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

Percentage Accurate: 85.4% → 92.9%

Time: 27.4s

Alternatives: 24

Speedup: 1.0×

• Unsound rule application detected in e-graph. Results may not be sound.

• 49.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.9% accurate, 0.1× speedup

Math

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

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.7%

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

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

   1. Initial program 0.0%

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

      1. sub-neg 0.0%

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

      2. +-commutative 0.0%

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

      3. associate-*l* 0.0%

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

      4. distribute-rgt-neg-in 0.0%

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

      5. fma-def 21.4%

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

      6. *-commutative 21.4%

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

      7. distribute-rgt-neg-in 21.4%

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

      8. metadata-eval 21.4%

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

      9. sub-neg 21.4%

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

      10. +-commutative 21.4%

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

      11. associate-*l* 21.4%

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

      12. distribute-rgt-neg-in 21.4%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in x around -inf 75.5%

      \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{-1 \cdot \left(\left(4 \cdot i + -18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \cdot x\right)}\right) \]
   5. Step-by-step derivation

      1. +-commutative 75.5%

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

      2. metadata-eval 75.5%

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

      3. cancel-sign-sub-inv 75.5%

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

      4. mul-1-neg 75.5%

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

      5. cancel-sign-sub-inv 75.5%

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

      6. metadata-eval 75.5%

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

      7. +-commutative 75.5%

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

      8. distribute-rgt-neg-in 75.5%

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

      9. *-commutative 75.5%

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

      10. fma-def 75.5%

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

      11. *-commutative 75.5%

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

      12. associate-*l* 75.5%

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

      13. *-commutative 75.5%

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

   6. Simplified 75.5%

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

4. Final simplification 93.5%

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

Alternative 2: 92.1% accurate, 0.5× speedup

Math

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

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

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

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

Python

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

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	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 * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	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[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $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 95.7%

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

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

   1. Initial program 0.0%

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

      1. sub-neg 0.0%

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

      2. associate-+l- 0.0%

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

      3. sub-neg 0.0%

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

      4. sub-neg 0.0%

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

      5. distribute-rgt-out-- 10.7%

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

      6. associate-*l* 14.3%

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

      7. distribute-lft-neg-in 14.3%

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

      8. cancel-sign-sub 14.3%

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

      9. associate-*l* 14.3%

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

      10. associate-*l* 14.3%

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

   3. Simplified 14.3%

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

   4. Taylor expanded in x around inf 71.8%

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

4. Final simplification 93.1%

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

Alternative 3: 78.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \left(a \cdot -4 - -18 \cdot t_1\right) - t_2\\ \mathbf{elif}\;t_2 \leq 10^{+131}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot t_1\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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 (* y (* x z))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -2e+108)
     (- (* t (- (* a -4.0) (* -18.0 t_1))) t_2)
     (if (<= t_2 1e+131)
       (- (- (* b c) (* t (- (* a 4.0) (* 18.0 t_1)))) (* 4.0 (* x i)))
       (+ (* -4.0 (* x i)) (* -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 t_1 = y * (x * z);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+108) {
		tmp = (t * ((a * -4.0) - (-18.0 * t_1))) - t_2;
	} else if (t_2 <= 1e+131) {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * t_1)))) - (4.0 * (x * i));
	} else {
		tmp = (-4.0 * (x * i)) + (-27.0 * (j * k));
	}
	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 = y * (x * z)
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-2d+108)) then
        tmp = (t * ((a * (-4.0d0)) - ((-18.0d0) * t_1))) - t_2
    else if (t_2 <= 1d+131) then
        tmp = ((b * c) - (t * ((a * 4.0d0) - (18.0d0 * t_1)))) - (4.0d0 * (x * i))
    else
        tmp = ((-4.0d0) * (x * i)) + ((-27.0d0) * (j * k))
    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 = y * (x * z);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -2e+108) {
		tmp = (t * ((a * -4.0) - (-18.0 * t_1))) - t_2;
	} else if (t_2 <= 1e+131) {
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * t_1)))) - (4.0 * (x * i));
	} else {
		tmp = (-4.0 * (x * i)) + (-27.0 * (j * k));
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = y * (x * z)
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -2e+108:
		tmp = (t * ((a * -4.0) - (-18.0 * t_1))) - t_2
	elif t_2 <= 1e+131:
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * t_1)))) - (4.0 * (x * i))
	else:
		tmp = (-4.0 * (x * i)) + (-27.0 * (j * k))
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -2e+108)
		tmp = Float64(Float64(t * Float64(Float64(a * -4.0) - Float64(-18.0 * t_1))) - t_2);
	elseif (t_2 <= 1e+131)
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(18.0 * t_1)))) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(-4.0 * Float64(x * i)) + Float64(-27.0 * Float64(j * k)));
	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 = y * (x * z);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -2e+108)
		tmp = (t * ((a * -4.0) - (-18.0 * t_1))) - t_2;
	elseif (t_2 <= 1e+131)
		tmp = ((b * c) - (t * ((a * 4.0) - (18.0 * t_1)))) - (4.0 * (x * i));
	else
		tmp = (-4.0 * (x * i)) + (-27.0 * (j * k));
	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[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+108], N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] - N[(-18.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$2, 1e+131], N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(18.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j 27) k) < -2.0000000000000001e108

