.7%

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

      1. fma-udef 85.7%

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

   5. Applied egg-rr 85.7%

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

   6. Taylor expanded in i around inf 53.9%

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

      1. *-commutative 53.9%

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

      2. *-commutative 53.9%

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

      3. associate-*l* 53.9%

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

      4. *-commutative 53.9%

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

   8. Simplified 53.9%

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

   if -3.3999999999999997e-27 < x < 2.4e-102

   1. Initial program 94.6%

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

      1. sub-neg 94.6%

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

      2. *-commutative 94.6%

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

      3. distribute-rgt-neg-in 94.6%

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

   3. Simplified 89.5%

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

      1. fma-udef 89.5%

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

   5. Applied egg-rr 89.5%

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

   6. Taylor expanded in b around inf 64.9%

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

   if 2.2e116 < x

   1. Initial program 62.5%

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

      1. sub-neg 62.5%

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

      2. associate-+l- 62.5%

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

      3. sub-neg 62.5%

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

      4. sub-neg 62.5%

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

      5. distribute-rgt-out-- 65.7%

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

      6. associate-*l* 71.8%

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

      7. distribute-lft-neg-in 71.8%

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

      8. cancel-sign-sub 71.8%

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

      9. associate-*l* 71.8%

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

      10. associate-*l* 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in t around inf 63.6%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-27}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-102}:\\ \;\;\;\;c \cdot b + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+116}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 16: 65.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+40} \lor \neg \left(i \leq 5.8 \cdot 10^{+191}\right):\\ \;\;\;\;c \cdot b - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot b + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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
 (if (or (<= i -1e+40) (not (<= i 5.8e+191)))
   (- (* c b) (+ (* 4.0 (* x i)) (* 4.0 (* t a))))
   (- (+ (* c b) (* -4.0 (* t a))) (* 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 tmp;
	if ((i <= -1e+40) || !(i <= 5.8e+191)) {
		tmp = (c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)));
	} else {
		tmp = ((c * b) + (-4.0 * (t * a))) - (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) :: tmp
    if ((i <= (-1d+40)) .or. (.not. (i <= 5.8d+191))) then
        tmp = (c * b) - ((4.0d0 * (x * i)) + (4.0d0 * (t * a)))
    else
        tmp = ((c * b) + ((-4.0d0) * (t * a))) - (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 tmp;
	if ((i <= -1e+40) || !(i <= 5.8e+191)) {
		tmp = (c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)));
	} else {
		tmp = ((c * b) + (-4.0 * (t * a))) - (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):
	tmp = 0
	if (i <= -1e+40) or not (i <= 5.8e+191):
		tmp = (c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)))
	else:
		tmp = ((c * b) + (-4.0 * (t * a))) - (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)
	tmp = 0.0
	if ((i <= -1e+40) || !(i <= 5.8e+191))
		tmp = Float64(Float64(c * b) - Float64(Float64(4.0 * Float64(x * i)) + Float64(4.0 * Float64(t * a))));
	else
		tmp = Float64(Float64(Float64(c * b) + Float64(-4.0 * Float64(t * a))) - 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)
	tmp = 0.0;
	if ((i <= -1e+40) || ~((i <= 5.8e+191)))
		tmp = (c * b) - ((4.0 * (x * i)) + (4.0 * (t * a)));
	else
		tmp = ((c * b) + (-4.0 * (t * a))) - (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_] := If[Or[LessEqual[i, -1e+40], N[Not[LessEqual[i, 5.8e+191]], $MachinePrecision]], N[(N[(c * b), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(c * b), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.00000000000000003e40 or 5.8000000000000003e191 < i

   1. Initial program 87.7%

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

   2. Taylor expanded in y around 0 87.1%

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

   3. Taylor expanded in j around 0 73.7%

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

   if -1.00000000000000003e40 < i < 5.8000000000000003e191

   1. Initial program 84.6%

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

      1. sub-neg 84.6%

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

      2. associate-+l- 84.6%

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

      3. sub-neg 84.6%

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

      4. sub-neg 84.6%

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

      5. distribute-rgt-out-- 86.3%

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

      6. associate-*l* 85.1%

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

      7. distribute-lft-neg-in 85.1%

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

      8. cancel-sign-sub 85.1%

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

      9. associate-*l* 85.1%

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

      10. associate-*l* 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in x around 0 72.1%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+40} \lor \neg \left(i \leq 5.8 \cdot 10^{+191}\right):\\ \;\;\;\;c \cdot b - \left(4 \cdot \left(x \cdot i\right) + 4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot b + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 17: 32.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -1.4 \cdot 10^{-35}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-196}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-114}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;c \leq 85000:\\ \;\;\;\;18 \cdot \left(y \cdot \left(\left(x \cdot z\right) \cdot t\right)\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+39}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

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 (<= c -1.4e-35)
   (* c b)
   (if (<= c 1.75e-196)
     (* -4.0 (* x i))
     (if (<= c 9.5e-114)
       (* -27.0 (* j k))
       (if (<= c 85000.0)
         (* 18.0 (* y (* (* x z) t)))
         (if (<= c 2.7e+39)
           (* c b)
           (if (<= c 2.6e+100) (* t (* -4.0 a)) (* c b))))))))

