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

Percentage Accurate: 85.4% → 89.0%

Time: 26.9s

Alternatives: 22

Speedup: 1.0×

• 50.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{+296}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x \cdot 18, y \cdot z, -4 \cdot a\right), \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

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)) -5e+296)
   (fma j (* k -27.0) (fma x (* i -4.0) (* b c)))
   (+
    (fma t (fma (* x 18.0) (* y z) (* -4.0 a)) (fma b c (* i (* x -4.0))))
    (* k (* j -27.0)))))

C

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)) <= -5e+296) {
		tmp = fma(j, (k * -27.0), fma(x, (i * -4.0), (b * c)));
	} else {
		tmp = fma(t, fma((x * 18.0), (y * z), (-4.0 * a)), fma(b, c, (i * (x * -4.0)))) + (k * (j * -27.0));
	}
	return tmp;
}

Julia

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)) <= -5e+296)
		tmp = fma(j, Float64(k * -27.0), fma(x, Float64(i * -4.0), Float64(b * c)));
	else
		tmp = Float64(fma(t, fma(Float64(x * 18.0), Float64(y * z), Float64(-4.0 * a)), fma(b, c, Float64(i * Float64(x * -4.0)))) + Float64(k * Float64(j * -27.0)));
	end
	return tmp
end

Wolfram

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], -5e+296], N[(j * N[(k * -27.0), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j 27) k) < -5.0000000000000001e296

   1. Initial program 63.2%

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

      1. sub-neg 63.2%

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

      2. +-commutative 63.2%

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

      3. associate-*l* 63.1%

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

      4. distribute-rgt-neg-in 63.1%

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

      5. fma-def 68.3%

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

      6. *-commutative 68.3%

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

      7. distribute-rgt-neg-in 68.3%

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

      8. metadata-eval 68.3%

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

      9. sub-neg 68.3%

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

      10. +-commutative 68.3%

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

      11. associate-*l* 68.3%

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

      12. distribute-rgt-neg-in 68.3%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in t around 0 94.7%

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

   if -5.0000000000000001e296 < (*.f64 (*.f64 j 27) k)

   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. Step-by-step derivation

      1. sub-neg 87.6%

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

      2. *-commutative 87.6%

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

      3. distribute-rgt-neg-in 87.6%

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

   3. Simplified 93.8%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \cdot \left(j \cdot 27\right) \leq -5 \cdot 10^{+296}:\\ \;\;\;\;\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \mathsf{fma}\left(x \cdot 18, y \cdot z, -4 \cdot a\right), \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 2: 90.9% accurate, 0.1× speedup

Math

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

FPCore

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
 (fma
  j
  (* k -27.0)
  (fma x (* i -4.0) (fma t (fma x (* 18.0 (* y z)) (* -4.0 a)) (* b c)))))

C

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 fma(j, (k * -27.0), fma(x, (i * -4.0), fma(t, fma(x, (18.0 * (y * z)), (-4.0 * a)), (b * c))));
}

Julia

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

Wolfram

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[(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[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.8%

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

   1. sub-neg 85.8%

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

   2. +-commutative 85.8%

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

   3. associate-*l* 85.8%

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

   4. distribute-rgt-neg-in 85.8%

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

   5. fma-def 86.6%

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

   6. *-commutative 86.6%

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

   7. distribute-rgt-neg-in 86.6%

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

   8. metadata-eval 86.6%

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

   9. sub-neg 86.6%

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

   10. +-commutative 86.6%

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

   11. associate-*l* 86.6%

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

   12. distribute-rgt-neg-in 86.6%

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

3. Simplified 93.5%

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

4. Final simplification 93.5%

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

Alternative 3: 90.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] + N[(-27.0 * N[(j * k), $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 94.7%

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

      1. sub-neg 94.7%

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

      2. associate-+l- 94.7%

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

      3. sub-neg 94.7%

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

      4. sub-neg 94.7%

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

      5. distribute-rgt-out-- 94.6%

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

      6. associate-*l* 96.7%

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

      7. distribute-lft-neg-in 96.7%

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

      8. cancel-sign-sub 96.7%

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

      9. associate-*l* 96.7%

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

      10. associate-*l* 96.7%

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

   3. Simplified 96.7%

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

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

   1. Initial program 0.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in t around 0 66.7%

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

4. Final simplification 93.9%

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

Alternative 4: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -4.4 \cdot 10^{+55}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \end{array} \]

FPCore

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 (<= i -4.4e+55)
   (- (+ (* b c) (* -4.0 (* t a))) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
   (-
    (+ (* b c) (* t (- (* (* y z) (* x 18.0)) (* a 4.0))))
    (+ (* x (* i 4.0)) (* j (* k 27.0))))))

C

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 <= -4.4e+55) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	}
	return tmp;
}

Fortran

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 <= (-4.4d+55)) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    else
        tmp = ((b * c) + (t * (((y * z) * (x * 18.0d0)) - (a * 4.0d0)))) - ((x * (i * 4.0d0)) + (j * (k * 27.0d0)))
    end if
    code = tmp
end function

Java

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 <= -4.4e+55) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} else {
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if i <= -4.4e+55:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	else:
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)))
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (i <= -4.4e+55)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(y * z) * Float64(x * 18.0)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(i * 4.0)) + Float64(j * Float64(k * 27.0))));
	end
	return tmp
end

MATLAB

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 <= -4.4e+55)
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	else
		tmp = ((b * c) + (t * (((y * z) * (x * 18.0)) - (a * 4.0)))) - ((x * (i * 4.0)) + (j * (k * 27.0)));
	end
	tmp_2 = tmp;
end

Wolfram

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[i, -4.4e+55], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $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 i < -4.40000000000000021e55

   1. Initial program 78.7%

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

      1. sub-neg 78.7%

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

      2. associate-+l- 78.7%

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

      3. sub-neg 78.7%

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

      4. sub-neg 78.7%

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

      5. distribute-rgt-out-- 81.1%

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

      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 y around 0 92.9%

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

   if -4.40000000000000021e55 < i

   1. Initial program 87.2%

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

      1. sub-neg 87.2%

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

      2. associate-+l- 87.2%

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

      3. sub-neg 87.2%

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

      4. sub-neg 87.2%

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

      5. distribute-rgt-out-- 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* 93.6%

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

      7. distribute-lft-neg-in 93.6%

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

      8. cancel-sign-sub 93.6%

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

      9. associate-*l* 93.6%

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

      10. associate-*l* 93.6%

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

   3. Simplified 93.6%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.4 \cdot 10^{+55}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right) - a \cdot 4\right)\right) - \left(x \cdot \left(i \cdot 4\right) + j \cdot \left(k \cdot 27\right)\right)\\ \end{array} \]

Alternative 5: 74.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c - \left(t_1 + 27 \cdot \left(j \cdot k\right)\right)\\ t_3 := b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -5.7 \cdot 10^{+102}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.66 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-79}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-114}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

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 (- (* b c) (+ t_1 (* 27.0 (* j k)))))
        (t_3 (+ (* b c) (* t (- (* 18.0 (* y (* x z))) (* a 4.0))))))
   (if (<= t -5.7e+102)
     t_3
     (if (<= t -1.66e-46)
       t_2
       (if (<= t -6e-79)
         t_3
         (if (<= t -2.6e-114)
           (- (+ (* b c) (* -4.0 (* t a))) t_1)
           (if (<= t 3.9e+64) t_2 t_3)))))))

C

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 = (b * c) - (t_1 + (27.0 * (j * k)));
	double t_3 = (b * c) + (t * ((18.0 * (y * (x * z))) - (a * 4.0)));
	double tmp;
	if (t <= -5.7e+102) {
		tmp = t_3;
	} else if (t <= -1.66e-46) {
		tmp = t_2;
	} else if (t <= -6e-79) {
		tmp = t_3;
	} else if (t <= -2.6e-114) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (t <= 3.9e+64) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

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 = 4.0d0 * (x * i)
    t_2 = (b * c) - (t_1 + (27.0d0 * (j * k)))
    t_3 = (b * c) + (t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0)))
    if (t <= (-5.7d+102)) then
        tmp = t_3
    else if (t <= (-1.66d-46)) then
        tmp = t_2
    else if (t <= (-6d-79)) then
        tmp = t_3
    else if (t <= (-2.6d-114)) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - t_1
    else if (t <= 3.9d+64) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

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 = (b * c) - (t_1 + (27.0 * (j * k)));
	double t_3 = (b * c) + (t * ((18.0 * (y * (x * z))) - (a * 4.0)));
	double tmp;
	if (t <= -5.7e+102) {
		tmp = t_3;
	} else if (t <= -1.66e-46) {
		tmp = t_2;
	} else if (t <= -6e-79) {
		tmp = t_3;
	} else if (t <= -2.6e-114) {
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	} else if (t <= 3.9e+64) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[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 = (b * c) - (t_1 + (27.0 * (j * k)))
	t_3 = (b * c) + (t * ((18.0 * (y * (x * z))) - (a * 4.0)))
	tmp = 0
	if t <= -5.7e+102:
		tmp = t_3
	elif t <= -1.66e-46:
		tmp = t_2
	elif t <= -6e-79:
		tmp = t_3
	elif t <= -2.6e-114:
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1
	elif t <= 3.9e+64:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

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(b * c) - Float64(t_1 + Float64(27.0 * Float64(j * k))))
	t_3 = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0))))
	tmp = 0.0
	if (t <= -5.7e+102)
		tmp = t_3;
	elseif (t <= -1.66e-46)
		tmp = t_2;
	elseif (t <= -6e-79)
		tmp = t_3;
	elseif (t <= -2.6e-114)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - t_1);
	elseif (t <= 3.9e+64)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

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 = (b * c) - (t_1 + (27.0 * (j * k)));
	t_3 = (b * c) + (t * ((18.0 * (y * (x * z))) - (a * 4.0)));
	tmp = 0.0;
	if (t <= -5.7e+102)
		tmp = t_3;
	elseif (t <= -1.66e-46)
		tmp = t_2;
	elseif (t <= -6e-79)
		tmp = t_3;
	elseif (t <= -2.6e-114)
		tmp = ((b * c) + (-4.0 * (t * a))) - t_1;
	elseif (t <= 3.9e+64)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

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[(b * c), $MachinePrecision] - N[(t$95$1 + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.7e+102], t$95$3, If[LessEqual[t, -1.66e-46], t$95$2, If[LessEqual[t, -6e-79], t$95$3, If[LessEqual[t, -2.6e-114], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 3.9e+64], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.6999999999999999e102 or -1.6599999999999999e-46 < t < -5.99999999999999999e-79 or 3.8999999999999998e64 < t

   1. Initial program 84.2%

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

      1. sub-neg 84.2%

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

      2. associate-+l- 84.2%

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

      3. sub-neg 84.2%

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

      4. sub-neg 84.2%

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

      5. distribute-rgt-out-- 91.3%

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

      6. associate-*l* 92.0%

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

      7. distribute-lft-neg-in 92.0%

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

      8. cancel-sign-sub 92.0%

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

      9. associate-*l* 92.0%

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

      10. associate-*l* 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in i around 0 91.2%

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

   5. Taylor expanded in k around 0 89.5%

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

   if -5.6999999999999999e102 < t < -1.6599999999999999e-46 or -2.60000000000000013e-114 < t < 3.8999999999999998e64

   1. Initial program 86.5%

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

      1. sub-neg 86.5%

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

      2. associate-+l- 86.5%

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

      3. sub-neg 86.5%

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

      4. sub-neg 86.5%

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

      5. distribute-rgt-out-- 86.5%

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

      6. associate-*l* 90.8%

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

      7. distribute-lft-neg-in 90.8%

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

      8. cancel-sign-sub 90.8%

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

      9. associate-*l* 90.8%

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

      10. associate-*l* 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around 0 79.4%