   1. Initial program 77.3%

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

   2. Taylor expanded in t around -inf 77.5%

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

   if -2.0000000000000001e108 < (*.f64 (*.f64 j 27) k) < 9.9999999999999991e130

   1. Initial program 88.6%

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

      1. sub-neg 88.6%

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

      2. associate-+l- 88.6%

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

      3. sub-neg 88.6%

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

      4. sub-neg 88.6%

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

      5. distribute-rgt-out-- 89.7%

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

      6. associate-*l* 87.0%

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

      7. distribute-lft-neg-in 87.0%

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

      8. cancel-sign-sub 87.0%

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

      9. associate-*l* 87.0%

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

      10. associate-*l* 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in j around 0 83.2%

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

   if 9.9999999999999991e130 < (*.f64 (*.f64 j 27) k)

   1. Initial program 79.3%

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

      1. sub-neg 79.3%

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

      2. +-commutative 79.3%

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

      3. associate-*l* 82.2%

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

      4. distribute-rgt-neg-in 82.2%

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

      5. fma-def 88.1%

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

      6. *-commutative 88.1%

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

      7. distribute-rgt-neg-in 88.1%

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

      8. metadata-eval 88.1%

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

      9. sub-neg 88.1%

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

      10. +-commutative 88.1%

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

      11. associate-*l* 88.1%

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

      12. distribute-rgt-neg-in 88.1%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in t around 0 83.0%

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

      1. fma-def 86.0%

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

      2. associate-*r* 86.0%

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

      3. *-commutative 86.0%

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

      4. fma-def 88.9%

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

      5. associate-*r* 88.9%

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

      6. *-commutative 88.9%

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

      7. *-commutative 88.9%

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

      8. *-commutative 88.9%

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

   6. Simplified 88.9%

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

   7. Taylor expanded in c around 0 80.3%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -2 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \left(a \cdot -4 - -18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;\left(j \cdot 27\right) \cdot k \leq 10^{+131}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 4: 86.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+182}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - \left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

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 (<= x -1.2e+182)
   (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))
   (-
    (- (* b c) (* t (- (* a 4.0) (* (* x 18.0) (* y z)))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 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 (x <= -1.2e+182) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - ((x * 18.0) * (y * z))))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	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 (x <= (-1.2d+182)) then
        tmp = x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))
    else
        tmp = ((b * c) - (t * ((a * 4.0d0) - ((x * 18.0d0) * (y * z))))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    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 (x <= -1.2e+182) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else {
		tmp = ((b * c) - (t * ((a * 4.0) - ((x * 18.0) * (y * z))))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -1.2e+182:
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	else:
		tmp = ((b * c) - (t * ((a * 4.0) - ((x * 18.0) * (y * z))))) - ((x * (4.0 * i)) + (j * (27.0 * 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 (x <= -1.2e+182)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(Float64(x * 18.0) * Float64(y * z))))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	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 (x <= -1.2e+182)
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	else
		tmp = ((b * c) - (t * ((a * 4.0) - ((x * 18.0) * (y * z))))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	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[x, -1.2e+182], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.20000000000000005e182

   1. Initial program 59.6%

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

      1. sub-neg 59.6%

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

      2. associate-+l- 59.6%

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

      3. sub-neg 59.6%

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

      4. sub-neg 59.6%

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

      5. distribute-rgt-out-- 59.6%

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

      6. associate-*l* 59.6%

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

      7. distribute-lft-neg-in 59.6%

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

      8. cancel-sign-sub 59.6%

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

      9. associate-*l* 59.6%

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

      10. associate-*l* 59.6%

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

   3. Simplified 59.6%

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

   4. Taylor expanded in x around inf 90.7%

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

   if -1.20000000000000005e182 < x

   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-- 89.5%

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

      6. associate-*l* 87.9%

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

      7. distribute-lft-neg-in 87.9%

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

      8. cancel-sign-sub 87.9%

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

      9. associate-*l* 87.9%

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

      10. associate-*l* 87.9%

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

   3. Simplified 87.9%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+182}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - t \cdot \left(a \cdot 4 - \left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]

Alternative 5: 75.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := t \cdot \left(a \cdot -4 - -18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right) - t_1\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-85}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+23}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* (* j 27.0) k))
        (t_2 (- (* t (- (* a -4.0) (* -18.0 (* y (* x z))))) t_1)))
   (if (<= t -1.25e+84)
     t_2
     (if (<= t -4.8e-85)
       (- (- (* b c) (* 4.0 (* t a))) t_1)
       (if (<= t -1.2e-115)
         (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))
         (if (<= t 1.3e+23)
           (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
           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 = (j * 27.0) * k;
	double t_2 = (t * ((a * -4.0) - (-18.0 * (y * (x * z))))) - t_1;
	double tmp;
	if (t <= -1.25e+84) {
		tmp = t_2;
	} else if (t <= -4.8e-85) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (t <= -1.2e-115) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else if (t <= 1.3e+23) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} 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 = (j * 27.0d0) * k
    t_2 = (t * ((a * (-4.0d0)) - ((-18.0d0) * (y * (x * z))))) - t_1
    if (t <= (-1.25d+84)) then
        tmp = t_2
    else if (t <= (-4.8d-85)) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (t <= (-1.2d-115)) then
        tmp = x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))
    else if (t <= 1.3d+23) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    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 = (j * 27.0) * k;
	double t_2 = (t * ((a * -4.0) - (-18.0 * (y * (x * z))))) - t_1;
	double tmp;
	if (t <= -1.25e+84) {
		tmp = t_2;
	} else if (t <= -4.8e-85) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (t <= -1.2e-115) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else if (t <= 1.3e+23) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} 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 = (j * 27.0) * k
	t_2 = (t * ((a * -4.0) - (-18.0 * (y * (x * z))))) - t_1
	tmp = 0
	if t <= -1.25e+84:
		tmp = t_2
	elif t <= -4.8e-85:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif t <= -1.2e-115:
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	elif t <= 1.3e+23:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	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(j * 27.0) * k)
	t_2 = Float64(Float64(t * Float64(Float64(a * -4.0) - Float64(-18.0 * Float64(y * Float64(x * z))))) - t_1)
	tmp = 0.0
	if (t <= -1.25e+84)
		tmp = t_2;
	elseif (t <= -4.8e-85)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (t <= -1.2e-115)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	elseif (t <= 1.3e+23)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	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 = (j * 27.0) * k;
	t_2 = (t * ((a * -4.0) - (-18.0 * (y * (x * z))))) - t_1;
	tmp = 0.0;
	if (t <= -1.25e+84)
		tmp = t_2;
	elseif (t <= -4.8e-85)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (t <= -1.2e-115)
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	elseif (t <= 1.3e+23)
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	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[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * N[(N[(a * -4.0), $MachinePrecision] - N[(-18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t, -1.25e+84], t$95$2, If[LessEqual[t, -4.8e-85], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, -1.2e-115], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+23], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.25e84 or 1.29999999999999996e23 < t