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 (c <= -1.4e-35) {
		tmp = c * b;
	} else if (c <= 1.75e-196) {
		tmp = -4.0 * (x * i);
	} else if (c <= 9.5e-114) {
		tmp = -27.0 * (j * k);
	} else if (c <= 85000.0) {
		tmp = 18.0 * (y * ((x * z) * t));
	} else if (c <= 2.7e+39) {
		tmp = c * b;
	} else if (c <= 2.6e+100) {
		tmp = t * (-4.0 * a);
	} else {
		tmp = c * b;
	}
	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 (c <= (-1.4d-35)) then
        tmp = c * b
    else if (c <= 1.75d-196) then
        tmp = (-4.0d0) * (x * i)
    else if (c <= 9.5d-114) then
        tmp = (-27.0d0) * (j * k)
    else if (c <= 85000.0d0) then
        tmp = 18.0d0 * (y * ((x * z) * t))
    else if (c <= 2.7d+39) then
        tmp = c * b
    else if (c <= 2.6d+100) then
        tmp = t * ((-4.0d0) * a)
    else
        tmp = c * b
    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 (c <= -1.4e-35) {
		tmp = c * b;
	} else if (c <= 1.75e-196) {
		tmp = -4.0 * (x * i);
	} else if (c <= 9.5e-114) {
		tmp = -27.0 * (j * k);
	} else if (c <= 85000.0) {
		tmp = 18.0 * (y * ((x * z) * t));
	} else if (c <= 2.7e+39) {
		tmp = c * b;
	} else if (c <= 2.6e+100) {
		tmp = t * (-4.0 * a);
	} else {
		tmp = c * b;
	}
	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 c <= -1.4e-35:
		tmp = c * b
	elif c <= 1.75e-196:
		tmp = -4.0 * (x * i)
	elif c <= 9.5e-114:
		tmp = -27.0 * (j * k)
	elif c <= 85000.0:
		tmp = 18.0 * (y * ((x * z) * t))
	elif c <= 2.7e+39:
		tmp = c * b
	elif c <= 2.6e+100:
		tmp = t * (-4.0 * a)
	else:
		tmp = c * b
	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 (c <= -1.4e-35)
		tmp = Float64(c * b);
	elseif (c <= 1.75e-196)
		tmp = Float64(-4.0 * Float64(x * i));
	elseif (c <= 9.5e-114)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (c <= 85000.0)
		tmp = Float64(18.0 * Float64(y * Float64(Float64(x * z) * t)));
	elseif (c <= 2.7e+39)
		tmp = Float64(c * b);
	elseif (c <= 2.6e+100)
		tmp = Float64(t * Float64(-4.0 * a));
	else
		tmp = Float64(c * b);
	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 (c <= -1.4e-35)
		tmp = c * b;
	elseif (c <= 1.75e-196)
		tmp = -4.0 * (x * i);
	elseif (c <= 9.5e-114)
		tmp = -27.0 * (j * k);
	elseif (c <= 85000.0)
		tmp = 18.0 * (y * ((x * z) * t));
	elseif (c <= 2.7e+39)
		tmp = c * b;
	elseif (c <= 2.6e+100)
		tmp = t * (-4.0 * a);
	else
		tmp = c * b;
	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[c, -1.4e-35], N[(c * b), $MachinePrecision], If[LessEqual[c, 1.75e-196], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.5e-114], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 85000.0], N[(18.0 * N[(y * N[(N[(x * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.7e+39], N[(c * b), $MachinePrecision], If[LessEqual[c, 2.6e+100], N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.4e-35 or 85000 < c < 2.70000000000000003e39 or 2.6000000000000002e100 < c

   1. Initial program 87.8%

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

      1. sub-neg 87.8%

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

      2. *-commutative 87.8%

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

      3. distribute-rgt-neg-in 87.8%

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

   3. Simplified 87.0%

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

      1. fma-udef 86.3%

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

   5. Applied egg-rr 86.3%

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

   6. Taylor expanded in a around 0 82.8%

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

      1. fma-def 83.5%

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

      2. fma-def 83.5%

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

      3. *-commutative 83.5%

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

      4. associate-*r* 82.8%

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

      5. *-commutative 82.8%

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

   8. Simplified 82.8%

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

   9. Taylor expanded in c around inf 42.3%

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

   if -1.4e-35 < c < 1.75000000000000002e-196

   1. Initial program 77.4%

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

      1. sub-neg 77.4%

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

      2. +-commutative 77.4%

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

      3. associate-*l* 77.4%

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

      4. distribute-rgt-neg-in 77.4%

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

      5. fma-def 81.9%

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

      6. *-commutative 81.9%

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

      7. distribute-rgt-neg-in 81.9%

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

      8. metadata-eval 81.9%

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

      9. sub-neg 81.9%

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

      10. +-commutative 81.9%

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

      11. associate-*l* 81.9%

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

      12. distribute-rgt-neg-in 81.9%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in i around inf 32.4%

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

      1. *-commutative 32.4%

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

   6. Simplified 32.4%

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

   if 1.75000000000000002e-196 < c < 9.49999999999999958e-114

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-*l* 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. fma-def 99.8%

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

      6. *-commutative 99.8%

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

      7. distribute-rgt-neg-in 99.8%

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

      8. metadata-eval 99.8%

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

      9. sub-neg 99.8%

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

      10. +-commutative 99.8%

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

      11. associate-*l* 99.8%

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

      12. distribute-rgt-neg-in 99.8%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in j around inf 42.9%