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

   if -5.99999999999999999e-79 < t < -2.60000000000000013e-114

   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* 100.0%

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

      7. distribute-lft-neg-in 100.0%

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

      8. cancel-sign-sub 100.0%

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

      9. associate-*l* 100.0%

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

      10. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in k around 0 100.0%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{+102}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.66 \cdot 10^{-46}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-79}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-114}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+64}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 6: 84.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;t \leq -8.4 \cdot 10^{+74} \lor \neg \left(t \leq 2.6 \cdot 10^{+49}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + t_1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 27.0 (* j k))))
   (if (or (<= t -8.4e+74) (not (<= t 2.6e+49)))
     (- (+ (* b c) (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))) t_1)
     (- (+ (* b c) (* -4.0 (* t a))) (+ (* 4.0 (* x i)) t_1)))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double tmp;
	if ((t <= -8.4e+74) || !(t <= 2.6e+49)) {
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) - (a * 4.0)))) - t_1;
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + t_1);
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (j * k)
    if ((t <= (-8.4d+74)) .or. (.not. (t <= 2.6d+49))) then
        tmp = ((b * c) + (t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0)))) - t_1
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((4.0d0 * (x * i)) + t_1)
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double tmp;
	if ((t <= -8.4e+74) || !(t <= 2.6e+49)) {
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) - (a * 4.0)))) - t_1;
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + t_1);
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	tmp = 0
	if (t <= -8.4e+74) or not (t <= 2.6e+49):
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) - (a * 4.0)))) - t_1
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + t_1)
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	tmp = 0.0
	if ((t <= -8.4e+74) || !(t <= 2.6e+49))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(4.0 * Float64(x * i)) + t_1));
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 27.0 * (j * k);
	tmp = 0.0;
	if ((t <= -8.4e+74) || ~((t <= 2.6e+49)))
		tmp = ((b * c) + (t * ((18.0 * (y * (x * z))) - (a * 4.0)))) - t_1;
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -8.4e+74], N[Not[LessEqual[t, 2.6e+49]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.3999999999999995e74 or 2.59999999999999989e49 < t

   1. Initial program 83.8%

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

      1. sub-neg 83.8%

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

      2. associate-+l- 83.8%

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

      3. sub-neg 83.8%

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

      4. sub-neg 83.8%

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

      5. distribute-rgt-out-- 90.6%

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

      6. associate-*l* 91.4%

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

      7. distribute-lft-neg-in 91.4%

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

      8. cancel-sign-sub 91.4%

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

      9. associate-*l* 91.4%

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

      10. associate-*l* 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in i around 0 90.6%

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

   if -8.3999999999999995e74 < t < 2.59999999999999989e49

   1. Initial program 87.5%

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

      1. sub-neg 87.5%

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

      2. associate-+l- 87.5%

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

      3. sub-neg 87.5%

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

      4. sub-neg 87.5%

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

      5. distribute-rgt-out-- 87.4%

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

      6. associate-*l* 91.6%

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

      7. distribute-lft-neg-in 91.6%

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

      8. cancel-sign-sub 91.6%

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

      9. associate-*l* 91.6%

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

      10. associate-*l* 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in y around 0 90.3%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{+74} \lor \neg \left(t \leq 2.6 \cdot 10^{+49}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \end{array} \]

Alternative 7: 55.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_2 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -480000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* j k))))
        (t_2 (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))))
   (if (<= t -6e+192)
     t_2
     (if (<= t -8.5e+144)
       t_1
       (if (<= t -480000000.0)
         t_2
         (if (<= t -4.1e-198)
           t_1
           (if (<= t -9.5e-298)
             (* x (* i -4.0))
             (if (<= t 1.95e+99) t_1 t_2))))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double t_2 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double tmp;
	if (t <= -6e+192) {
		tmp = t_2;
	} else if (t <= -8.5e+144) {
		tmp = t_1;
	} else if (t <= -480000000.0) {
		tmp = t_2;
	} else if (t <= -4.1e-198) {
		tmp = t_1;
	} else if (t <= -9.5e-298) {
		tmp = x * (i * -4.0);
	} else if (t <= 1.95e+99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - (27.0d0 * (j * k))
    t_2 = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    if (t <= (-6d+192)) then
        tmp = t_2
    else if (t <= (-8.5d+144)) then
        tmp = t_1
    else if (t <= (-480000000.0d0)) then
        tmp = t_2
    else if (t <= (-4.1d-198)) then
        tmp = t_1
    else if (t <= (-9.5d-298)) then
        tmp = x * (i * (-4.0d0))
    else if (t <= 1.95d+99) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double t_2 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double tmp;
	if (t <= -6e+192) {
		tmp = t_2;
	} else if (t <= -8.5e+144) {
		tmp = t_1;
	} else if (t <= -480000000.0) {
		tmp = t_2;
	} else if (t <= -4.1e-198) {
		tmp = t_1;
	} else if (t <= -9.5e-298) {
		tmp = x * (i * -4.0);
	} else if (t <= 1.95e+99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (27.0 * (j * k))
	t_2 = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	tmp = 0
	if t <= -6e+192:
		tmp = t_2
	elif t <= -8.5e+144:
		tmp = t_1
	elif t <= -480000000.0:
		tmp = t_2
	elif t <= -4.1e-198:
		tmp = t_1
	elif t <= -9.5e-298:
		tmp = x * (i * -4.0)
	elif t <= 1.95e+99:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -6e+192)
		tmp = t_2;
	elseif (t <= -8.5e+144)
		tmp = t_1;
	elseif (t <= -480000000.0)
		tmp = t_2;
	elseif (t <= -4.1e-198)
		tmp = t_1;
	elseif (t <= -9.5e-298)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (t <= 1.95e+99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (27.0 * (j * k));
	t_2 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -6e+192)
		tmp = t_2;
	elseif (t <= -8.5e+144)
		tmp = t_1;
	elseif (t <= -480000000.0)
		tmp = t_2;
	elseif (t <= -4.1e-198)
		tmp = t_1;
	elseif (t <= -9.5e-298)
		tmp = x * (i * -4.0);
	elseif (t <= 1.95e+99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+192], t$95$2, If[LessEqual[t, -8.5e+144], t$95$1, If[LessEqual[t, -480000000.0], t$95$2, If[LessEqual[t, -4.1e-198], t$95$1, If[LessEqual[t, -9.5e-298], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+99], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6e192 or -8.4999999999999998e144 < t < -4.8e8 or 1.94999999999999997e99 < t

   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. Taylor expanded in i around 0 74.7%

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

   3. Taylor expanded in t around inf 83.3%

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

   if -6e192 < t < -8.4999999999999998e144 or -4.8e8 < t < -4.10000000000000012e-198 or -9.50000000000000012e-298 < t < 1.94999999999999997e99

   1. Initial program 87.2%

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

   2. Taylor expanded in i around 0 75.5%

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

   3. Taylor expanded in t around 0 58.3%

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

   if -4.10000000000000012e-198 < t < -9.50000000000000012e-298

   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* 88.4%

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

      4. distribute-rgt-neg-in 88.4%

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

      5. fma-def 88.4%

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

      6. *-commutative 88.4%

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

      7. distribute-rgt-neg-in 88.4%

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

      8. metadata-eval 88.4%

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

      9. sub-neg 88.4%

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

      10. +-commutative 88.4%

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

      11. associate-*l* 88.4%

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

      12. distribute-rgt-neg-in 88.4%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in i around inf 55.2%

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

      1. associate-*r* 55.2%

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

      2. *-commutative 55.2%

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

   6. Simplified 55.2%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+192}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+144}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -480000000:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+99}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 8: 55.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_2 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -6.6 \cdot 10^{+192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -490000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* j k))))
        (t_2 (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))))
   (if (<= t -6.6e+192)
     t_2
     (if (<= t -8.5e+144)
       t_1
       (if (<= t -490000000.0)
         t_2
         (if (<= t -3.8e-198)
           t_1
           (if (<= t -9.5e-298)
             (* x (* i -4.0))
             (if (<= t 2.9e+100)
               t_1
               (* t (- (* 18.0 (* z (* x y))) (* a 4.0)))))))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double t_2 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double tmp;
	if (t <= -6.6e+192) {
		tmp = t_2;
	} else if (t <= -8.5e+144) {
		tmp = t_1;
	} else if (t <= -490000000.0) {
		tmp = t_2;
	} else if (t <= -3.8e-198) {
		tmp = t_1;
	} else if (t <= -9.5e-298) {
		tmp = x * (i * -4.0);
	} else if (t <= 2.9e+100) {
		tmp = t_1;
	} else {
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - (27.0d0 * (j * k))
    t_2 = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    if (t <= (-6.6d+192)) then
        tmp = t_2
    else if (t <= (-8.5d+144)) then
        tmp = t_1
    else if (t <= (-490000000.0d0)) then
        tmp = t_2
    else if (t <= (-3.8d-198)) then
        tmp = t_1
    else if (t <= (-9.5d-298)) then
        tmp = x * (i * (-4.0d0))
    else if (t <= 2.9d+100) then
        tmp = t_1
    else
        tmp = t * ((18.0d0 * (z * (x * y))) - (a * 4.0d0))
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double t_2 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double tmp;
	if (t <= -6.6e+192) {
		tmp = t_2;
	} else if (t <= -8.5e+144) {
		tmp = t_1;
	} else if (t <= -490000000.0) {
		tmp = t_2;
	} else if (t <= -3.8e-198) {
		tmp = t_1;
	} else if (t <= -9.5e-298) {
		tmp = x * (i * -4.0);
	} else if (t <= 2.9e+100) {
		tmp = t_1;
	} else {
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (27.0 * (j * k))
	t_2 = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	tmp = 0
	if t <= -6.6e+192:
		tmp = t_2
	elif t <= -8.5e+144:
		tmp = t_1
	elif t <= -490000000.0:
		tmp = t_2
	elif t <= -3.8e-198:
		tmp = t_1
	elif t <= -9.5e-298:
		tmp = x * (i * -4.0)
	elif t <= 2.9e+100:
		tmp = t_1
	else:
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0))
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -6.6e+192)
		tmp = t_2;
	elseif (t <= -8.5e+144)
		tmp = t_1;
	elseif (t <= -490000000.0)
		tmp = t_2;
	elseif (t <= -3.8e-198)
		tmp = t_1;
	elseif (t <= -9.5e-298)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (t <= 2.9e+100)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (27.0 * (j * k));
	t_2 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -6.6e+192)
		tmp = t_2;
	elseif (t <= -8.5e+144)
		tmp = t_1;
	elseif (t <= -490000000.0)
		tmp = t_2;
	elseif (t <= -3.8e-198)
		tmp = t_1;
	elseif (t <= -9.5e-298)
		tmp = x * (i * -4.0);
	elseif (t <= 2.9e+100)
		tmp = t_1;
	else
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.6e+192], t$95$2, If[LessEqual[t, -8.5e+144], t$95$1, If[LessEqual[t, -490000000.0], t$95$2, If[LessEqual[t, -3.8e-198], t$95$1, If[LessEqual[t, -9.5e-298], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+100], t$95$1, N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.60000000000000019e192 or -8.4999999999999998e144 < t < -4.9e8

   1. Initial program 78.4%

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

   2. Taylor expanded in i around 0 76.2%

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

   3. Taylor expanded in t around inf 80.7%

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

   if -6.60000000000000019e192 < t < -8.4999999999999998e144 or -4.9e8 < t < -3.8000000000000002e-198 or -9.50000000000000012e-298 < t < 2.9e100