   1. Initial program 80.5%

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

   2. Taylor expanded in t around -inf 80.7%

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

   if -1.25e84 < t < -4.8000000000000001e-85

   1. Initial program 97.3%

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

   2. Taylor expanded in x around 0 80.6%

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

   if -4.8000000000000001e-85 < t < -1.20000000000000011e-115

   1. Initial program 89.5%

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

      1. sub-neg 89.5%

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

      2. associate-+l- 89.5%

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

      3. sub-neg 89.5%

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

      4. sub-neg 89.5%

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

      5. distribute-rgt-out-- 89.5%

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

      6. associate-*l* 89.5%

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

      7. distribute-lft-neg-in 89.5%

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

      8. cancel-sign-sub 89.5%

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

      9. associate-*l* 89.5%

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

      10. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in x around inf 72.5%

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

   if -1.20000000000000011e-115 < t < 1.29999999999999996e23

   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-- 86.1%

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

      6. associate-*l* 86.1%

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

      7. distribute-lft-neg-in 86.1%

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

      8. cancel-sign-sub 86.1%

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

      9. associate-*l* 86.1%

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

      10. associate-*l* 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in t around 0 78.9%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \left(a \cdot -4 - -18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-85}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-115}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+23}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4 - -18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 6: 33.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ t_3 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{+214}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{+176}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-289}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-280}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-235}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\\ \end{array} \end{array} \]

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 (* t (* a -4.0)))
        (t_2 (* -27.0 (* j k)))
        (t_3 (* 18.0 (* y (* t (* x z))))))
   (if (<= x -8e+214)
     t_3
     (if (<= x -1.18e+176)
       (* x (* i -4.0))
       (if (<= x -1.7e-60)
         t_3
         (if (<= x -4e-170)
           t_1
           (if (<= x -5.2e-289)
             t_2
             (if (<= x 8.2e-280)
               (* b c)
               (if (<= x 3.6e-235)
                 t_2
                 (if (<= x 9.5e-69) t_1 (* (* (* (* x 18.0) y) z) t)))))))))))