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

   if 9.49999999999999958e-114 < c < 85000

   1. Initial program 79.8%

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

      1. sub-neg 79.8%

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

      2. *-commutative 79.8%

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

      3. distribute-rgt-neg-in 79.8%

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

   3. Simplified 80.2%

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

      1. fma-udef 80.2%

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

   5. Applied egg-rr 80.2%

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

   6. Taylor expanded in a around 0 75.9%

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

      1. fma-def 75.9%

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

      2. fma-def 75.9%

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

      3. *-commutative 75.9%

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

      4. associate-*r* 75.8%

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

      5. *-commutative 75.8%

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

   8. Simplified 75.8%

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

      1. fma-udef 75.8%

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

      2. *-commutative 75.8%

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

      3. associate-*r* 75.8%

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

      4. *-commutative 75.8%

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

      5. associate-*r* 75.8%

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

      6. associate-*l* 75.9%

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

      7. *-commutative 75.9%

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

      8. associate-*r* 60.6%

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

   10. Applied egg-rr 60.6%

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

   11. Taylor expanded in y around inf 37.1%

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

   if 2.70000000000000003e39 < c < 2.6000000000000002e100

   1. Initial program 94.4%

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

      1. sub-neg 94.4%

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

      2. associate-+l- 94.4%

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

      3. sub-neg 94.4%

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

      4. sub-neg 94.4%

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

      5. distribute-rgt-out-- 94.4%

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

      6. associate-*l* 94.4%

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

      7. distribute-lft-neg-in 94.4%

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

      8. cancel-sign-sub 94.4%

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

      9. associate-*l* 94.4%

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

      10. associate-*l* 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in x around 0 74.6%

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

   5. Taylor expanded in a around inf 42.5%

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

      1. associate-*r* 42.5%

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

      2. *-commutative 42.5%

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

   7. Simplified 42.5%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.4 \cdot 10^{-35}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-196}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-114}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;c \leq 85000:\\ \;\;\;\;18 \cdot \left(y \cdot \left(\left(x \cdot z\right) \cdot t\right)\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+39}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \]

Alternative 18: 50.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := c \cdot b + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -420000:\\ \;\;\;\;t_1 + a \cdot \left(-4 \cdot t\right)\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+155}:\\ \;\;\;\;c \cdot b + t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
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))) (t_2 (+ (* c b) (* -4.0 (* t a)))))
   (if (<= a -4.8e+80)
     t_2
     (if (<= a -420000.0)
       (+ t_1 (* a (* -4.0 t)))
       (if (<= a -2.05e-44)
         (* x (* (* 18.0 y) (* z t)))
         (if (<= a 7.5e+155) (+ (* c b) t_1) 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 = k * (j * -27.0);
	double t_2 = (c * b) + (-4.0 * (t * a));
	double tmp;
	if (a <= -4.8e+80) {
		tmp = t_2;
	} else if (a <= -420000.0) {
		tmp = t_1 + (a * (-4.0 * t));
	} else if (a <= -2.05e-44) {
		tmp = x * ((18.0 * y) * (z * t));
	} else if (a <= 7.5e+155) {
		tmp = (c * b) + t_1;
	} else {
		tmp = 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 = k * (j * (-27.0d0))
    t_2 = (c * b) + ((-4.0d0) * (t * a))
    if (a <= (-4.8d+80)) then
        tmp = t_2
    else if (a <= (-420000.0d0)) then
        tmp = t_1 + (a * ((-4.0d0) * t))
    else if (a <= (-2.05d-44)) then
        tmp = x * ((18.0d0 * y) * (z * t))
    else if (a <= 7.5d+155) then
        tmp = (c * b) + t_1
    else
        tmp = 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 = k * (j * -27.0);
	double t_2 = (c * b) + (-4.0 * (t * a));
	double tmp;
	if (a <= -4.8e+80) {
		tmp = t_2;
	} else if (a <= -420000.0) {
		tmp = t_1 + (a * (-4.0 * t));
	} else if (a <= -2.05e-44) {
		tmp = x * ((18.0 * y) * (z * t));
	} else if (a <= 7.5e+155) {
		tmp = (c * b) + t_1;
	} else {
		tmp = 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 = k * (j * -27.0)
	t_2 = (c * b) + (-4.0 * (t * a))
	tmp = 0
	if a <= -4.8e+80:
		tmp = t_2
	elif a <= -420000.0:
		tmp = t_1 + (a * (-4.0 * t))
	elif a <= -2.05e-44:
		tmp = x * ((18.0 * y) * (z * t))
	elif a <= 7.5e+155:
		tmp = (c * b) + t_1
	else:
		tmp = 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(k * Float64(j * -27.0))
	t_2 = Float64(Float64(c * b) + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (a <= -4.8e+80)
		tmp = t_2;
	elseif (a <= -420000.0)
		tmp = Float64(t_1 + Float64(a * Float64(-4.0 * t)));
	elseif (a <= -2.05e-44)
		tmp = Float64(x * Float64(Float64(18.0 * y) * Float64(z * t)));
	elseif (a <= 7.5e+155)
		tmp = Float64(Float64(c * b) + t_1);
	else
		tmp = 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 = k * (j * -27.0);
	t_2 = (c * b) + (-4.0 * (t * a));
	tmp = 0.0;
	if (a <= -4.8e+80)
		tmp = t_2;
	elseif (a <= -420000.0)
		tmp = t_1 + (a * (-4.0 * t));
	elseif (a <= -2.05e-44)
		tmp = x * ((18.0 * y) * (z * t));
	elseif (a <= 7.5e+155)
		tmp = (c * b) + t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
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]}, Block[{t$95$2 = N[(N[(c * b), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+80], t$95$2, If[LessEqual[a, -420000.0], N[(t$95$1 + N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.05e-44], N[(x * N[(N[(18.0 * y), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e+155], N[(N[(c * b), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.79999999999999958e80 or 7.4999999999999999e155 < a