   1. Initial program 87.2%

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

   2. Taylor expanded in i around 0 75.5%

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

   3. Taylor expanded in t around 0 58.3%

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

   if -3.8000000000000002e-198 < t < -9.50000000000000012e-298

   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* 88.4%

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

      4. distribute-rgt-neg-in 88.4%

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

      5. fma-def 88.4%

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

      6. *-commutative 88.4%

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

      7. distribute-rgt-neg-in 88.4%

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

      8. metadata-eval 88.4%

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

      9. sub-neg 88.4%

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

      10. +-commutative 88.4%

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

      11. associate-*l* 88.4%

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

      12. distribute-rgt-neg-in 88.4%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in i around inf 55.2%

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

      1. associate-*r* 55.2%

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

      2. *-commutative 55.2%

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

   6. Simplified 55.2%

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

   if 2.9e100 < t

   1. Initial program 87.5%

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

   2. Taylor expanded in i around 0 73.6%

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

   3. Taylor expanded in t around inf 85.1%

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

      1. pow1 85.1%

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

   5. Applied egg-rr 85.1%

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

      1. unpow1 85.1%

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

      2. *-commutative 85.1%

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

      3. associate-*l* 86.6%

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

   7. Simplified 86.6%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+192}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+144}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -490000000:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+100}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 9: 81.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{+86}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+69}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_2\\ \end{array} \end{array} \]

FPCore

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 (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))))
   (if (<= t -1.02e+86)
     (- t_2 t_1)
     (if (<= t 1.75e+69)
       (- (+ (* b c) (* -4.0 (* t a))) (+ (* 4.0 (* x i)) t_1))
       (+ (* b c) t_2)))))

C

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 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.02e+86) {
		tmp = t_2 - t_1;
	} else if (t <= 1.75e+69) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + t_1);
	} else {
		tmp = (b * c) + t_2;
	}
	return tmp;
}

Fortran

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 = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    if (t <= (-1.02d+86)) then
        tmp = t_2 - t_1
    else if (t <= 1.75d+69) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - ((4.0d0 * (x * i)) + t_1)
    else
        tmp = (b * c) + t_2
    end if
    code = tmp
end function

Java

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 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.02e+86) {
		tmp = t_2 - t_1;
	} else if (t <= 1.75e+69) {
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + t_1);
	} else {
		tmp = (b * c) + t_2;
	}
	return tmp;
}

Python

[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 = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	tmp = 0
	if t <= -1.02e+86:
		tmp = t_2 - t_1
	elif t <= 1.75e+69:
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + t_1)
	else:
		tmp = (b * c) + t_2
	return tmp

Julia

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(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -1.02e+86)
		tmp = Float64(t_2 - t_1);
	elseif (t <= 1.75e+69)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(Float64(4.0 * Float64(x * i)) + t_1));
	else
		tmp = Float64(Float64(b * c) + t_2);
	end
	return tmp
end

MATLAB

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 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -1.02e+86)
		tmp = t_2 - t_1;
	elseif (t <= 1.75e+69)
		tmp = ((b * c) + (-4.0 * (t * a))) - ((4.0 * (x * i)) + t_1);
	else
		tmp = (b * c) + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

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[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.02e+86], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[t, 1.75e+69], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.01999999999999996e86

   1. Initial program 76.2%

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

      1. sub-neg 76.2%

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

      2. associate-+l- 76.2%

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

      3. sub-neg 76.2%

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

      4. sub-neg 76.2%

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

      5. distribute-rgt-out-- 78.4%

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

      6. associate-*l* 82.5%

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

      7. distribute-lft-neg-in 82.5%

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

      8. cancel-sign-sub 82.5%

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

      9. associate-*l* 82.5%

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

      10. associate-*l* 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in i around 0 82.6%

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

   5. Taylor expanded in c around 0 80.6%

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

   if -1.01999999999999996e86 < t < 1.74999999999999994e69

   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. associate-+l- 87.7%

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

      3. sub-neg 87.7%

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

      4. sub-neg 87.7%

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

      5. distribute-rgt-out-- 87.7%

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

      6. associate-*l* 91.8%

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

      7. distribute-lft-neg-in 91.8%

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

      8. cancel-sign-sub 91.8%

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

      9. associate-*l* 91.8%

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

      10. associate-*l* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in y around 0 89.8%

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

   if 1.74999999999999994e69 < t

   1. Initial program 88.2%

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

      1. sub-neg 88.2%

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

      2. associate-+l- 88.2%

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

      3. sub-neg 88.2%

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

      4. sub-neg 88.2%

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

      5. distribute-rgt-out-- 98.5%

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

      6. associate-*l* 97.0%

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

      7. distribute-lft-neg-in 97.0%

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

      8. cancel-sign-sub 97.0%

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

      9. associate-*l* 97.0%

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

      10. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in i around 0 95.5%

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

   5. Taylor expanded in k around 0 94.1%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+69}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 10: 48.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := b \cdot c - t_1\\ t_3 := x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{-198}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-304}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-105}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-8}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 27.0 (* j k)))
        (t_2 (- (* b c) t_1))
        (t_3 (* x (- (* 18.0 (* y (* t z))) (* i 4.0)))))
   (if (<= z -2.2e-198)
     t_3
     (if (<= z -9.5e-304)
       t_2
       (if (<= z 1.9e-105)
         (- (* -4.0 (* t a)) t_1)
         (if (<= z 1.4e-8)
           t_3
           (if (<= z 3.2e+63)
             t_2
             (* t (- (* 18.0 (* y (* x z))) (* a 4.0))))))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double t_2 = (b * c) - t_1;
	double t_3 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	double tmp;
	if (z <= -2.2e-198) {
		tmp = t_3;
	} else if (z <= -9.5e-304) {
		tmp = t_2;
	} else if (z <= 1.9e-105) {
		tmp = (-4.0 * (t * a)) - t_1;
	} else if (z <= 1.4e-8) {
		tmp = t_3;
	} else if (z <= 3.2e+63) {
		tmp = t_2;
	} else {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	}
	return tmp;
}

Fortran

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 = 27.0d0 * (j * k)
    t_2 = (b * c) - t_1
    t_3 = x * ((18.0d0 * (y * (t * z))) - (i * 4.0d0))
    if (z <= (-2.2d-198)) then
        tmp = t_3
    else if (z <= (-9.5d-304)) then
        tmp = t_2
    else if (z <= 1.9d-105) then
        tmp = ((-4.0d0) * (t * a)) - t_1
    else if (z <= 1.4d-8) then
        tmp = t_3
    else if (z <= 3.2d+63) then
        tmp = t_2
    else
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double t_2 = (b * c) - t_1;
	double t_3 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	double tmp;
	if (z <= -2.2e-198) {
		tmp = t_3;
	} else if (z <= -9.5e-304) {
		tmp = t_2;
	} else if (z <= 1.9e-105) {
		tmp = (-4.0 * (t * a)) - t_1;
	} else if (z <= 1.4e-8) {
		tmp = t_3;
	} else if (z <= 3.2e+63) {
		tmp = t_2;
	} else {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	t_2 = (b * c) - t_1
	t_3 = x * ((18.0 * (y * (t * z))) - (i * 4.0))
	tmp = 0
	if z <= -2.2e-198:
		tmp = t_3
	elif z <= -9.5e-304:
		tmp = t_2
	elif z <= 1.9e-105:
		tmp = (-4.0 * (t * a)) - t_1
	elif z <= 1.4e-8:
		tmp = t_3
	elif z <= 3.2e+63:
		tmp = t_2
	else:
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	t_2 = Float64(Float64(b * c) - t_1)
	t_3 = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(i * 4.0)))
	tmp = 0.0
	if (z <= -2.2e-198)
		tmp = t_3;
	elseif (z <= -9.5e-304)
		tmp = t_2;
	elseif (z <= 1.9e-105)
		tmp = Float64(Float64(-4.0 * Float64(t * a)) - t_1);
	elseif (z <= 1.4e-8)
		tmp = t_3;
	elseif (z <= 3.2e+63)
		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

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 27.0 * (j * k);
	t_2 = (b * c) - t_1;
	t_3 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	tmp = 0.0;
	if (z <= -2.2e-198)
		tmp = t_3;
	elseif (z <= -9.5e-304)
		tmp = t_2;
	elseif (z <= 1.9e-105)
		tmp = (-4.0 * (t * a)) - t_1;
	elseif (z <= 1.4e-8)
		tmp = t_3;
	elseif (z <= 3.2e+63)
		tmp = t_2;
	else
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e-198], t$95$3, If[LessEqual[z, -9.5e-304], t$95$2, If[LessEqual[z, 1.9e-105], N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[z, 1.4e-8], t$95$3, If[LessEqual[z, 3.2e+63], 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 4 regimes

2. if z < -2.2e-198 or 1.8999999999999999e-105 < z < 1.4e-8

   1. Initial program 81.0%

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

      1. sub-neg 81.0%

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

      2. associate-+l- 81.0%

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

      3. sub-neg 81.0%

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

      4. sub-neg 81.0%

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

      5. distribute-rgt-out-- 85.8%

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

      6. associate-*l* 86.6%

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

      7. distribute-lft-neg-in 86.6%

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

      8. cancel-sign-sub 86.6%

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

      9. associate-*l* 86.6%

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

      10. associate-*l* 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in x around inf 53.3%

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

   if -2.2e-198 < z < -9.50000000000000023e-304 or 1.4e-8 < z < 3.20000000000000011e63

   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. Taylor expanded in i around 0 78.6%

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

   3. Taylor expanded in t around 0 60.5%

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

   if -9.50000000000000023e-304 < z < 1.8999999999999999e-105

   1. Initial program 86.7%

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

      1. sub-neg 86.7%

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

      2. associate-+l- 86.7%

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

      3. sub-neg 86.7%

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

      4. sub-neg 86.7%

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

      5. distribute-rgt-out-- 86.7%

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

      6. associate-*l* 97.7%

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

      7. distribute-lft-neg-in 97.7%

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

      8. cancel-sign-sub 97.7%

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

      9. associate-*l* 97.7%

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

      10. associate-*l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in x around 0 70.7%

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

   5. Taylor expanded in c around 0 56.6%

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

   if 3.20000000000000011e63 < z

   1. Initial program 90.2%

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

   2. Taylor expanded in i around 0 68.5%

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

   3. Taylor expanded in t around inf 59.4%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-304}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-105}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+63}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 11: 70.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+144}:\\ \;\;\;\;b \cdot c - t_1\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+106}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

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 (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))))
   (if (<= t -6e+192)
     t_2
     (if (<= t -8e+144)
       (- (* b c) t_1)
       (if (<= t -1.45e+107)
         t_2
         (if (<= t 4.3e+106)
           (- (* b c) (+ (* 4.0 (* x i)) t_1))
           (* t (- (* 18.0 (* z (* x y))) (* a 4.0)))))))))

C

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 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double tmp;
	if (t <= -6e+192) {
		tmp = t_2;
	} else if (t <= -8e+144) {
		tmp = (b * c) - t_1;
	} else if (t <= -1.45e+107) {
		tmp = t_2;
	} else if (t <= 4.3e+106) {
		tmp = (b * c) - ((4.0 * (x * i)) + t_1);
	} else {
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	}
	return tmp;
}

Fortran

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 = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    if (t <= (-6d+192)) then
        tmp = t_2
    else if (t <= (-8d+144)) then
        tmp = (b * c) - t_1
    else if (t <= (-1.45d+107)) then
        tmp = t_2
    else if (t <= 4.3d+106) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + t_1)
    else
        tmp = t * ((18.0d0 * (z * (x * y))) - (a * 4.0d0))
    end if
    code = tmp
end function