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 = t * (a * -4.0);
	double t_2 = -27.0 * (j * k);
	double t_3 = 18.0 * (y * (t * (x * z)));
	double tmp;
	if (x <= -8e+214) {
		tmp = t_3;
	} else if (x <= -1.18e+176) {
		tmp = x * (i * -4.0);
	} else if (x <= -1.7e-60) {
		tmp = t_3;
	} else if (x <= -4e-170) {
		tmp = t_1;
	} else if (x <= -5.2e-289) {
		tmp = t_2;
	} else if (x <= 8.2e-280) {
		tmp = b * c;
	} else if (x <= 3.6e-235) {
		tmp = t_2;
	} else if (x <= 9.5e-69) {
		tmp = t_1;
	} else {
		tmp = (((x * 18.0) * y) * z) * t;
	}
	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 = t * (a * (-4.0d0))
    t_2 = (-27.0d0) * (j * k)
    t_3 = 18.0d0 * (y * (t * (x * z)))
    if (x <= (-8d+214)) then
        tmp = t_3
    else if (x <= (-1.18d+176)) then
        tmp = x * (i * (-4.0d0))
    else if (x <= (-1.7d-60)) then
        tmp = t_3
    else if (x <= (-4d-170)) then
        tmp = t_1
    else if (x <= (-5.2d-289)) then
        tmp = t_2
    else if (x <= 8.2d-280) then
        tmp = b * c
    else if (x <= 3.6d-235) then
        tmp = t_2
    else if (x <= 9.5d-69) then
        tmp = t_1
    else
        tmp = (((x * 18.0d0) * y) * z) * t
    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 = t * (a * -4.0);
	double t_2 = -27.0 * (j * k);
	double t_3 = 18.0 * (y * (t * (x * z)));
	double tmp;
	if (x <= -8e+214) {
		tmp = t_3;
	} else if (x <= -1.18e+176) {
		tmp = x * (i * -4.0);
	} else if (x <= -1.7e-60) {
		tmp = t_3;
	} else if (x <= -4e-170) {
		tmp = t_1;
	} else if (x <= -5.2e-289) {
		tmp = t_2;
	} else if (x <= 8.2e-280) {
		tmp = b * c;
	} else if (x <= 3.6e-235) {
		tmp = t_2;
	} else if (x <= 9.5e-69) {
		tmp = t_1;
	} else {
		tmp = (((x * 18.0) * y) * z) * t;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	t_2 = -27.0 * (j * k)
	t_3 = 18.0 * (y * (t * (x * z)))
	tmp = 0
	if x <= -8e+214:
		tmp = t_3
	elif x <= -1.18e+176:
		tmp = x * (i * -4.0)
	elif x <= -1.7e-60:
		tmp = t_3
	elif x <= -4e-170:
		tmp = t_1
	elif x <= -5.2e-289:
		tmp = t_2
	elif x <= 8.2e-280:
		tmp = b * c
	elif x <= 3.6e-235:
		tmp = t_2
	elif x <= 9.5e-69:
		tmp = t_1
	else:
		tmp = (((x * 18.0) * y) * z) * t
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	t_2 = Float64(-27.0 * Float64(j * k))
	t_3 = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))))
	tmp = 0.0
	if (x <= -8e+214)
		tmp = t_3;
	elseif (x <= -1.18e+176)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (x <= -1.7e-60)
		tmp = t_3;
	elseif (x <= -4e-170)
		tmp = t_1;
	elseif (x <= -5.2e-289)
		tmp = t_2;
	elseif (x <= 8.2e-280)
		tmp = Float64(b * c);
	elseif (x <= 3.6e-235)
		tmp = t_2;
	elseif (x <= 9.5e-69)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t);
	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 = t * (a * -4.0);
	t_2 = -27.0 * (j * k);
	t_3 = 18.0 * (y * (t * (x * z)));
	tmp = 0.0;
	if (x <= -8e+214)
		tmp = t_3;
	elseif (x <= -1.18e+176)
		tmp = x * (i * -4.0);
	elseif (x <= -1.7e-60)
		tmp = t_3;
	elseif (x <= -4e-170)
		tmp = t_1;
	elseif (x <= -5.2e-289)
		tmp = t_2;
	elseif (x <= 8.2e-280)
		tmp = b * c;
	elseif (x <= 3.6e-235)
		tmp = t_2;
	elseif (x <= 9.5e-69)
		tmp = t_1;
	else
		tmp = (((x * 18.0) * y) * z) * t;
	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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+214], t$95$3, If[LessEqual[x, -1.18e+176], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.7e-60], t$95$3, If[LessEqual[x, -4e-170], t$95$1, If[LessEqual[x, -5.2e-289], t$95$2, If[LessEqual[x, 8.2e-280], N[(b * c), $MachinePrecision], If[LessEqual[x, 3.6e-235], t$95$2, If[LessEqual[x, 9.5e-69], t$95$1, N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -7.9999999999999996e214 or -1.18000000000000006e176 < x < -1.70000000000000003e-60

   1. Initial program 77.2%

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

      1. sub-neg 77.2%

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

      2. associate-+l- 77.2%

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

      3. sub-neg 77.2%

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

      4. sub-neg 77.2%

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

      5. distribute-rgt-out-- 77.2%

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

      6. associate-*l* 78.6%

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

      7. distribute-lft-neg-in 78.6%

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

      8. cancel-sign-sub 78.6%

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

      9. associate-*l* 78.6%

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

      10. associate-*l* 78.7%

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

   3. Simplified 78.7%

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

   4. Taylor expanded in t around inf 49.5%

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

   5. Taylor expanded in y around inf 50.7%

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

   if -7.9999999999999996e214 < x < -1.18000000000000006e176

   1. Initial program 70.0%

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

      1. sub-neg 70.0%

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

      2. associate-+l- 70.0%

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

      3. sub-neg 70.0%

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

      4. sub-neg 70.0%

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

      5. distribute-rgt-out-- 70.0%

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

      6. associate-*l* 70.0%

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

      7. distribute-lft-neg-in 70.0%

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

      8. cancel-sign-sub 70.0%

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

      9. associate-*l* 70.0%

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

      10. associate-*l* 70.0%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in x around inf 90.0%

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

   5. Taylor expanded in y around 0 70.4%

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

   if -1.70000000000000003e-60 < x < -3.99999999999999993e-170 or 3.59999999999999999e-235 < x < 9.50000000000000094e-69

   1. Initial program 92.9%

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

      1. sub-neg 92.9%

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

      2. associate-+l- 92.9%

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

      3. sub-neg 92.9%

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

      4. sub-neg 92.9%

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

      5. distribute-rgt-out-- 94.7%

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

      6. associate-*l* 91.3%

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

      7. distribute-lft-neg-in 91.3%

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

      8. cancel-sign-sub 91.3%

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

      9. associate-*l* 91.3%

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

      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 inf 57.4%

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

   5. Taylor expanded in y around 0 49.0%

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

   if -3.99999999999999993e-170 < x < -5.1999999999999998e-289 or 8.2000000000000003e-280 < x < 3.59999999999999999e-235