   1. Initial program 78.8%

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

      1. sub-neg 78.8%

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

      2. associate-+l- 78.8%

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

      3. sub-neg 78.8%

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

      4. sub-neg 78.8%

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

      5. distribute-rgt-out-- 83.8%

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

      6. associate-*l* 80.0%

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

      7. distribute-lft-neg-in 80.0%

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

      8. cancel-sign-sub 80.0%

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

      9. associate-*l* 80.0%

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

      10. associate-*l* 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in x around 0 74.1%

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

   5. Taylor expanded in k around 0 66.9%

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

   if -4.79999999999999958e80 < a < -4.2e5

   1. Initial program 73.3%

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

      1. sub-neg 73.3%

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

      2. *-commutative 73.3%

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

      3. distribute-rgt-neg-in 73.3%

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

   3. Simplified 81.5%

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

      1. fma-udef 81.5%

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

   5. Applied egg-rr 81.5%

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

   6. Taylor expanded in a around inf 72.7%

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

      1. associate-*r* 72.7%

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

      2. *-commutative 72.7%

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

      3. associate-*l* 72.7%

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

   8. Simplified 72.7%

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

   if -4.2e5 < a < -2.04999999999999996e-44

   1. Initial program 88.9%

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

      1. sub-neg 88.9%

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

      2. associate-+l- 88.9%

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

      3. sub-neg 88.9%

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

      4. sub-neg 88.9%

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

      5. distribute-rgt-out-- 88.9%

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

      6. associate-*l* 88.9%

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

      7. distribute-lft-neg-in 88.9%

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

      8. cancel-sign-sub 88.9%

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

      9. associate-*l* 88.9%

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

      10. associate-*l* 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in x around inf 76.6%

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

   5. Taylor expanded in y around inf 52.3%

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

      1. associate-*r* 52.3%

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

      2. *-commutative 52.3%

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

   7. Simplified 52.3%

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

   if -2.04999999999999996e-44 < a < 7.4999999999999999e155

   1. Initial program 89.7%

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

      1. sub-neg 89.7%

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

      2. *-commutative 89.7%

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

      3. distribute-rgt-neg-in 89.7%

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

   3. Simplified 88.6%

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

      1. fma-udef 88.6%

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

   5. Applied egg-rr 88.6%

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

   6. Taylor expanded in b around inf 54.2%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+80}:\\ \;\;\;\;c \cdot b + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;a \leq -420000:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + a \cdot \left(-4 \cdot t\right)\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+155}:\\ \;\;\;\;c \cdot b + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 19: 30.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;i \leq -5.8 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -3.7 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.65 \cdot 10^{+20}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{+194}:\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* -27.0 (* j k))) (t_2 (* -4.0 (* x i))))
   (if (<= i -5.8e+39)
     t_2
     (if (<= i -3.7e-202)
       t_1
       (if (<= i 2.65e+20)
         (* c b)
         (if (<= i 2.1e+127) t_1 (if (<= i 3.8e+194) (* c b) 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 = -27.0 * (j * k);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if (i <= -5.8e+39) {
		tmp = t_2;
	} else if (i <= -3.7e-202) {
		tmp = t_1;
	} else if (i <= 2.65e+20) {
		tmp = c * b;
	} else if (i <= 2.1e+127) {
		tmp = t_1;
	} else if (i <= 3.8e+194) {
		tmp = c * b;
	} else {
		tmp = 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 = (-27.0d0) * (j * k)
    t_2 = (-4.0d0) * (x * i)
    if (i <= (-5.8d+39)) then
        tmp = t_2
    else if (i <= (-3.7d-202)) then
        tmp = t_1
    else if (i <= 2.65d+20) then
        tmp = c * b
    else if (i <= 2.1d+127) then
        tmp = t_1
    else if (i <= 3.8d+194) then
        tmp = c * b
    else
        tmp = 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 = -27.0 * (j * k);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if (i <= -5.8e+39) {
		tmp = t_2;
	} else if (i <= -3.7e-202) {
		tmp = t_1;
	} else if (i <= 2.65e+20) {
		tmp = c * b;
	} else if (i <= 2.1e+127) {
		tmp = t_1;
	} else if (i <= 3.8e+194) {
		tmp = c * b;
	} else {
		tmp = 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 = -27.0 * (j * k)
	t_2 = -4.0 * (x * i)
	tmp = 0
	if i <= -5.8e+39:
		tmp = t_2
	elif i <= -3.7e-202:
		tmp = t_1
	elif i <= 2.65e+20:
		tmp = c * b
	elif i <= 2.1e+127:
		tmp = t_1
	elif i <= 3.8e+194:
		tmp = c * b
	else:
		tmp = 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(-27.0 * Float64(j * k))
	t_2 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (i <= -5.8e+39)
		tmp = t_2;
	elseif (i <= -3.7e-202)
		tmp = t_1;
	elseif (i <= 2.65e+20)
		tmp = Float64(c * b);
	elseif (i <= 2.1e+127)
		tmp = t_1;
	elseif (i <= 3.8e+194)
		tmp = Float64(c * b);
	else
		tmp = 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 = -27.0 * (j * k);
	t_2 = -4.0 * (x * i);
	tmp = 0.0;
	if (i <= -5.8e+39)
		tmp = t_2;
	elseif (i <= -3.7e-202)
		tmp = t_1;
	elseif (i <= 2.65e+20)
		tmp = c * b;
	elseif (i <= 2.1e+127)
		tmp = t_1;
	elseif (i <= 3.8e+194)
		tmp = c * b;
	else
		tmp = 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[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.8e+39], t$95$2, If[LessEqual[i, -3.7e-202], t$95$1, If[LessEqual[i, 2.65e+20], N[(c * b), $MachinePrecision], If[LessEqual[i, 2.1e+127], t$95$1, If[LessEqual[i, 3.8e+194], N[(c * b), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -5.80000000000000059e39 or 3.7999999999999999e194 < i