Java

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 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double tmp;
	if (t <= -6e+192) {
		tmp = t_2;
	} else if (t <= -8e+144) {
		tmp = (b * c) - t_1;
	} else if (t <= -1.45e+107) {
		tmp = t_2;
	} else if (t <= 4.3e+106) {
		tmp = (b * c) - ((4.0 * (x * i)) + t_1);
	} else {
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	}
	return tmp;
}

Python

[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 = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	tmp = 0
	if t <= -6e+192:
		tmp = t_2
	elif t <= -8e+144:
		tmp = (b * c) - t_1
	elif t <= -1.45e+107:
		tmp = t_2
	elif t <= 4.3e+106:
		tmp = (b * c) - ((4.0 * (x * i)) + t_1)
	else:
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0))
	return tmp

Julia

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(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -6e+192)
		tmp = t_2;
	elseif (t <= -8e+144)
		tmp = Float64(Float64(b * c) - t_1);
	elseif (t <= -1.45e+107)
		tmp = t_2;
	elseif (t <= 4.3e+106)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + t_1));
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

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 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -6e+192)
		tmp = t_2;
	elseif (t <= -8e+144)
		tmp = (b * c) - t_1;
	elseif (t <= -1.45e+107)
		tmp = t_2;
	elseif (t <= 4.3e+106)
		tmp = (b * c) - ((4.0 * (x * i)) + t_1);
	else
		tmp = t * ((18.0 * (z * (x * y))) - (a * 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

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[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+192], t$95$2, If[LessEqual[t, -8e+144], N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, -1.45e+107], t$95$2, If[LessEqual[t, 4.3e+106], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6e192 or -8.00000000000000019e144 < t < -1.44999999999999994e107

   1. Initial program 75.2%

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

   2. Taylor expanded in i around 0 75.0%

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

   3. Taylor expanded in t around inf 89.0%

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

   if -6e192 < t < -8.00000000000000019e144

   1. Initial program 80.0%

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

   2. Taylor expanded in i around 0 80.0%

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

   3. Taylor expanded in t around 0 100.0%

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

   if -1.44999999999999994e107 < t < 4.3e106

   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. associate-+l- 87.8%

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

      3. sub-neg 87.8%

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

      4. sub-neg 87.8%

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

      5. distribute-rgt-out-- 87.8%

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

      6. associate-*l* 91.6%

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

      7. distribute-lft-neg-in 91.6%

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

      8. cancel-sign-sub 91.6%

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

      9. associate-*l* 91.6%

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

      10. associate-*l* 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in t around 0 77.8%

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

   if 4.3e106 < t

   1. Initial program 87.5%

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

   2. Taylor expanded in i around 0 73.6%

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

   3. Taylor expanded in t around inf 85.1%

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

      1. pow1 85.1%

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

   5. Applied egg-rr 85.1%

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

      1. unpow1 85.1%

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

      2. *-commutative 85.1%

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

      3. associate-*l* 86.6%

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

   7. Simplified 86.6%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+192}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+144}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{+107}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+106}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 12: 33.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ t_2 := a \cdot \left(-4 \cdot t\right)\\ \mathbf{if}\;a \leq -1.08 \cdot 10^{+200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{+187}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-105}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;a \leq 0.0092:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+67}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* t (* x (* y z))))) (t_2 (* a (* -4.0 t))))
   (if (<= a -1.08e+200)
     t_2
     (if (<= a -3.5e+187)
       (* k (* j -27.0))
       (if (<= a -2.1e+45)
         t_2
         (if (<= a 1.1e-145)
           t_1
           (if (<= a 5.8e-105)
             (* j (* k -27.0))
             (if (<= a 0.0092) t_1 (if (<= a 3e+67) (* b c) t_2)))))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (x * (y * z)));
	double t_2 = a * (-4.0 * t);
	double tmp;
	if (a <= -1.08e+200) {
		tmp = t_2;
	} else if (a <= -3.5e+187) {
		tmp = k * (j * -27.0);
	} else if (a <= -2.1e+45) {
		tmp = t_2;
	} else if (a <= 1.1e-145) {
		tmp = t_1;
	} else if (a <= 5.8e-105) {
		tmp = j * (k * -27.0);
	} else if (a <= 0.0092) {
		tmp = t_1;
	} else if (a <= 3e+67) {
		tmp = b * c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

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 = 18.0d0 * (t * (x * (y * z)))
    t_2 = a * ((-4.0d0) * t)
    if (a <= (-1.08d+200)) then
        tmp = t_2
    else if (a <= (-3.5d+187)) then
        tmp = k * (j * (-27.0d0))
    else if (a <= (-2.1d+45)) then
        tmp = t_2
    else if (a <= 1.1d-145) then
        tmp = t_1
    else if (a <= 5.8d-105) then
        tmp = j * (k * (-27.0d0))
    else if (a <= 0.0092d0) then
        tmp = t_1
    else if (a <= 3d+67) then
        tmp = b * c
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (x * (y * z)));
	double t_2 = a * (-4.0 * t);
	double tmp;
	if (a <= -1.08e+200) {
		tmp = t_2;
	} else if (a <= -3.5e+187) {
		tmp = k * (j * -27.0);
	} else if (a <= -2.1e+45) {
		tmp = t_2;
	} else if (a <= 1.1e-145) {
		tmp = t_1;
	} else if (a <= 5.8e-105) {
		tmp = j * (k * -27.0);
	} else if (a <= 0.0092) {
		tmp = t_1;
	} else if (a <= 3e+67) {
		tmp = b * c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (x * (y * z)))
	t_2 = a * (-4.0 * t)
	tmp = 0
	if a <= -1.08e+200:
		tmp = t_2
	elif a <= -3.5e+187:
		tmp = k * (j * -27.0)
	elif a <= -2.1e+45:
		tmp = t_2
	elif a <= 1.1e-145:
		tmp = t_1
	elif a <= 5.8e-105:
		tmp = j * (k * -27.0)
	elif a <= 0.0092:
		tmp = t_1
	elif a <= 3e+67:
		tmp = b * c
	else:
		tmp = t_2
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	t_2 = Float64(a * Float64(-4.0 * t))
	tmp = 0.0
	if (a <= -1.08e+200)
		tmp = t_2;
	elseif (a <= -3.5e+187)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (a <= -2.1e+45)
		tmp = t_2;
	elseif (a <= 1.1e-145)
		tmp = t_1;
	elseif (a <= 5.8e-105)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (a <= 0.0092)
		tmp = t_1;
	elseif (a <= 3e+67)
		tmp = Float64(b * c);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (t * (x * (y * z)));
	t_2 = a * (-4.0 * t);
	tmp = 0.0;
	if (a <= -1.08e+200)
		tmp = t_2;
	elseif (a <= -3.5e+187)
		tmp = k * (j * -27.0);
	elseif (a <= -2.1e+45)
		tmp = t_2;
	elseif (a <= 1.1e-145)
		tmp = t_1;
	elseif (a <= 5.8e-105)
		tmp = j * (k * -27.0);
	elseif (a <= 0.0092)
		tmp = t_1;
	elseif (a <= 3e+67)
		tmp = b * c;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.08e+200], t$95$2, If[LessEqual[a, -3.5e+187], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.1e+45], t$95$2, If[LessEqual[a, 1.1e-145], t$95$1, If[LessEqual[a, 5.8e-105], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.0092], t$95$1, If[LessEqual[a, 3e+67], N[(b * c), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.07999999999999996e200 or -3.4999999999999998e187 < a < -2.09999999999999995e45 or 3.0000000000000001e67 < a

   1. Initial program 79.7%

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

   2. Taylor expanded in i around 0 69.7%

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

   3. Taylor expanded in t around inf 66.9%

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

   4. Taylor expanded in y around 0 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-*r* 52.4%

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

   6. Simplified 52.4%

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

   if -1.07999999999999996e200 < a < -3.4999999999999998e187

   1. Initial program 80.0%

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

      1. sub-neg 80.0%

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

      2. associate-+l- 80.0%

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

      3. sub-neg 80.0%

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

      4. sub-neg 80.0%

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

      5. distribute-rgt-out-- 80.0%

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

      6. associate-*l* 100.0%

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

      7. distribute-lft-neg-in 100.0%

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

      8. cancel-sign-sub 100.0%

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

      9. associate-*l* 100.0%

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

      10. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

      1. add-cbrt-cube 80.0%

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

      2. *-commutative 80.0%

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

      3. *-commutative 80.0%

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

      4. *-commutative 80.0%

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

   5. Applied egg-rr 80.0%

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

   6. Taylor expanded in j around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*l* 100.0%

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

   8. Simplified 100.0%

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

   if -2.09999999999999995e45 < a < 1.1e-145 or 5.80000000000000007e-105 < a < 0.0091999999999999998

   1. Initial program 89.8%

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

   2. Taylor expanded in i around 0 76.9%

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

   3. Taylor expanded in t around inf 43.7%

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

   4. Taylor expanded in y around inf 38.8%

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

      1. *-commutative 38.8%

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

      2. associate-*l* 39.6%

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

      3. *-commutative 39.6%

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

   6. Simplified 39.6%

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

   7. Taylor expanded in t around 0 38.8%

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

      1. *-commutative 38.8%

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

      2. *-commutative 38.8%

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

      3. associate-*r* 39.6%

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

      4. associate-*l* 39.6%

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

   9. Simplified 39.6%

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

   if 1.1e-145 < a < 5.80000000000000007e-105

   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* 100.0%

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

      7. distribute-lft-neg-in 100.0%

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

      8. cancel-sign-sub 100.0%

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

      9. associate-*l* 100.0%

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

      10. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

      1. add-cbrt-cube 91.5%

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

      2. *-commutative 91.5%

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

      3. *-commutative 91.5%

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

      4. *-commutative 91.5%

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

   5. Applied egg-rr 91.5%

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

   6. Taylor expanded in y around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l* 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in j around inf 51.2%

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

       1. associate-*r* 59.0%

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

   11. Simplified 59.0%

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

   if 0.0091999999999999998 < a < 3.0000000000000001e67

   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-- 84.6%

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

      6. associate-*l* 92.3%

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

      7. distribute-lft-neg-in 92.3%

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

      8. cancel-sign-sub 92.3%

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

      9. associate-*l* 92.3%

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

      10. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

      1. add-cbrt-cube 61.8%

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

      2. *-commutative 61.8%

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

      3. *-commutative 61.8%

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

      4. *-commutative 61.8%

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

   5. Applied egg-rr 61.8%

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

   6. Taylor expanded in b around inf 62.6%

      \[\leadsto \color{blue}{c \cdot b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{+200}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{+187}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-145}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-105}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;a \leq 0.0092:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+67}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right)\\ \end{array} \]

Alternative 13: 33.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := a \cdot \left(-4 \cdot t\right)\\ \mathbf{if}\;a \leq -1.08 \cdot 10^{+200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{+187}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-145}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-101}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;a \leq 0.0205:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+67}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

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 (* a (* -4.0 t))))
   (if (<= a -1.08e+200)
     t_1
     (if (<= a -3.5e+187)
       (* k (* j -27.0))
       (if (<= a -1.15e+46)
         t_1
         (if (<= a 3.1e-145)
           (* 18.0 (* t (* x (* y z))))
           (if (<= a 6.6e-101)
             (* j (* k -27.0))
             (if (<= a 0.0205)
               (* 18.0 (* t (* y (* x z))))
               (if (<= a 7.5e+67) (* b c) t_1)))))))))