   1. Initial program 94.6%

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

      1. sub-neg 94.6%

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

      2. +-commutative 94.6%

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

      3. associate-*l* 94.5%

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

      4. distribute-rgt-neg-in 94.5%

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

      5. fma-def 97.2%

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

      6. *-commutative 97.2%

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

      7. distribute-rgt-neg-in 97.2%

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

      8. metadata-eval 97.2%

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

      9. sub-neg 97.2%

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

      10. +-commutative 97.2%

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

      11. associate-*l* 97.2%

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

      12. distribute-rgt-neg-in 97.2%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in j around inf 46.1%

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

   if -5.1999999999999998e-289 < x < 8.2000000000000003e-280

   1. Initial program 92.3%

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

      1. sub-neg 92.3%

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

      2. associate-+l- 92.3%

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

      3. sub-neg 92.3%

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

      4. sub-neg 92.3%

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

      5. distribute-rgt-out-- 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* 85.2%

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

      7. distribute-lft-neg-in 85.2%

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

      8. cancel-sign-sub 85.2%

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

      9. associate-*l* 85.2%

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

      10. associate-*l* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in j around 0 85.0%

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

   5. Taylor expanded in c around inf 62.4%

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

   if 9.50000000000000094e-69 < x

   1. Initial program 82.6%

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

      1. sub-neg 82.6%

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

      2. associate-+l- 82.6%

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

      3. sub-neg 82.6%

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

      4. sub-neg 82.6%

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

      5. distribute-rgt-out-- 85.5%

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

      6. associate-*l* 86.9%

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

      7. distribute-lft-neg-in 86.9%

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

      8. cancel-sign-sub 86.9%

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

      9. associate-*l* 86.9%

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

      10. associate-*l* 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in t around inf 52.3%

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

      1. pow1 52.3%

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

      2. *-commutative 52.3%

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

   6. Applied egg-rr 52.3%

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

      1. unpow1 52.3%

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

      2. *-commutative 52.3%

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

      3. associate-*l* 55.1%

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

      4. *-commutative 55.1%

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

   8. Simplified 55.1%

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

   9. Taylor expanded in x around inf 44.0%

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

       1. *-commutative 44.0%

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

       2. *-commutative 44.0%

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

       3. associate-*l* 42.6%

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

       4. *-commutative 42.6%

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

       5. associate-*r* 43.9%

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

       6. *-commutative 43.9%

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

       7. associate-*r* 43.9%

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

       8. *-commutative 43.9%

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

       9. associate-*r* 43.9%

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

       10. *-commutative 43.9%

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

       11. associate-*l* 42.5%

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

   11. Simplified 42.5%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+214}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{+176}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-60}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-170}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-289}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-280}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-235}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-69}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\\ \end{array} \]

Alternative 7: 33.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ t_2 := t \cdot \left(a \cdot -4\right)\\ t_3 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{+214}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.62 \cdot 10^{-288}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-277}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-236}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* x (* 18.0 (* y (* z t)))))
        (t_2 (* t (* a -4.0)))
        (t_3 (* -27.0 (* j k))))
   (if (<= x -8e+214)
     (* 18.0 (* y (* t (* x z))))
     (if (<= x -7.8e+170)
       (* x (* i -4.0))
       (if (<= x -2.8e-61)
         t_1
         (if (<= x -3.5e-169)
           t_2
           (if (<= x -1.62e-288)
             t_3
             (if (<= x 2.1e-277)
               (* b c)
               (if (<= x 3.1e-236) t_3 (if (<= x 6.2e-68) t_2 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 = x * (18.0 * (y * (z * t)));
	double t_2 = t * (a * -4.0);
	double t_3 = -27.0 * (j * k);
	double tmp;
	if (x <= -8e+214) {
		tmp = 18.0 * (y * (t * (x * z)));
	} else if (x <= -7.8e+170) {
		tmp = x * (i * -4.0);
	} else if (x <= -2.8e-61) {
		tmp = t_1;
	} else if (x <= -3.5e-169) {
		tmp = t_2;
	} else if (x <= -1.62e-288) {
		tmp = t_3;
	} else if (x <= 2.1e-277) {
		tmp = b * c;
	} else if (x <= 3.1e-236) {
		tmp = t_3;
	} else if (x <= 6.2e-68) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (18.0d0 * (y * (z * t)))
    t_2 = t * (a * (-4.0d0))
    t_3 = (-27.0d0) * (j * k)
    if (x <= (-8d+214)) then
        tmp = 18.0d0 * (y * (t * (x * z)))
    else if (x <= (-7.8d+170)) then
        tmp = x * (i * (-4.0d0))
    else if (x <= (-2.8d-61)) then
        tmp = t_1
    else if (x <= (-3.5d-169)) then
        tmp = t_2
    else if (x <= (-1.62d-288)) then
        tmp = t_3
    else if (x <= 2.1d-277) then
        tmp = b * c
    else if (x <= 3.1d-236) then
        tmp = t_3
    else if (x <= 6.2d-68) then
        tmp = t_2
    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 = x * (18.0 * (y * (z * t)));
	double t_2 = t * (a * -4.0);
	double t_3 = -27.0 * (j * k);
	double tmp;
	if (x <= -8e+214) {
		tmp = 18.0 * (y * (t * (x * z)));
	} else if (x <= -7.8e+170) {
		tmp = x * (i * -4.0);
	} else if (x <= -2.8e-61) {
		tmp = t_1;
	} else if (x <= -3.5e-169) {
		tmp = t_2;
	} else if (x <= -1.62e-288) {
		tmp = t_3;
	} else if (x <= 2.1e-277) {
		tmp = b * c;
	} else if (x <= 3.1e-236) {
		tmp = t_3;
	} else if (x <= 6.2e-68) {
		tmp = t_2;
	} 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 = x * (18.0 * (y * (z * t)))
	t_2 = t * (a * -4.0)
	t_3 = -27.0 * (j * k)
	tmp = 0
	if x <= -8e+214:
		tmp = 18.0 * (y * (t * (x * z)))
	elif x <= -7.8e+170:
		tmp = x * (i * -4.0)
	elif x <= -2.8e-61:
		tmp = t_1
	elif x <= -3.5e-169:
		tmp = t_2
	elif x <= -1.62e-288:
		tmp = t_3
	elif x <= 2.1e-277:
		tmp = b * c
	elif x <= 3.1e-236:
		tmp = t_3
	elif x <= 6.2e-68:
		tmp = t_2
	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(x * Float64(18.0 * Float64(y * Float64(z * t))))
	t_2 = Float64(t * Float64(a * -4.0))
	t_3 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (x <= -8e+214)
		tmp = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))));
	elseif (x <= -7.8e+170)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (x <= -2.8e-61)
		tmp = t_1;
	elseif (x <= -3.5e-169)
		tmp = t_2;
	elseif (x <= -1.62e-288)
		tmp = t_3;
	elseif (x <= 2.1e-277)
		tmp = Float64(b * c);
	elseif (x <= 3.1e-236)
		tmp = t_3;
	elseif (x <= 6.2e-68)
		tmp = t_2;
	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 = x * (18.0 * (y * (z * t)));
	t_2 = t * (a * -4.0);
	t_3 = -27.0 * (j * k);
	tmp = 0.0;
	if (x <= -8e+214)
		tmp = 18.0 * (y * (t * (x * z)));
	elseif (x <= -7.8e+170)
		tmp = x * (i * -4.0);
	elseif (x <= -2.8e-61)
		tmp = t_1;
	elseif (x <= -3.5e-169)
		tmp = t_2;
	elseif (x <= -1.62e-288)
		tmp = t_3;
	elseif (x <= 2.1e-277)
		tmp = b * c;
	elseif (x <= 3.1e-236)
		tmp = t_3;
	elseif (x <= 6.2e-68)
		tmp = t_2;
	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[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+214], N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.8e+170], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.8e-61], t$95$1, If[LessEqual[x, -3.5e-169], t$95$2, If[LessEqual[x, -1.62e-288], t$95$3, If[LessEqual[x, 2.1e-277], N[(b * c), $MachinePrecision], If[LessEqual[x, 3.1e-236], t$95$3, If[LessEqual[x, 6.2e-68], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -7.9999999999999996e214