   1. Initial program 87.7%

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

      1. sub-neg 87.7%

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

      2. +-commutative 87.7%

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

      3. associate-*l* 87.7%

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

      4. distribute-rgt-neg-in 87.7%

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

      5. fma-def 88.9%

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

      6. *-commutative 88.9%

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

      7. distribute-rgt-neg-in 88.9%

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

      8. metadata-eval 88.9%

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

      9. sub-neg 88.9%

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

      10. +-commutative 88.9%

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

      11. associate-*l* 88.9%

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

      12. distribute-rgt-neg-in 88.9%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in i around inf 56.7%

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

      1. *-commutative 56.7%

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

   6. Simplified 56.7%

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

   if -5.80000000000000059e39 < i < -3.69999999999999991e-202 or 2.65e20 < i < 2.09999999999999992e127

   1. Initial program 83.0%

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

      1. sub-neg 83.0%

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

      2. +-commutative 83.0%

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

      3. associate-*l* 83.0%

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

      4. distribute-rgt-neg-in 83.0%

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

      5. fma-def 85.5%

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

      6. *-commutative 85.5%

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

      7. distribute-rgt-neg-in 85.5%

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

      8. metadata-eval 85.5%

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

      9. sub-neg 85.5%

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

      10. +-commutative 85.5%

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

      11. associate-*l* 85.5%

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

      12. distribute-rgt-neg-in 85.5%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in j around inf 41.0%

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

   if -3.69999999999999991e-202 < i < 2.65e20 or 2.09999999999999992e127 < i < 3.7999999999999999e194

   1. Initial program 85.9%

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

      1. sub-neg 85.9%

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

      2. *-commutative 85.9%

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

      3. distribute-rgt-neg-in 85.9%

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

   3. Simplified 84.8%

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

      1. fma-udef 84.8%

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

   5. Applied egg-rr 84.8%

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

   6. Taylor expanded in a around 0 73.1%

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

      1. fma-def 74.2%

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

      2. fma-def 74.2%

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

      3. *-commutative 74.2%

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

      4. associate-*r* 73.1%

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

      5. *-commutative 73.1%

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

   8. Simplified 73.1%

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

   9. Taylor expanded in c around inf 39.0%

      \[\leadsto \color{blue}{c \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.8 \cdot 10^{+39}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;i \leq -3.7 \cdot 10^{-202}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;i \leq 2.65 \cdot 10^{+20}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{+127}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{+194}:\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 20: 30.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;i \leq -1.25 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.9 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+18}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{+191}:\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* j (* k -27.0))) (t_2 (* -4.0 (* x i))))
   (if (<= i -1.25e+38)
     t_2
     (if (<= i -1.9e-202)
       t_1
       (if (<= i 7.8e+18)
         (* c b)
         (if (<= i 1.05e+90) t_1 (if (<= i 8.5e+191) (* c b) 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 = j * (k * -27.0);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if (i <= -1.25e+38) {
		tmp = t_2;
	} else if (i <= -1.9e-202) {
		tmp = t_1;
	} else if (i <= 7.8e+18) {
		tmp = c * b;
	} else if (i <= 1.05e+90) {
		tmp = t_1;
	} else if (i <= 8.5e+191) {
		tmp = c * b;
	} else {
		tmp = 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 = j * (k * (-27.0d0))
    t_2 = (-4.0d0) * (x * i)
    if (i <= (-1.25d+38)) then
        tmp = t_2
    else if (i <= (-1.9d-202)) then
        tmp = t_1
    else if (i <= 7.8d+18) then
        tmp = c * b
    else if (i <= 1.05d+90) then
        tmp = t_1
    else if (i <= 8.5d+191) then
        tmp = c * b
    else
        tmp = 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 = j * (k * -27.0);
	double t_2 = -4.0 * (x * i);
	double tmp;
	if (i <= -1.25e+38) {
		tmp = t_2;
	} else if (i <= -1.9e-202) {
		tmp = t_1;
	} else if (i <= 7.8e+18) {
		tmp = c * b;
	} else if (i <= 1.05e+90) {
		tmp = t_1;
	} else if (i <= 8.5e+191) {
		tmp = c * b;
	} else {
		tmp = 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 = j * (k * -27.0)
	t_2 = -4.0 * (x * i)
	tmp = 0
	if i <= -1.25e+38:
		tmp = t_2
	elif i <= -1.9e-202:
		tmp = t_1
	elif i <= 7.8e+18:
		tmp = c * b
	elif i <= 1.05e+90:
		tmp = t_1
	elif i <= 8.5e+191:
		tmp = c * b
	else:
		tmp = 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(j * Float64(k * -27.0))
	t_2 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (i <= -1.25e+38)
		tmp = t_2;
	elseif (i <= -1.9e-202)
		tmp = t_1;
	elseif (i <= 7.8e+18)
		tmp = Float64(c * b);
	elseif (i <= 1.05e+90)
		tmp = t_1;
	elseif (i <= 8.5e+191)
		tmp = Float64(c * b);
	else
		tmp = 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 = j * (k * -27.0);
	t_2 = -4.0 * (x * i);
	tmp = 0.0;
	if (i <= -1.25e+38)
		tmp = t_2;
	elseif (i <= -1.9e-202)
		tmp = t_1;
	elseif (i <= 7.8e+18)
		tmp = c * b;
	elseif (i <= 1.05e+90)
		tmp = t_1;
	elseif (i <= 8.5e+191)
		tmp = c * b;
	else
		tmp = 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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.25e+38], t$95$2, If[LessEqual[i, -1.9e-202], t$95$1, If[LessEqual[i, 7.8e+18], N[(c * b), $MachinePrecision], If[LessEqual[i, 1.05e+90], t$95$1, If[LessEqual[i, 8.5e+191], N[(c * b), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.24999999999999992e38 or 8.4999999999999999e191 < i