C

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 = a * (-4.0 * t);
	double tmp;
	if (a <= -1.08e+200) {
		tmp = t_1;
	} else if (a <= -3.5e+187) {
		tmp = k * (j * -27.0);
	} else if (a <= -1.15e+46) {
		tmp = t_1;
	} else if (a <= 3.1e-145) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (a <= 6.6e-101) {
		tmp = j * (k * -27.0);
	} else if (a <= 0.0205) {
		tmp = 18.0 * (t * (y * (x * z)));
	} else if (a <= 7.5e+67) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 = a * ((-4.0d0) * t)
    if (a <= (-1.08d+200)) then
        tmp = t_1
    else if (a <= (-3.5d+187)) then
        tmp = k * (j * (-27.0d0))
    else if (a <= (-1.15d+46)) then
        tmp = t_1
    else if (a <= 3.1d-145) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (a <= 6.6d-101) then
        tmp = j * (k * (-27.0d0))
    else if (a <= 0.0205d0) then
        tmp = 18.0d0 * (t * (y * (x * z)))
    else if (a <= 7.5d+67) then
        tmp = b * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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 = a * (-4.0 * t);
	double tmp;
	if (a <= -1.08e+200) {
		tmp = t_1;
	} else if (a <= -3.5e+187) {
		tmp = k * (j * -27.0);
	} else if (a <= -1.15e+46) {
		tmp = t_1;
	} else if (a <= 3.1e-145) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (a <= 6.6e-101) {
		tmp = j * (k * -27.0);
	} else if (a <= 0.0205) {
		tmp = 18.0 * (t * (y * (x * z)));
	} else if (a <= 7.5e+67) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = a * (-4.0 * t)
	tmp = 0
	if a <= -1.08e+200:
		tmp = t_1
	elif a <= -3.5e+187:
		tmp = k * (j * -27.0)
	elif a <= -1.15e+46:
		tmp = t_1
	elif a <= 3.1e-145:
		tmp = 18.0 * (t * (x * (y * z)))
	elif a <= 6.6e-101:
		tmp = j * (k * -27.0)
	elif a <= 0.0205:
		tmp = 18.0 * (t * (y * (x * z)))
	elif a <= 7.5e+67:
		tmp = b * c
	else:
		tmp = t_1
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(a * Float64(-4.0 * t))
	tmp = 0.0
	if (a <= -1.08e+200)
		tmp = t_1;
	elseif (a <= -3.5e+187)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (a <= -1.15e+46)
		tmp = t_1;
	elseif (a <= 3.1e-145)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (a <= 6.6e-101)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (a <= 0.0205)
		tmp = Float64(18.0 * Float64(t * Float64(y * Float64(x * z))));
	elseif (a <= 7.5e+67)
		tmp = Float64(b * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = a * (-4.0 * t);
	tmp = 0.0;
	if (a <= -1.08e+200)
		tmp = t_1;
	elseif (a <= -3.5e+187)
		tmp = k * (j * -27.0);
	elseif (a <= -1.15e+46)
		tmp = t_1;
	elseif (a <= 3.1e-145)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (a <= 6.6e-101)
		tmp = j * (k * -27.0);
	elseif (a <= 0.0205)
		tmp = 18.0 * (t * (y * (x * z)));
	elseif (a <= 7.5e+67)
		tmp = b * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.08e+200], t$95$1, If[LessEqual[a, -3.5e+187], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.15e+46], t$95$1, If[LessEqual[a, 3.1e-145], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.6e-101], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.0205], N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e+67], N[(b * c), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.07999999999999996e200 or -3.4999999999999998e187 < a < -1.15e46 or 7.5000000000000005e67 < a

   1. Initial program 79.7%

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

   2. Taylor expanded in i around 0 69.7%

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

   3. Taylor expanded in t around inf 66.9%

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

   4. Taylor expanded in y around 0 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-*r* 52.4%

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

   6. Simplified 52.4%

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

   if -1.07999999999999996e200 < a < -3.4999999999999998e187

   1. Initial program 80.0%

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

      1. sub-neg 80.0%

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

      2. associate-+l- 80.0%

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

      3. sub-neg 80.0%

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

      4. sub-neg 80.0%

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

      5. distribute-rgt-out-- 80.0%

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

      6. associate-*l* 100.0%

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

      7. distribute-lft-neg-in 100.0%

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

      8. cancel-sign-sub 100.0%

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

      9. associate-*l* 100.0%

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

      10. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

      1. add-cbrt-cube 80.0%

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

      2. *-commutative 80.0%

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

      3. *-commutative 80.0%

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

      4. *-commutative 80.0%

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

   5. Applied egg-rr 80.0%

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

   6. Taylor expanded in j around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-*l* 100.0%

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

   8. Simplified 100.0%

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

   if -1.15e46 < a < 3.1e-145

   1. Initial program 90.0%

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

   2. Taylor expanded in i around 0 78.8%

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

   3. Taylor expanded in t around inf 43.8%

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

   4. Taylor expanded in y around inf 39.0%

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

      1. *-commutative 39.0%

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

      2. associate-*l* 39.1%

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

      3. *-commutative 39.1%

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

   6. Simplified 39.1%

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

   7. Taylor expanded in t around 0 39.0%

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

      1. *-commutative 39.0%

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

      2. *-commutative 39.0%

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

      3. associate-*r* 39.1%

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

      4. associate-*l* 39.1%

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

   9. Simplified 39.1%

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

   if 3.1e-145 < a < 6.59999999999999968e-101

   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* 100.0%

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

      7. distribute-lft-neg-in 100.0%

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

      8. cancel-sign-sub 100.0%

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

      9. associate-*l* 100.0%

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

      10. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

      1. add-cbrt-cube 91.5%

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

      2. *-commutative 91.5%

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

      3. *-commutative 91.5%

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

      4. *-commutative 91.5%

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

   5. Applied egg-rr 91.5%

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

   6. Taylor expanded in y around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l* 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in j around inf 51.2%

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

       1. associate-*r* 59.0%

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

   11. Simplified 59.0%

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

   if 6.59999999999999968e-101 < a < 0.0205000000000000009

   1. Initial program 88.2%

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

   2. Taylor expanded in i around 0 64.6%

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

   3. Taylor expanded in t around inf 42.8%

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

   4. Taylor expanded in y around inf 37.5%

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

      1. *-commutative 37.5%

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

      2. associate-*l* 42.8%

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

      3. *-commutative 42.8%

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

   6. Simplified 42.8%

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

   if 0.0205000000000000009 < a < 7.5000000000000005e67

   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-- 84.6%

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

      6. associate-*l* 92.3%

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

      7. distribute-lft-neg-in 92.3%

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

      8. cancel-sign-sub 92.3%

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

      9. associate-*l* 92.3%

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

      10. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

      1. add-cbrt-cube 61.8%

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

      2. *-commutative 61.8%

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

      3. *-commutative 61.8%

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

      4. *-commutative 61.8%

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

   5. Applied egg-rr 61.8%

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

   6. Taylor expanded in b around inf 62.6%

      \[\leadsto \color{blue}{c \cdot b} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.08 \cdot 10^{+200}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{+187}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-145}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-101}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;a \leq 0.0205:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+67}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right)\\ \end{array} \]

Alternative 14: 75.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{-19}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+63}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_2\\ \end{array} \end{array} \]

FPCore

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 (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))))
   (if (<= t -2.2e-19)
     (- t_2 t_1)
     (if (<= t 4.2e+63) (- (* b c) (+ (* 4.0 (* x i)) t_1)) (+ (* b c) t_2)))))

C

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 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double tmp;
	if (t <= -2.2e-19) {
		tmp = t_2 - t_1;
	} else if (t <= 4.2e+63) {
		tmp = (b * c) - ((4.0 * (x * i)) + t_1);
	} else {
		tmp = (b * c) + t_2;
	}
	return tmp;
}

Fortran

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 = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    if (t <= (-2.2d-19)) then
        tmp = t_2 - t_1
    else if (t <= 4.2d+63) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + t_1)
    else
        tmp = (b * c) + t_2
    end if
    code = tmp
end function

Java

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 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double tmp;
	if (t <= -2.2e-19) {
		tmp = t_2 - t_1;
	} else if (t <= 4.2e+63) {
		tmp = (b * c) - ((4.0 * (x * i)) + t_1);
	} else {
		tmp = (b * c) + t_2;
	}
	return tmp;
}

Python

[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 = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	tmp = 0
	if t <= -2.2e-19:
		tmp = t_2 - t_1
	elif t <= 4.2e+63:
		tmp = (b * c) - ((4.0 * (x * i)) + t_1)
	else:
		tmp = (b * c) + t_2
	return tmp

Julia

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(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -2.2e-19)
		tmp = Float64(t_2 - t_1);
	elseif (t <= 4.2e+63)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + t_1));
	else
		tmp = Float64(Float64(b * c) + t_2);
	end
	return tmp
end

MATLAB

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 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -2.2e-19)
		tmp = t_2 - t_1;
	elseif (t <= 4.2e+63)
		tmp = (b * c) - ((4.0 * (x * i)) + t_1);
	else
		tmp = (b * c) + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

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[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e-19], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[t, 4.2e+63], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1999999999999998e-19

   1. Initial program 80.1%

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

      1. sub-neg 80.1%

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

      2. associate-+l- 80.1%

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

      3. sub-neg 80.1%

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

      4. sub-neg 80.1%

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

      5. distribute-rgt-out-- 81.9%

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

      6. associate-*l* 85.4%

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

      7. distribute-lft-neg-in 85.4%

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

      8. cancel-sign-sub 85.4%

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

      9. associate-*l* 85.4%

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

      10. associate-*l* 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in i around 0 83.7%

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

   5. Taylor expanded in c around 0 80.2%

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

   if -2.1999999999999998e-19 < t < 4.2000000000000004e63

   1. Initial program 86.9%

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

      1. sub-neg 86.9%

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

      2. associate-+l- 86.9%

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

      3. sub-neg 86.9%

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

      4. sub-neg 86.9%

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

      5. distribute-rgt-out-- 86.9%

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

      6. associate-*l* 91.2%

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

      7. distribute-lft-neg-in 91.2%

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

      8. cancel-sign-sub 91.2%

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

      9. associate-*l* 91.2%

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

      10. associate-*l* 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in t around 0 79.1%

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

   if 4.2000000000000004e63 < t

   1. Initial program 88.2%

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

      1. sub-neg 88.2%

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

      2. associate-+l- 88.2%

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

      3. sub-neg 88.2%

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

      4. sub-neg 88.2%

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

      5. distribute-rgt-out-- 98.5%

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

      6. associate-*l* 97.0%

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

      7. distribute-lft-neg-in 97.0%

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

      8. cancel-sign-sub 97.0%

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

      9. associate-*l* 97.0%

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

      10. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in i around 0 95.5%

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

   5. Taylor expanded in k around 0 94.1%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-19}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+63}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 15: 50.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := b \cdot c - t_1\\ t_3 := -4 \cdot \left(t \cdot a\right) - t_1\\ \mathbf{if}\;a \leq -4800000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-169}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 27.0 (* j k)))
        (t_2 (- (* b c) t_1))
        (t_3 (- (* -4.0 (* t a)) t_1)))
   (if (<= a -4800000.0)
     t_3
     (if (<= a 7e-246)
       t_2
       (if (<= a 7.5e-169)
         (* t (* z (* y (* x 18.0))))
         (if (<= a 7.2e+67) t_2 t_3))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double t_2 = (b * c) - t_1;
	double t_3 = (-4.0 * (t * a)) - t_1;
	double tmp;
	if (a <= -4800000.0) {
		tmp = t_3;
	} else if (a <= 7e-246) {
		tmp = t_2;
	} else if (a <= 7.5e-169) {
		tmp = t * (z * (y * (x * 18.0)));
	} else if (a <= 7.2e+67) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