   1. Initial program 58.4%

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

      1. sub-neg 58.4%

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

      2. associate-+l- 58.4%

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

      3. sub-neg 58.4%

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

      4. sub-neg 58.4%

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

      5. distribute-rgt-out-- 58.4%

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

      6. associate-*l* 58.4%

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

      7. distribute-lft-neg-in 58.4%

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

      8. cancel-sign-sub 58.4%

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

      9. associate-*l* 58.4%

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

      10. associate-*l* 58.4%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in t around inf 64.5%

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

   5. Taylor expanded in y around inf 64.4%

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

   if -7.9999999999999996e214 < x < -7.8000000000000005e170

   1. Initial program 70.0%

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

      1. sub-neg 70.0%

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

      2. associate-+l- 70.0%

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

      3. sub-neg 70.0%

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

      4. sub-neg 70.0%

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

      5. distribute-rgt-out-- 70.0%

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

      6. associate-*l* 70.0%

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

      7. distribute-lft-neg-in 70.0%

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

      8. cancel-sign-sub 70.0%

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

      9. associate-*l* 70.0%

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

      10. associate-*l* 70.0%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in x around inf 90.0%

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

   5. Taylor expanded in y around 0 70.4%

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

   if -7.8000000000000005e170 < x < -2.8000000000000001e-61 or 6.1999999999999999e-68 < x

   1. Initial program 83.3%

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

      1. sub-neg 83.3%

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

      2. associate-+l- 83.3%

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

      3. sub-neg 83.3%

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

      4. sub-neg 83.3%

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

      5. distribute-rgt-out-- 85.0%

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

      6. associate-*l* 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* 85.8%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in x around inf 63.2%

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

   5. Taylor expanded in y around inf 46.9%

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

   if -2.8000000000000001e-61 < x < -3.5000000000000003e-169 or 3.0999999999999998e-236 < x < 6.1999999999999999e-68

   1. Initial program 92.9%

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

      1. sub-neg 92.9%

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

      2. associate-+l- 92.9%

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

      3. sub-neg 92.9%

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

      4. sub-neg 92.9%

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

      5. distribute-rgt-out-- 94.7%

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

      6. associate-*l* 91.3%

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

      7. distribute-lft-neg-in 91.3%

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

      8. cancel-sign-sub 91.3%

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

      9. associate-*l* 91.3%

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

      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 inf 57.4%

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

   5. Taylor expanded in y around 0 49.0%

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

   if -3.5000000000000003e-169 < x < -1.6200000000000001e-288 or 2.09999999999999995e-277 < x < 3.0999999999999998e-236