   1. Initial program 87.7%

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

      1. sub-neg 87.7%

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

      2. +-commutative 87.7%

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

      3. associate-*l* 87.7%

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

      4. distribute-rgt-neg-in 87.7%

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

      5. fma-def 88.9%

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

      6. *-commutative 88.9%

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

      7. distribute-rgt-neg-in 88.9%

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

      8. metadata-eval 88.9%

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

      9. sub-neg 88.9%

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

      10. +-commutative 88.9%

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

      11. associate-*l* 88.9%

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

      12. distribute-rgt-neg-in 88.9%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in i around inf 56.7%

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

      1. *-commutative 56.7%

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

   6. Simplified 56.7%

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

   if -1.24999999999999992e38 < i < -1.90000000000000007e-202 or 7.8e18 < i < 1.0499999999999999e90

   1. Initial program 83.9%

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

      1. sub-neg 83.9%

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

      2. *-commutative 83.9%

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

      3. distribute-rgt-neg-in 83.9%

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

   3. Simplified 86.7%

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

      1. fma-udef 86.7%

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

   5. Applied egg-rr 86.7%

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

   6. Taylor expanded in a around 0 73.0%

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

      1. fma-def 73.0%

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

      2. fma-def 73.0%

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

      3. *-commutative 73.0%

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

      4. associate-*r* 73.0%

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

      5. *-commutative 73.0%

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

   8. Simplified 73.0%

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

   9. Taylor expanded in k around inf 41.2%

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

       1. associate-*r* 41.3%

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

   11. Simplified 41.3%

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

   if -1.90000000000000007e-202 < i < 7.8e18 or 1.0499999999999999e90 < i < 8.4999999999999999e191

   1. Initial program 85.1%

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

      1. sub-neg 85.1%

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

      2. *-commutative 85.1%

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

      3. distribute-rgt-neg-in 85.1%

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

   3. Simplified 84.0%

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

      1. fma-udef 84.0%

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

   5. Applied egg-rr 84.0%

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

   6. Taylor expanded in a around 0 73.3%

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

      1. fma-def 74.3%

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

      2. fma-def 74.3%

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

      3. *-commutative 74.3%

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

      4. associate-*r* 73.3%

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

      5. *-commutative 73.3%

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

   8. Simplified 73.3%

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

   9. Taylor expanded in c around inf 39.0%

      \[\leadsto \color{blue}{c \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.25 \cdot 10^{+38}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;i \leq -1.9 \cdot 10^{-202}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{+18}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+90}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{+191}:\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 21: 33.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -9.6 \cdot 10^{+193} \lor \neg \left(j \leq -1.15 \cdot 10^{+162}\right) \land \left(j \leq -1.7 \cdot 10^{+44} \lor \neg \left(j \leq 4.9 \cdot 10^{-36}\right)\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

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 (<= j -9.6e+193)
         (and (not (<= j -1.15e+162))
              (or (<= j -1.7e+44) (not (<= j 4.9e-36)))))
   (* -27.0 (* j k))
   (* c b)))

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 ((j <= -9.6e+193) || (!(j <= -1.15e+162) && ((j <= -1.7e+44) || !(j <= 4.9e-36)))) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = c * b;
	}
	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 ((j <= (-9.6d+193)) .or. (.not. (j <= (-1.15d+162))) .and. (j <= (-1.7d+44)) .or. (.not. (j <= 4.9d-36))) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = c * b
    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 ((j <= -9.6e+193) || (!(j <= -1.15e+162) && ((j <= -1.7e+44) || !(j <= 4.9e-36)))) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = c * b;
	}
	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 (j <= -9.6e+193) or (not (j <= -1.15e+162) and ((j <= -1.7e+44) or not (j <= 4.9e-36))):
		tmp = -27.0 * (j * k)
	else:
		tmp = c * b
	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 ((j <= -9.6e+193) || (!(j <= -1.15e+162) && ((j <= -1.7e+44) || !(j <= 4.9e-36))))
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(c * b);
	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 ((j <= -9.6e+193) || (~((j <= -1.15e+162)) && ((j <= -1.7e+44) || ~((j <= 4.9e-36)))))
		tmp = -27.0 * (j * k);
	else
		tmp = c * b;
	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[j, -9.6e+193], And[N[Not[LessEqual[j, -1.15e+162]], $MachinePrecision], Or[LessEqual[j, -1.7e+44], N[Not[LessEqual[j, 4.9e-36]], $MachinePrecision]]]], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -9.6e193 or -1.14999999999999997e162 < j < -1.7e44 or 4.8999999999999997e-36 < j

   1. Initial program 81.2%

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

      1. sub-neg 81.2%

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

      2. +-commutative 81.2%

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

      3. associate-*l* 81.2%

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

      4. distribute-rgt-neg-in 81.2%

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

      5. fma-def 84.4%

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

      6. *-commutative 84.4%

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

      7. distribute-rgt-neg-in 84.4%

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

      8. metadata-eval 84.4%

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

      9. sub-neg 84.4%

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

      10. +-commutative 84.4%

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

      11. associate-*l* 84.4%

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

      12. distribute-rgt-neg-in 84.4%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in j around inf 42.0%