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 = 27.0d0 * (j * k)
    t_2 = (b * c) - t_1
    t_3 = ((-4.0d0) * (t * a)) - t_1
    if (a <= (-4800000.0d0)) then
        tmp = t_3
    else if (a <= 7d-246) then
        tmp = t_2
    else if (a <= 7.5d-169) then
        tmp = t * (z * (y * (x * 18.0d0)))
    else if (a <= 7.2d+67) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double t_2 = (b * c) - t_1;
	double t_3 = (-4.0 * (t * a)) - t_1;
	double tmp;
	if (a <= -4800000.0) {
		tmp = t_3;
	} else if (a <= 7e-246) {
		tmp = t_2;
	} else if (a <= 7.5e-169) {
		tmp = t * (z * (y * (x * 18.0)));
	} else if (a <= 7.2e+67) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	t_2 = (b * c) - t_1
	t_3 = (-4.0 * (t * a)) - t_1
	tmp = 0
	if a <= -4800000.0:
		tmp = t_3
	elif a <= 7e-246:
		tmp = t_2
	elif a <= 7.5e-169:
		tmp = t * (z * (y * (x * 18.0)))
	elif a <= 7.2e+67:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	t_2 = Float64(Float64(b * c) - t_1)
	t_3 = Float64(Float64(-4.0 * Float64(t * a)) - t_1)
	tmp = 0.0
	if (a <= -4800000.0)
		tmp = t_3;
	elseif (a <= 7e-246)
		tmp = t_2;
	elseif (a <= 7.5e-169)
		tmp = Float64(t * Float64(z * Float64(y * Float64(x * 18.0))));
	elseif (a <= 7.2e+67)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 27.0 * (j * k);
	t_2 = (b * c) - t_1;
	t_3 = (-4.0 * (t * a)) - t_1;
	tmp = 0.0;
	if (a <= -4800000.0)
		tmp = t_3;
	elseif (a <= 7e-246)
		tmp = t_2;
	elseif (a <= 7.5e-169)
		tmp = t * (z * (y * (x * 18.0)));
	elseif (a <= 7.2e+67)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[a, -4800000.0], t$95$3, If[LessEqual[a, 7e-246], t$95$2, If[LessEqual[a, 7.5e-169], N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e+67], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.8e6 or 7.1999999999999998e67 < a

   1. Initial program 80.3%

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

      1. sub-neg 80.3%

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

      2. associate-+l- 80.3%

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

      3. sub-neg 80.3%

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

      4. sub-neg 80.3%

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

      5. distribute-rgt-out-- 87.2%

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

      6. associate-*l* 88.8%

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

      7. distribute-lft-neg-in 88.8%

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

      8. cancel-sign-sub 88.8%

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

      9. associate-*l* 88.8%

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

      10. associate-*l* 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in x around 0 69.8%

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

   5. Taylor expanded in c around 0 60.7%

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

   if -4.8e6 < a < 7.0000000000000003e-246 or 7.49999999999999978e-169 < a < 7.1999999999999998e67

   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. Taylor expanded in i around 0 73.4%

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

   3. Taylor expanded in t around 0 51.6%

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

   if 7.0000000000000003e-246 < a < 7.49999999999999978e-169

   1. Initial program 99.8%

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

   2. Taylor expanded in i around 0 88.8%

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

   3. Taylor expanded in y around inf 56.7%

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

      1. associate-*r* 56.8%

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

      2. *-commutative 56.8%

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

      3. associate-*r* 62.1%

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

      4. associate-*r* 62.0%

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

      5. *-commutative 62.0%

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

      6. associate-*r* 62.2%

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

      7. associate-*r* 62.1%

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

      8. *-commutative 62.1%

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

      9. associate-*l* 62.2%

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

   5. Simplified 62.2%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4800000:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-246}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-169}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+67}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 16: 45.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{+216}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* j k)))))
   (if (<= t -9e+216)
     (* a (* -4.0 t))
     (if (<= t -3.8e-198)
       t_1
       (if (<= t -5.2e-298)
         (* x (* i -4.0))
         (if (<= t 1.6e+111) t_1 (* t (* z (* y (* x 18.0))))))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double tmp;
	if (t <= -9e+216) {
		tmp = a * (-4.0 * t);
	} else if (t <= -3.8e-198) {
		tmp = t_1;
	} else if (t <= -5.2e-298) {
		tmp = x * (i * -4.0);
	} else if (t <= 1.6e+111) {
		tmp = t_1;
	} else {
		tmp = t * (z * (y * (x * 18.0)));
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) - (27.0d0 * (j * k))
    if (t <= (-9d+216)) then
        tmp = a * ((-4.0d0) * t)
    else if (t <= (-3.8d-198)) then
        tmp = t_1
    else if (t <= (-5.2d-298)) then
        tmp = x * (i * (-4.0d0))
    else if (t <= 1.6d+111) then
        tmp = t_1
    else
        tmp = t * (z * (y * (x * 18.0d0)))
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double tmp;
	if (t <= -9e+216) {
		tmp = a * (-4.0 * t);
	} else if (t <= -3.8e-198) {
		tmp = t_1;
	} else if (t <= -5.2e-298) {
		tmp = x * (i * -4.0);
	} else if (t <= 1.6e+111) {
		tmp = t_1;
	} else {
		tmp = t * (z * (y * (x * 18.0)));
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (27.0 * (j * k))
	tmp = 0
	if t <= -9e+216:
		tmp = a * (-4.0 * t)
	elif t <= -3.8e-198:
		tmp = t_1
	elif t <= -5.2e-298:
		tmp = x * (i * -4.0)
	elif t <= 1.6e+111:
		tmp = t_1
	else:
		tmp = t * (z * (y * (x * 18.0)))
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	tmp = 0.0
	if (t <= -9e+216)
		tmp = Float64(a * Float64(-4.0 * t));
	elseif (t <= -3.8e-198)
		tmp = t_1;
	elseif (t <= -5.2e-298)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (t <= 1.6e+111)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(z * Float64(y * Float64(x * 18.0))));
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (27.0 * (j * k));
	tmp = 0.0;
	if (t <= -9e+216)
		tmp = a * (-4.0 * t);
	elseif (t <= -3.8e-198)
		tmp = t_1;
	elseif (t <= -5.2e-298)
		tmp = x * (i * -4.0);
	elseif (t <= 1.6e+111)
		tmp = t_1;
	else
		tmp = t * (z * (y * (x * 18.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+216], N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e-198], t$95$1, If[LessEqual[t, -5.2e-298], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+111], t$95$1, N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.0000000000000005e216

   1. Initial program 65.1%

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

   2. Taylor expanded in i around 0 65.0%

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

   3. Taylor expanded in t around inf 85.0%

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

   4. Taylor expanded in y around 0 66.2%

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

      1. *-commutative 66.2%

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

      2. associate-*r* 66.2%

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

   6. Simplified 66.2%

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

   if -9.0000000000000005e216 < t < -3.8000000000000002e-198 or -5.1999999999999998e-298 < t < 1.6e111

   1. Initial program 87.5%

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

   2. Taylor expanded in i around 0 77.0%

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

   3. Taylor expanded in t around 0 52.6%

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

   if -3.8000000000000002e-198 < t < -5.1999999999999998e-298

   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* 88.4%

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

      4. distribute-rgt-neg-in 88.4%

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

      5. fma-def 88.4%

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

      6. *-commutative 88.4%

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

      7. distribute-rgt-neg-in 88.4%

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

      8. metadata-eval 88.4%

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

      9. sub-neg 88.4%

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

      10. +-commutative 88.4%

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

      11. associate-*l* 88.4%

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

      12. distribute-rgt-neg-in 88.4%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in i around inf 55.2%

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

      1. associate-*r* 55.2%

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

      2. *-commutative 55.2%

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

   6. Simplified 55.2%

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

   if 1.6e111 < t

   1. Initial program 87.5%

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

   2. Taylor expanded in i around 0 73.6%

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

   3. Taylor expanded in y around inf 48.4%

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

      1. associate-*r* 48.4%

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

      2. *-commutative 48.4%

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

      3. associate-*r* 51.3%

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

      4. associate-*r* 51.3%

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

      5. *-commutative 51.3%

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

      6. associate-*r* 51.3%

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

      7. associate-*r* 51.3%

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

      8. *-commutative 51.3%

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

      9. associate-*l* 51.4%

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

   5. Simplified 51.4%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+216}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-198}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+111}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)\\ \end{array} \]

Alternative 17: 32.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;k \leq -5.3 \cdot 10^{+53}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq -4.4 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-245}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 3 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 5.1 \cdot 10^{+113}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* i -4.0))))
   (if (<= k -5.3e+53)
     (* -27.0 (* j k))
     (if (<= k -4.4e-279)
       t_1
       (if (<= k 9.5e-245)
         (* b c)
         (if (<= k 3e-166)
           t_1
           (if (<= k 5.1e+113) (* b c) (* k (* j -27.0)))))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if (k <= -5.3e+53) {
		tmp = -27.0 * (j * k);
	} else if (k <= -4.4e-279) {
		tmp = t_1;
	} else if (k <= 9.5e-245) {
		tmp = b * c;
	} else if (k <= 3e-166) {
		tmp = t_1;
	} else if (k <= 5.1e+113) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (i * (-4.0d0))
    if (k <= (-5.3d+53)) then
        tmp = (-27.0d0) * (j * k)
    else if (k <= (-4.4d-279)) then
        tmp = t_1
    else if (k <= 9.5d-245) then
        tmp = b * c
    else if (k <= 3d-166) then
        tmp = t_1
    else if (k <= 5.1d+113) then
        tmp = b * c
    else
        tmp = k * (j * (-27.0d0))
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if (k <= -5.3e+53) {
		tmp = -27.0 * (j * k);
	} else if (k <= -4.4e-279) {
		tmp = t_1;
	} else if (k <= 9.5e-245) {
		tmp = b * c;
	} else if (k <= 3e-166) {
		tmp = t_1;
	} else if (k <= 5.1e+113) {
		tmp = b * c;
	} else {
		tmp = k * (j * -27.0);
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (i * -4.0)
	tmp = 0
	if k <= -5.3e+53:
		tmp = -27.0 * (j * k)
	elif k <= -4.4e-279:
		tmp = t_1
	elif k <= 9.5e-245:
		tmp = b * c
	elif k <= 3e-166:
		tmp = t_1
	elif k <= 5.1e+113:
		tmp = b * c
	else:
		tmp = k * (j * -27.0)
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (k <= -5.3e+53)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (k <= -4.4e-279)
		tmp = t_1;
	elseif (k <= 9.5e-245)
		tmp = Float64(b * c);
	elseif (k <= 3e-166)
		tmp = t_1;
	elseif (k <= 5.1e+113)
		tmp = Float64(b * c);
	else
		tmp = Float64(k * Float64(j * -27.0));
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (i * -4.0);
	tmp = 0.0;
	if (k <= -5.3e+53)
		tmp = -27.0 * (j * k);
	elseif (k <= -4.4e-279)
		tmp = t_1;
	elseif (k <= 9.5e-245)
		tmp = b * c;
	elseif (k <= 3e-166)
		tmp = t_1;
	elseif (k <= 5.1e+113)
		tmp = b * c;
	else
		tmp = k * (j * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -5.3e+53], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4.4e-279], t$95$1, If[LessEqual[k, 9.5e-245], N[(b * c), $MachinePrecision], If[LessEqual[k, 3e-166], t$95$1, If[LessEqual[k, 5.1e+113], N[(b * c), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -5.3000000000000002e53

   1. Initial program 75.5%

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

      1. sub-neg 75.5%

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

      2. +-commutative 75.5%

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

      3. associate-*l* 75.5%

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

      4. distribute-rgt-neg-in 75.5%

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

      5. fma-def 75.5%

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

      6. *-commutative 75.5%

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

      7. distribute-rgt-neg-in 75.5%

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

      8. metadata-eval 75.5%

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

      9. sub-neg 75.5%

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

      10. +-commutative 75.5%

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

      11. associate-*l* 75.5%

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

      12. distribute-rgt-neg-in 75.5%

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

   3. Simplified 79.6%

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

   4. Taylor expanded in j around inf 40.6%

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

   if -5.3000000000000002e53 < k < -4.40000000000000001e-279 or 9.5000000000000002e-245 < k < 3.0000000000000003e-166