   1. Initial program 94.6%

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

      1. sub-neg 94.6%

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

      2. +-commutative 94.6%

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

      3. associate-*l* 94.5%

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

      4. distribute-rgt-neg-in 94.5%

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

      5. fma-def 97.2%

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

      6. *-commutative 97.2%

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

      7. distribute-rgt-neg-in 97.2%

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

      8. metadata-eval 97.2%

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

      9. sub-neg 97.2%

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

      10. +-commutative 97.2%

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

      11. associate-*l* 97.2%

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

      12. distribute-rgt-neg-in 97.2%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in j around inf 46.1%

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

   if -1.6200000000000001e-288 < x < 2.09999999999999995e-277

   1. Initial program 92.3%

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

      1. sub-neg 92.3%

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

      2. associate-+l- 92.3%

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

      3. sub-neg 92.3%

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

      4. sub-neg 92.3%

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

      5. distribute-rgt-out-- 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* 85.2%

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

      7. distribute-lft-neg-in 85.2%

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

      8. cancel-sign-sub 85.2%

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

      9. associate-*l* 85.2%

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

      10. associate-*l* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in j around 0 85.0%

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

   5. Taylor expanded in c around inf 62.4%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+214}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-169}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;x \leq -1.62 \cdot 10^{-288}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-277}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-236}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-68}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 8: 46.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ t_3 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-104}:\\ \;\;\;\;\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(t \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+179}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

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 (+ (* b c) (* k (* j -27.0))))
        (t_2 (+ (* -4.0 (* x i)) (* -27.0 (* j k))))
        (t_3 (+ (* b c) (* -4.0 (* t a)))))
   (if (<= a -1.6e+39)
     t_3
     (if (<= a 6.5e-253)
       t_2
       (if (<= a 8.4e-153)
         t_1
         (if (<= a 2e-104)
           (* (* (* (* x 18.0) y) z) t)
           (if (<= a 1.8e-24)
             t_1
             (if (<= a 3.9e+108)
               (* x (* t (* y (* 18.0 z))))
               (if (<= a 8.4e+179) 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 = (b * c) + (k * (j * -27.0));
	double t_2 = (-4.0 * (x * i)) + (-27.0 * (j * k));
	double t_3 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if (a <= -1.6e+39) {
		tmp = t_3;
	} else if (a <= 6.5e-253) {
		tmp = t_2;
	} else if (a <= 8.4e-153) {
		tmp = t_1;
	} else if (a <= 2e-104) {
		tmp = (((x * 18.0) * y) * z) * t;
	} else if (a <= 1.8e-24) {
		tmp = t_1;
	} else if (a <= 3.9e+108) {
		tmp = x * (t * (y * (18.0 * z)));
	} else if (a <= 8.4e+179) {
		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 = (b * c) + (k * (j * (-27.0d0)))
    t_2 = ((-4.0d0) * (x * i)) + ((-27.0d0) * (j * k))
    t_3 = (b * c) + ((-4.0d0) * (t * a))
    if (a <= (-1.6d+39)) then
        tmp = t_3
    else if (a <= 6.5d-253) then
        tmp = t_2
    else if (a <= 8.4d-153) then
        tmp = t_1
    else if (a <= 2d-104) then
        tmp = (((x * 18.0d0) * y) * z) * t
    else if (a <= 1.8d-24) then
        tmp = t_1
    else if (a <= 3.9d+108) then
        tmp = x * (t * (y * (18.0d0 * z)))
    else if (a <= 8.4d+179) 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 = (b * c) + (k * (j * -27.0));
	double t_2 = (-4.0 * (x * i)) + (-27.0 * (j * k));
	double t_3 = (b * c) + (-4.0 * (t * a));
	double tmp;
	if (a <= -1.6e+39) {
		tmp = t_3;
	} else if (a <= 6.5e-253) {
		tmp = t_2;
	} else if (a <= 8.4e-153) {
		tmp = t_1;
	} else if (a <= 2e-104) {
		tmp = (((x * 18.0) * y) * z) * t;
	} else if (a <= 1.8e-24) {
		tmp = t_1;
	} else if (a <= 3.9e+108) {
		tmp = x * (t * (y * (18.0 * z)));
	} else if (a <= 8.4e+179) {
		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 = (b * c) + (k * (j * -27.0))
	t_2 = (-4.0 * (x * i)) + (-27.0 * (j * k))
	t_3 = (b * c) + (-4.0 * (t * a))
	tmp = 0
	if a <= -1.6e+39:
		tmp = t_3
	elif a <= 6.5e-253:
		tmp = t_2
	elif a <= 8.4e-153:
		tmp = t_1
	elif a <= 2e-104:
		tmp = (((x * 18.0) * y) * z) * t
	elif a <= 1.8e-24:
		tmp = t_1
	elif a <= 3.9e+108:
		tmp = x * (t * (y * (18.0 * z)))
	elif a <= 8.4e+179:
		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(Float64(b * c) + Float64(k * Float64(j * -27.0)))
	t_2 = Float64(Float64(-4.0 * Float64(x * i)) + Float64(-27.0 * Float64(j * k)))
	t_3 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (a <= -1.6e+39)
		tmp = t_3;
	elseif (a <= 6.5e-253)
		tmp = t_2;
	elseif (a <= 8.4e-153)
		tmp = t_1;
	elseif (a <= 2e-104)
		tmp = Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t);
	elseif (a <= 1.8e-24)
		tmp = t_1;
	elseif (a <= 3.9e+108)
		tmp = Float64(x * Float64(t * Float64(y * Float64(18.0 * z))));
	elseif (a <= 8.4e+179)
		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 = (b * c) + (k * (j * -27.0));
	t_2 = (-4.0 * (x * i)) + (-27.0 * (j * k));
	t_3 = (b * c) + (-4.0 * (t * a));
	tmp = 0.0;
	if (a <= -1.6e+39)
		tmp = t_3;
	elseif (a <= 6.5e-253)
		tmp = t_2;
	elseif (a <= 8.4e-153)
		tmp = t_1;
	elseif (a <= 2e-104)
		tmp = (((x * 18.0) * y) * z) * t;
	elseif (a <= 1.8e-24)
		tmp = t_1;
	elseif (a <= 3.9e+108)
		tmp = x * (t * (y * (18.0 * z)));
	elseif (a <= 8.4e+179)
		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[(N[(b * c), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e+39], t$95$3, If[LessEqual[a, 6.5e-253], t$95$2, If[LessEqual[a, 8.4e-153], t$95$1, If[LessEqual[a, 2e-104], N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[a, 1.8e-24], t$95$1, If[LessEqual[a, 3.9e+108], N[(x * N[(t * N[(y * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.4e+179], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.59999999999999996e39 or 8.3999999999999994e179 < a