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

   if -9.6e193 < j < -1.14999999999999997e162 or -1.7e44 < j < 4.8999999999999997e-36

   1. Initial program 89.6%

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

      1. sub-neg 89.6%

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

      2. *-commutative 89.6%

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

      3. distribute-rgt-neg-in 89.6%

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

   3. Simplified 91.1%

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

      1. fma-udef 90.4%

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

   5. Applied egg-rr 90.4%

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

   6. Taylor expanded in a around 0 79.7%

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

      1. fma-def 80.5%

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

      2. fma-def 80.5%

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

      3. *-commutative 80.5%

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

      4. associate-*r* 80.5%

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

      5. *-commutative 80.5%

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

   8. Simplified 80.5%

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

   9. Taylor expanded in c around inf 33.4%

      \[\leadsto \color{blue}{c \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.6 \cdot 10^{+193} \lor \neg \left(j \leq -1.15 \cdot 10^{+162}\right) \land \left(j \leq -1.7 \cdot 10^{+44} \lor \neg \left(j \leq 4.9 \cdot 10^{-36}\right)\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \]

Alternative 22: 51.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -6.7 \cdot 10^{+109} \lor \neg \left(a \leq 2.05 \cdot 10^{+149}\right):\\ \;\;\;\;c \cdot b + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b + k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

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 (<= a -6.7e+109) (not (<= a 2.05e+149)))
   (+ (* c b) (* -4.0 (* t a)))
   (+ (* c b) (* 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 ((a <= -6.7e+109) || !(a <= 2.05e+149)) {
		tmp = (c * b) + (-4.0 * (t * a));
	} else {
		tmp = (c * b) + (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 ((a <= (-6.7d+109)) .or. (.not. (a <= 2.05d+149))) then
        tmp = (c * b) + ((-4.0d0) * (t * a))
    else
        tmp = (c * b) + (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 ((a <= -6.7e+109) || !(a <= 2.05e+149)) {
		tmp = (c * b) + (-4.0 * (t * a));
	} else {
		tmp = (c * b) + (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 (a <= -6.7e+109) or not (a <= 2.05e+149):
		tmp = (c * b) + (-4.0 * (t * a))
	else:
		tmp = (c * b) + (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 ((a <= -6.7e+109) || !(a <= 2.05e+149))
		tmp = Float64(Float64(c * b) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(c * b) + 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 ((a <= -6.7e+109) || ~((a <= 2.05e+149)))
		tmp = (c * b) + (-4.0 * (t * a));
	else
		tmp = (c * b) + (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[a, -6.7e+109], N[Not[LessEqual[a, 2.05e+149]], $MachinePrecision]], N[(N[(c * b), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * b), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.70000000000000036e109 or 2.0499999999999998e149 < a

   1. Initial program 80.2%

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

      1. sub-neg 80.2%

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

      2. associate-+l- 80.2%

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

      3. sub-neg 80.2%

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

      4. sub-neg 80.2%

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

      5. distribute-rgt-out-- 85.5%

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

      6. associate-*l* 82.8%

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

      7. distribute-lft-neg-in 82.8%

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

      8. cancel-sign-sub 82.8%

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

      9. associate-*l* 82.8%

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

      10. associate-*l* 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in x around 0 74.6%

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

   5. Taylor expanded in k around 0 67.0%

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

   if -6.70000000000000036e109 < a < 2.0499999999999998e149

   1. Initial program 87.8%

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

      1. sub-neg 87.8%

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

      2. *-commutative 87.8%

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

      3. distribute-rgt-neg-in 87.8%

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

   3. Simplified 86.8%

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

      1. fma-udef 86.8%

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

   5. Applied egg-rr 86.8%

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

   6. Taylor expanded in b around inf 52.8%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.7 \cdot 10^{+109} \lor \neg \left(a \leq 2.05 \cdot 10^{+149}\right):\\ \;\;\;\;c \cdot b + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 23: 47.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -2.85 \cdot 10^{+194}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-36}:\\ \;\;\;\;c \cdot b + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
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 (<= j -2.85e+194)
   (* j (* k -27.0))
   (if (<= j 4.8e-36) (+ (* c b) (* -4.0 (* t a))) (* -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 tmp;
	if (j <= -2.85e+194) {
		tmp = j * (k * -27.0);
	} else if (j <= 4.8e-36) {
		tmp = (c * b) + (-4.0 * (t * a));
	} else {
		tmp = -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) :: tmp
    if (j <= (-2.85d+194)) then
        tmp = j * (k * (-27.0d0))
    else if (j <= 4.8d-36) then
        tmp = (c * b) + ((-4.0d0) * (t * a))
    else
        tmp = (-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 tmp;
	if (j <= -2.85e+194) {
		tmp = j * (k * -27.0);
	} else if (j <= 4.8e-36) {
		tmp = (c * b) + (-4.0 * (t * a));
	} else {
		tmp = -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):
	tmp = 0
	if j <= -2.85e+194:
		tmp = j * (k * -27.0)
	elif j <= 4.8e-36:
		tmp = (c * b) + (-4.0 * (t * a))
	else:
		tmp = -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)
	tmp = 0.0
	if (j <= -2.85e+194)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (j <= 4.8e-36)
		tmp = Float64(Float64(c * b) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = 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)
	tmp = 0.0;
	if (j <= -2.85e+194)
		tmp = j * (k * -27.0);
	elseif (j <= 4.8e-36)
		tmp = (c * b) + (-4.0 * (t * a));
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
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[j, -2.85e+194], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.8e-36], N[(N[(c * b), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.84999999999999992e194