   1. Initial program 87.1%

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

      1. sub-neg 87.1%

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

      2. +-commutative 87.1%

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

      3. associate-*l* 87.1%

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

      4. distribute-rgt-neg-in 87.1%

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

      5. fma-def 87.1%

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

      6. *-commutative 87.1%

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

      7. distribute-rgt-neg-in 87.1%

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

      8. metadata-eval 87.1%

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

      9. sub-neg 87.1%

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

      10. +-commutative 87.1%

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

      11. associate-*l* 87.1%

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

      12. distribute-rgt-neg-in 87.1%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in i around inf 33.3%

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

      1. associate-*r* 33.3%

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

      2. *-commutative 33.3%

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

   6. Simplified 33.3%

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

   if -4.40000000000000001e-279 < k < 9.5000000000000002e-245 or 3.0000000000000003e-166 < k < 5.09999999999999994e113

   1. Initial program 89.8%

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

      1. sub-neg 89.8%

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

      2. associate-+l- 89.8%

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

      3. sub-neg 89.8%

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

      4. sub-neg 89.8%

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

      5. distribute-rgt-out-- 92.3%

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

      6. associate-*l* 94.7%

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

      7. distribute-lft-neg-in 94.7%

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

      8. cancel-sign-sub 94.7%

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

      9. associate-*l* 94.7%

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

      10. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

      1. add-cbrt-cube 82.4%

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

      2. *-commutative 82.4%

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

      3. *-commutative 82.4%

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

      4. *-commutative 82.4%

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

   5. Applied egg-rr 82.4%

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

   6. Taylor expanded in b around inf 30.6%

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

   if 5.09999999999999994e113 < k

   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. Step-by-step derivation

      1. sub-neg 87.6%

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

      2. associate-+l- 87.6%

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

      3. sub-neg 87.6%

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

      4. sub-neg 87.6%

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

      5. distribute-rgt-out-- 90.1%

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

      6. associate-*l* 92.7%

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

      7. distribute-lft-neg-in 92.7%

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

      8. cancel-sign-sub 92.7%

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

      9. associate-*l* 92.7%

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

      10. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

      1. add-cbrt-cube 85.0%

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

      2. *-commutative 85.0%

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

      3. *-commutative 85.0%

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

      4. *-commutative 85.0%

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

   5. Applied egg-rr 85.0%

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

   6. Taylor expanded in j around inf 46.8%

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

      1. *-commutative 46.8%

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

      2. *-commutative 46.8%

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

      3. *-commutative 46.8%

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

      4. associate-*l* 46.8%

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

   8. Simplified 46.8%

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

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -5.3 \cdot 10^{+53}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq -4.4 \cdot 10^{-279}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-245}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 3 \cdot 10^{-166}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;k \leq 5.1 \cdot 10^{+113}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 18: 32.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;k \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq -4.2 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 8.6 \cdot 10^{-245}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.65 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.62 \cdot 10^{+117}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* i -4.0))))
   (if (<= k -1.25e+50)
     (* -27.0 (* j k))
     (if (<= k -4.2e-279)
       t_1
       (if (<= k 8.6e-245)
         (* b c)
         (if (<= k 1.65e-168)
           t_1
           (if (<= k 1.62e+117) (* b c) (* j (* k -27.0)))))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if (k <= -1.25e+50) {
		tmp = -27.0 * (j * k);
	} else if (k <= -4.2e-279) {
		tmp = t_1;
	} else if (k <= 8.6e-245) {
		tmp = b * c;
	} else if (k <= 1.65e-168) {
		tmp = t_1;
	} else if (k <= 1.62e+117) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (i * (-4.0d0))
    if (k <= (-1.25d+50)) then
        tmp = (-27.0d0) * (j * k)
    else if (k <= (-4.2d-279)) then
        tmp = t_1
    else if (k <= 8.6d-245) then
        tmp = b * c
    else if (k <= 1.65d-168) then
        tmp = t_1
    else if (k <= 1.62d+117) then
        tmp = b * c
    else
        tmp = j * (k * (-27.0d0))
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if (k <= -1.25e+50) {
		tmp = -27.0 * (j * k);
	} else if (k <= -4.2e-279) {
		tmp = t_1;
	} else if (k <= 8.6e-245) {
		tmp = b * c;
	} else if (k <= 1.65e-168) {
		tmp = t_1;
	} else if (k <= 1.62e+117) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (i * -4.0)
	tmp = 0
	if k <= -1.25e+50:
		tmp = -27.0 * (j * k)
	elif k <= -4.2e-279:
		tmp = t_1
	elif k <= 8.6e-245:
		tmp = b * c
	elif k <= 1.65e-168:
		tmp = t_1
	elif k <= 1.62e+117:
		tmp = b * c
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (k <= -1.25e+50)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (k <= -4.2e-279)
		tmp = t_1;
	elseif (k <= 8.6e-245)
		tmp = Float64(b * c);
	elseif (k <= 1.65e-168)
		tmp = t_1;
	elseif (k <= 1.62e+117)
		tmp = Float64(b * c);
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (i * -4.0);
	tmp = 0.0;
	if (k <= -1.25e+50)
		tmp = -27.0 * (j * k);
	elseif (k <= -4.2e-279)
		tmp = t_1;
	elseif (k <= 8.6e-245)
		tmp = b * c;
	elseif (k <= 1.65e-168)
		tmp = t_1;
	elseif (k <= 1.62e+117)
		tmp = b * c;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.25e+50], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4.2e-279], t$95$1, If[LessEqual[k, 8.6e-245], N[(b * c), $MachinePrecision], If[LessEqual[k, 1.65e-168], t$95$1, If[LessEqual[k, 1.62e+117], N[(b * c), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -1.25e50

   1. Initial program 76.5%

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

      1. sub-neg 76.5%

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

      2. +-commutative 76.5%

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

      3. associate-*l* 76.4%

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

      4. distribute-rgt-neg-in 76.4%

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

      5. fma-def 76.4%

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

      6. *-commutative 76.4%

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

      7. distribute-rgt-neg-in 76.4%

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

      8. metadata-eval 76.4%

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

      9. sub-neg 76.4%

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

      10. +-commutative 76.4%

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

      11. associate-*l* 76.4%

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

      12. distribute-rgt-neg-in 76.4%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in j around inf 39.1%

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

   if -1.25e50 < k < -4.20000000000000011e-279 or 8.60000000000000005e-245 < k < 1.6500000000000001e-168

   1. Initial program 86.3%

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

      1. sub-neg 86.3%

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

      2. +-commutative 86.3%

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

      3. associate-*l* 86.4%

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

      4. distribute-rgt-neg-in 86.4%

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

      5. fma-def 86.4%

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

      6. *-commutative 86.4%

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

      7. distribute-rgt-neg-in 86.4%

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

      8. metadata-eval 86.4%

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

      9. sub-neg 86.4%

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

      10. +-commutative 86.4%

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

      11. associate-*l* 86.4%

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

      12. distribute-rgt-neg-in 86.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in i around inf 32.8%

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

      1. associate-*r* 32.8%

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

      2. *-commutative 32.8%

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

   6. Simplified 32.8%

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

   if -4.20000000000000011e-279 < k < 8.60000000000000005e-245 or 1.6500000000000001e-168 < k < 1.61999999999999997e117

   1. Initial program 90.1%

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

      1. sub-neg 90.1%

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

      2. associate-+l- 90.1%

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

      3. sub-neg 90.1%

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

      4. sub-neg 90.1%

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

      5. distribute-rgt-out-- 92.6%

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

      6. associate-*l* 94.9%

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

      7. distribute-lft-neg-in 94.9%

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

      8. cancel-sign-sub 94.9%

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

      9. associate-*l* 94.9%

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

      10. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

      1. add-cbrt-cube 83.1%

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

      2. *-commutative 83.1%

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

      3. *-commutative 83.1%

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

      4. *-commutative 83.1%

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

   5. Applied egg-rr 83.1%

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

   6. Taylor expanded in b around inf 29.5%

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

   if 1.61999999999999997e117 < k

   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. Step-by-step derivation

      1. sub-neg 87.6%

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

      2. associate-+l- 87.6%

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

      3. sub-neg 87.6%

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

      4. sub-neg 87.6%

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

      5. distribute-rgt-out-- 90.1%

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

      6. associate-*l* 92.7%

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

      7. distribute-lft-neg-in 92.7%

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

      8. cancel-sign-sub 92.7%

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

      9. associate-*l* 92.7%

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

      10. associate-*l* 92.7%

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

   3. Simplified 92.7%

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

      1. add-cbrt-cube 85.0%

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

      2. *-commutative 85.0%

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

      3. *-commutative 85.0%

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

      4. *-commutative 85.0%

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

   5. Applied egg-rr 85.0%

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

   6. Taylor expanded in y around 0 79.7%

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

      1. *-commutative 79.7%

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

      2. *-commutative 79.7%

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

      3. associate-*l* 79.7%

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

   8. Simplified 79.7%

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

   9. Taylor expanded in j around inf 46.8%

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

       1. associate-*r* 51.6%

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

   11. Simplified 51.6%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq -4.2 \cdot 10^{-279}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;k \leq 8.6 \cdot 10^{-245}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.65 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;k \leq 1.62 \cdot 10^{+117}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 19: 32.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ \mathbf{if}\;k \leq -3.3 \cdot 10^{+57}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq -4.2 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.45 \cdot 10^{-244}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 4 \cdot 10^{+96}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* i -4.0))))
   (if (<= k -3.3e+57)
     (* -27.0 (* j k))
     (if (<= k -4.2e-279)
       t_1
       (if (<= k 1.45e-244)
         (* b c)
         (if (<= k 6e-152)
           t_1
           (if (<= k 4e+96) (* a (* -4.0 t)) (* j (* k -27.0)))))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if (k <= -3.3e+57) {
		tmp = -27.0 * (j * k);
	} else if (k <= -4.2e-279) {
		tmp = t_1;
	} else if (k <= 1.45e-244) {
		tmp = b * c;
	} else if (k <= 6e-152) {
		tmp = t_1;
	} else if (k <= 4e+96) {
		tmp = a * (-4.0 * t);
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (i * (-4.0d0))
    if (k <= (-3.3d+57)) then
        tmp = (-27.0d0) * (j * k)
    else if (k <= (-4.2d-279)) then
        tmp = t_1
    else if (k <= 1.45d-244) then
        tmp = b * c
    else if (k <= 6d-152) then
        tmp = t_1
    else if (k <= 4d+96) then
        tmp = a * ((-4.0d0) * t)
    else
        tmp = j * (k * (-27.0d0))
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (i * -4.0);
	double tmp;
	if (k <= -3.3e+57) {
		tmp = -27.0 * (j * k);
	} else if (k <= -4.2e-279) {
		tmp = t_1;
	} else if (k <= 1.45e-244) {
		tmp = b * c;
	} else if (k <= 6e-152) {
		tmp = t_1;
	} else if (k <= 4e+96) {
		tmp = a * (-4.0 * t);
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (i * -4.0)
	tmp = 0
	if k <= -3.3e+57:
		tmp = -27.0 * (j * k)
	elif k <= -4.2e-279:
		tmp = t_1
	elif k <= 1.45e-244:
		tmp = b * c
	elif k <= 6e-152:
		tmp = t_1
	elif k <= 4e+96:
		tmp = a * (-4.0 * t)
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(i * -4.0))
	tmp = 0.0
	if (k <= -3.3e+57)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (k <= -4.2e-279)
		tmp = t_1;
	elseif (k <= 1.45e-244)
		tmp = Float64(b * c);
	elseif (k <= 6e-152)
		tmp = t_1;
	elseif (k <= 4e+96)
		tmp = Float64(a * Float64(-4.0 * t));
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (i * -4.0);
	tmp = 0.0;
	if (k <= -3.3e+57)
		tmp = -27.0 * (j * k);
	elseif (k <= -4.2e-279)
		tmp = t_1;
	elseif (k <= 1.45e-244)
		tmp = b * c;
	elseif (k <= 6e-152)
		tmp = t_1;
	elseif (k <= 4e+96)
		tmp = a * (-4.0 * t);
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -3.3e+57], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, -4.2e-279], t$95$1, If[LessEqual[k, 1.45e-244], N[(b * c), $MachinePrecision], If[LessEqual[k, 6e-152], t$95$1, If[LessEqual[k, 4e+96], N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -3.3000000000000001e57

   1. Initial program 75.0%

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

      1. sub-neg 75.0%

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

      2. +-commutative 75.0%

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

      3. associate-*l* 74.9%

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

      4. distribute-rgt-neg-in 74.9%

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

      5. fma-def 74.9%

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

      6. *-commutative 74.9%

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

      7. distribute-rgt-neg-in 74.9%

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

      8. metadata-eval 74.9%

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

      9. sub-neg 74.9%

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

      10. +-commutative 74.9%

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

      11. associate-*l* 74.9%

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

      12. distribute-rgt-neg-in 74.9%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in j around inf 41.5%

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

   if -3.3000000000000001e57 < k < -4.20000000000000011e-279 or 1.44999999999999998e-244 < k < 6e-152

   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. Step-by-step derivation

      1. sub-neg 87.6%

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

      2. +-commutative 87.6%

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

      3. associate-*l* 87.6%

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

      4. distribute-rgt-neg-in 87.6%

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

      5. fma-def 87.6%

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

      6. *-commutative 87.6%

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

      7. distribute-rgt-neg-in 87.6%

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

      8. metadata-eval 87.6%

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

      9. sub-neg 87.6%

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

      10. +-commutative 87.6%

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

      11. associate-*l* 87.6%

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

      12. distribute-rgt-neg-in 87.6%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in i around inf 32.0%

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

      1. associate-*r* 32.0%

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

      2. *-commutative 32.0%

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

   6. Simplified 32.0%

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

   if -4.20000000000000011e-279 < k < 1.44999999999999998e-244

   1. Initial program 95.8%

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

      1. sub-neg 95.8%

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

      2. associate-+l- 95.8%

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

      3. sub-neg 95.8%

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

      4. sub-neg 95.8%

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

      5. distribute-rgt-out-- 95.8%

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

      6. associate-*l* 99.9%

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

      7. distribute-lft-neg-in 99.9%

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

      8. cancel-sign-sub 99.9%

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

      9. associate-*l* 99.9%

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

      10. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

      1. add-cbrt-cube 78.9%

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

      2. *-commutative 78.9%

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

      3. *-commutative 78.9%

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

      4. *-commutative 78.9%

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

   5. Applied egg-rr 78.9%

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

   6. Taylor expanded in b around inf 38.9%

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

   if 6e-152 < k < 4.0000000000000002e96

   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. Taylor expanded in i around 0 80.0%

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

   3. Taylor expanded in t around inf 54.9%

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

   4. Taylor expanded in y around 0 34.6%

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

      1. *-commutative 34.6%

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

      2. associate-*r* 34.6%

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

   6. Simplified 34.6%

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

   if 4.0000000000000002e96 < k

   1. Initial program 86.1%

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

      1. sub-neg 86.1%

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

      2. associate-+l- 86.1%

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

      3. sub-neg 86.1%

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

      4. sub-neg 86.1%

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

      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* 93.2%

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

      7. distribute-lft-neg-in 93.2%

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

      8. cancel-sign-sub 93.2%

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

      9. associate-*l* 93.2%

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

      10. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

      1. add-cbrt-cube 81.3%

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

      2. *-commutative 81.3%

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

      3. *-commutative 81.3%

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

      4. *-commutative 81.3%

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

   5. Applied egg-rr 81.3%

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

   6. Taylor expanded in y around 0 81.1%

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

      1. *-commutative 81.1%

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

      2. *-commutative 81.1%

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

      3. associate-*l* 81.1%

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

   8. Simplified 81.1%

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

   9. Taylor expanded in j around inf 46.0%

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

       1. associate-*r* 50.5%

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

   11. Simplified 50.5%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.3 \cdot 10^{+57}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq -4.2 \cdot 10^{-279}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;k \leq 1.45 \cdot 10^{-244}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 6 \cdot 10^{-152}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;k \leq 4 \cdot 10^{+96}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 20: 32.6% accurate, 3.4× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+78}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{-89}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= b -1.25e+78) (* b c) (if (<= b 5.9e-89) (* -27.0 (* j k)) (* b c))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (b <= -1.25e+78) {
		tmp = b * c;
	} else if (b <= 5.9e-89) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (b <= (-1.25d+78)) then
        tmp = b * c
    else if (b <= 5.9d-89) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (b <= -1.25e+78) {
		tmp = b * c;
	} else if (b <= 5.9e-89) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if b <= -1.25e+78:
		tmp = b * c
	elif b <= 5.9e-89:
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (b <= -1.25e+78)
		tmp = Float64(b * c);
	elseif (b <= 5.9e-89)
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (b <= -1.25e+78)
		tmp = b * c;
	elseif (b <= 5.9e-89)
		tmp = -27.0 * (j * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

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[b, -1.25e+78], N[(b * c), $MachinePrecision], If[LessEqual[b, 5.9e-89], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.24999999999999996e78 or 5.90000000000000021e-89 < b

   1. Initial program 87.5%

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

      1. sub-neg 87.5%

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

      2. associate-+l- 87.5%

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

      3. sub-neg 87.5%

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

      4. sub-neg 87.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 90.5%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 91.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 91.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 91.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 91.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 91.1%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. add-cbrt-cube 79.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\sqrt[3]{\left(\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right) \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\right) \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 79.6%

         \[\leadsto \left(t \cdot \left(\sqrt[3]{\left(\color{blue}{\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)} \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\right) \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 79.6%

         \[\leadsto \left(t \cdot \left(\sqrt[3]{\left(\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)}\right) \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 79.6%

         \[\leadsto \left(t \cdot \left(\sqrt[3]{\left(\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 79.6%

      \[\leadsto \left(t \cdot \left(\color{blue}{\sqrt[3]{\left(\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\right) \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in b around inf 35.6%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -1.24999999999999996e78 < b < 5.90000000000000021e-89

   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%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 83.9%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 83.9%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 84.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 84.7%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 84.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 84.7%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 84.7%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 84.7%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 84.7%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 84.7%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 92.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 24.6%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+78}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{-89}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 21: 32.6% accurate, 3.4× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+77}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-88}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= b -7e+77) (* b c) (if (<= b 2.15e-88) (* k (* j -27.0)) (* b c))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (b <= -7e+77) {
		tmp = b * c;
	} else if (b <= 2.15e-88) {
		tmp = k * (j * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (b <= (-7d+77)) then
        tmp = b * c
    else if (b <= 2.15d-88) then
        tmp = k * (j * (-27.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (b <= -7e+77) {
		tmp = b * c;
	} else if (b <= 2.15e-88) {
		tmp = k * (j * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if b <= -7e+77:
		tmp = b * c
	elif b <= 2.15e-88:
		tmp = k * (j * -27.0)
	else:
		tmp = b * c
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (b <= -7e+77)
		tmp = Float64(b * c);
	elseif (b <= 2.15e-88)
		tmp = Float64(k * Float64(j * -27.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (b <= -7e+77)
		tmp = b * c;
	elseif (b <= 2.15e-88)
		tmp = k * (j * -27.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

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[b, -7e+77], N[(b * c), $MachinePrecision], If[LessEqual[b, 2.15e-88], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -7.0000000000000003e77 or 2.1499999999999999e-88 < b

   1. Initial program 87.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 87.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 87.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 87.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 87.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 90.5%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 91.1%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 91.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 91.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 91.1%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 91.1%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. add-cbrt-cube 79.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\sqrt[3]{\left(\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right) \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\right) \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 79.6%

         \[\leadsto \left(t \cdot \left(\sqrt[3]{\left(\color{blue}{\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)} \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\right) \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 79.6%

         \[\leadsto \left(t \cdot \left(\sqrt[3]{\left(\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)}\right) \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 79.6%

         \[\leadsto \left(t \cdot \left(\sqrt[3]{\left(\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 79.6%

      \[\leadsto \left(t \cdot \left(\color{blue}{\sqrt[3]{\left(\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\right) \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in b around inf 35.6%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -7.0000000000000003e77 < b < 2.1499999999999999e-88

   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. associate-+l- 83.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 83.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 83.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 87.1%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 91.9%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 91.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 91.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 91.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 92.0%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
   4. Step-by-step derivation

      1. add-cbrt-cube 82.4%

         \[\leadsto \left(t \cdot \left(\color{blue}{\sqrt[3]{\left(\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right) \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\right) \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 82.4%

         \[\leadsto \left(t \cdot \left(\sqrt[3]{\left(\color{blue}{\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)} \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\right) \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. *-commutative 82.4%

         \[\leadsto \left(t \cdot \left(\sqrt[3]{\left(\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)}\right) \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. *-commutative 82.4%

         \[\leadsto \left(t \cdot \left(\sqrt[3]{\left(\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 82.4%

      \[\leadsto \left(t \cdot \left(\color{blue}{\sqrt[3]{\left(\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\right) \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Taylor expanded in j around inf 24.6%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 24.6%

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative 24.6%

         \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} \]

      3. *-commutative 24.6%

         \[\leadsto \color{blue}{\left(k \cdot j\right)} \cdot -27 \]

      4. associate-*l* 24.6%

         \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   8. Simplified 24.6%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+77}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-88}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 22: 22.9% accurate, 10.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ b \cdot c \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* b c))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = b * c
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = b * c;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(b * c), $MachinePrecision]

Derivation

1. Initial program 85.8%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Step-by-step derivation

   1. sub-neg 85.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

   2. associate-+l- 85.8%

      \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

   3. sub-neg 85.8%

      \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

   4. sub-neg 85.8%

      \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

   5. distribute-rgt-out-- 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* 91.5%

      \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

   7. distribute-lft-neg-in 91.5%

      \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

   8. cancel-sign-sub 91.5%

      \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

   9. associate-*l* 91.5%

      \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

   10. associate-*l* 91.5%

       \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

3. Simplified 91.5%

   \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]
4. Step-by-step derivation

   1. add-cbrt-cube 81.0%

      \[\leadsto \left(t \cdot \left(\color{blue}{\sqrt[3]{\left(\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right) \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\right) \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   2. *-commutative 81.0%

      \[\leadsto \left(t \cdot \left(\sqrt[3]{\left(\color{blue}{\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)} \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\right) \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   3. *-commutative 81.0%

      \[\leadsto \left(t \cdot \left(\sqrt[3]{\left(\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)}\right) \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   4. *-commutative 81.0%

      \[\leadsto \left(t \cdot \left(\sqrt[3]{\left(\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\right) \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

5. Applied egg-rr 81.0%

   \[\leadsto \left(t \cdot \left(\color{blue}{\sqrt[3]{\left(\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right) \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)\right) \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)}} - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

6. Taylor expanded in b around inf 22.3%

   \[\leadsto \color{blue}{c \cdot b} \]

7. Final simplification 22.3%

   \[\leadsto b \cdot c \]

Developer target: 89.6% 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 2023230 
(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)))