   1. Initial program 67.7%

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

      1. sub-neg 67.7%

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

      2. *-commutative 67.7%

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

      3. distribute-rgt-neg-in 67.7%

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

   3. Simplified 67.7%

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

      1. fma-udef 67.7%

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

   5. Applied egg-rr 67.7%

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

   6. Taylor expanded in a around 0 68.0%

      \[\leadsto \color{blue}{\left(c \cdot b + \left(-4 \cdot \left(i \cdot x\right) + 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right)\right)} + k \cdot \left(j \cdot -27\right) \]
   7. Step-by-step derivation

      1. fma-def 68.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, -4 \cdot \left(i \cdot x\right) + 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right)} + k \cdot \left(j \cdot -27\right) \]

      2. fma-def 68.0%

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-4, i \cdot x, 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right)}\right) + k \cdot \left(j \cdot -27\right) \]

      3. *-commutative 68.0%

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4, \color{blue}{x \cdot i}, 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right)\right) + k \cdot \left(j \cdot -27\right) \]

      4. associate-*r* 68.0%

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)}\right)\right) + k \cdot \left(j \cdot -27\right) \]

      5. *-commutative 68.0%

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4, x \cdot i, \left(18 \cdot y\right) \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)}\right)\right) + k \cdot \left(j \cdot -27\right) \]

   8. Simplified 68.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-4, x \cdot i, \left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right)\right)\right)} + k \cdot \left(j \cdot -27\right) \]

   9. Taylor expanded in k around inf 56.6%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 56.7%

          \[\leadsto \color{blue}{\left(-27 \cdot k\right) \cdot j} \]

   11. Simplified 56.7%

       \[\leadsto \color{blue}{\left(-27 \cdot k\right) \cdot j} \]

   if -2.84999999999999992e194 < j < 4.8e-36

   1. Initial program 88.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 88.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 88.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 88.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 88.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 90.2%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 88.9%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 88.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 88.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 88.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 88.9%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around 0 58.1%

      \[\leadsto \color{blue}{\left(c \cdot b + -4 \cdot \left(a \cdot t\right)\right) - 27 \cdot \left(k \cdot j\right)} \]

   5. Taylor expanded in k around 0 45.8%

      \[\leadsto \color{blue}{c \cdot b + -4 \cdot \left(a \cdot t\right)} \]

   if 4.8e-36 < j

   1. Initial program 85.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 85.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. +-commutative 85.7%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 85.6%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 85.6%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 88.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 88.2%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 88.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 88.2%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 88.2%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 88.2%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 88.2%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 88.2%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 93.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 34.5%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.85 \cdot 10^{+194}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-36}:\\ \;\;\;\;c \cdot b + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 24: 24.2% accurate, 10.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ c \cdot b \end{array} \]

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 (* c b))

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 c * b;
}

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 = c * b
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 c * b;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return c * b

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(c * b)
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 = c * b;
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[(c * b), $MachinePrecision]

Derivation

1. Initial program 85.6%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Step-by-step derivation

   1. sub-neg 85.6%

      \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

   2. *-commutative 85.6%

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\color{blue}{k \cdot \left(j \cdot 27\right)}\right) \]

   3. distribute-rgt-neg-in 85.6%

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \color{blue}{k \cdot \left(-j \cdot 27\right)} \]

3. Simplified 86.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x \cdot 18, y \cdot z, a \cdot -4\right), \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right) + k \cdot \left(j \cdot -27\right)} \]
4. Step-by-step derivation

   1. fma-udef 85.6%

      \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(x \cdot 18, y \cdot z, a \cdot -4\right), \color{blue}{b \cdot c + i \cdot \left(x \cdot -4\right)}\right) + k \cdot \left(j \cdot -27\right) \]

5. Applied egg-rr 85.6%

   \[\leadsto \mathsf{fma}\left(t, \mathsf{fma}\left(x \cdot 18, y \cdot z, a \cdot -4\right), \color{blue}{b \cdot c + i \cdot \left(x \cdot -4\right)}\right) + k \cdot \left(j \cdot -27\right) \]

6. Taylor expanded in a around 0 75.1%

   \[\leadsto \color{blue}{\left(c \cdot b + \left(-4 \cdot \left(i \cdot x\right) + 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right)\right)} + k \cdot \left(j \cdot -27\right) \]
7. Step-by-step derivation

   1. fma-def 75.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, -4 \cdot \left(i \cdot x\right) + 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right)} + k \cdot \left(j \cdot -27\right) \]

   2. fma-def 75.9%

      \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(-4, i \cdot x, 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right)}\right) + k \cdot \left(j \cdot -27\right) \]

   3. *-commutative 75.9%

      \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4, \color{blue}{x \cdot i}, 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right)\right) + k \cdot \left(j \cdot -27\right) \]

   4. associate-*r* 75.5%

      \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4, x \cdot i, \color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)}\right)\right) + k \cdot \left(j \cdot -27\right) \]

   5. *-commutative 75.5%

      \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(-4, x \cdot i, \left(18 \cdot y\right) \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)}\right)\right) + k \cdot \left(j \cdot -27\right) \]

8. Simplified 75.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(-4, x \cdot i, \left(18 \cdot y\right) \cdot \left(\left(z \cdot x\right) \cdot t\right)\right)\right)} + k \cdot \left(j \cdot -27\right) \]

9. Taylor expanded in c around inf 26.0%

   \[\leadsto \color{blue}{c \cdot b} \]

10. Final simplification 26.0%

    \[\leadsto c \cdot b \]

Developer target: 89.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023278 
(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)))