   1. Initial program 82.7%

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

      1. sub-neg 82.7%

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

      2. associate-+l- 82.7%

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

      3. sub-neg 82.7%

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

      4. sub-neg 82.7%

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

      5. distribute-rgt-out-- 86.1%

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

      6. associate-*l* 87.3%

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

      7. distribute-lft-neg-in 87.3%

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

      8. cancel-sign-sub 87.3%

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

      9. associate-*l* 87.3%

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

      10. associate-*l* 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in j around 0 76.2%

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

   5. Taylor expanded in x around 0 60.2%

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

   if -1.59999999999999996e39 < a < 6.4999999999999998e-253 or 3.89999999999999985e108 < a < 8.3999999999999994e179

   1. Initial program 85.5%

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

      1. sub-neg 85.5%

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

      2. +-commutative 85.5%

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

      3. associate-*l* 84.5%

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

      4. distribute-rgt-neg-in 84.5%

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

      5. fma-def 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 83.6%

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

   4. Taylor expanded in t around 0 65.1%

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

      1. fma-def 67.2%

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

      2. associate-*r* 67.2%

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

      3. *-commutative 67.2%

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

      4. fma-def 67.2%

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

      5. associate-*r* 67.2%

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

      6. *-commutative 67.2%

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

      7. *-commutative 67.2%

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

      8. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in c around 0 55.6%

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

   if 6.4999999999999998e-253 < a < 8.40000000000000017e-153 or 1.99999999999999985e-104 < a < 1.8e-24

   1. Initial program 84.1%

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

      1. sub-neg 84.1%

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

      2. *-commutative 84.1%

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

      3. distribute-rgt-neg-in 84.1%

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

   3. Simplified 90.2%

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

      1. fma-udef 87.0%

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

      2. fma-udef 87.0%

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

      3. associate-*l* 87.1%

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

      4. fma-udef 87.1%

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

   5. Applied egg-rr 87.1%

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

   6. Taylor expanded in b around inf 63.3%

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

   if 8.40000000000000017e-153 < a < 1.99999999999999985e-104

   1. Initial program 93.5%

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

      1. sub-neg 93.5%

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

      2. associate-+l- 93.5%

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

      3. sub-neg 93.5%

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

      4. sub-neg 93.5%

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

      5. distribute-rgt-out-- 93.5%

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

      6. associate-*l* 87.8%

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

      7. distribute-lft-neg-in 87.8%

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

      8. cancel-sign-sub 87.8%

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

      9. associate-*l* 87.8%

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

      10. associate-*l* 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in t around inf 69.3%

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

      1. pow1 69.3%

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

      2. *-commutative 69.3%

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

   6. Applied egg-rr 69.3%

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

      1. unpow1 69.3%

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

      2. *-commutative 69.3%

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

      3. associate-*l* 63.6%

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

      4. *-commutative 63.6%

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

   8. Simplified 63.6%

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

   9. Taylor expanded in x around inf 63.5%

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

       1. *-commutative 63.5%

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

       2. *-commutative 63.5%

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

       3. associate-*l* 69.4%

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

       4. *-commutative 69.4%

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

       5. associate-*r* 63.5%

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

       6. *-commutative 63.5%

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

       7. associate-*r* 63.6%

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

       8. *-commutative 63.6%

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

       9. associate-*r* 63.6%

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

       10. *-commutative 63.6%

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

       11. associate-*l* 69.3%

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

   11. Simplified 69.3%

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

   if 1.8e-24 < a < 3.89999999999999985e108

   1. Initial program 88.7%

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

      1. sub-neg 88.7%

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

      2. associate-+l- 88.7%

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

      3. sub-neg 88.7%

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

      4. sub-neg 88.7%

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

      5. distribute-rgt-out-- 88.7%

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

      6. associate-*l* 85.3%

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

      7. distribute-lft-neg-in 85.3%

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

      8. cancel-sign-sub 85.3%

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

      9. associate-*l* 85.3%

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

      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 x around inf 66.3%

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

   5. Taylor expanded in y around inf 51.9%

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

      1. associate-*r* 51.9%

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

      2. *-commutative 51.9%

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

      3. associate-*r* 51.9%

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

      4. associate-*r* 51.9%

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

      5. *-commutative 51.9%

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

      6. associate-*r* 51.9%

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

   7. Simplified 51.9%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+39}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-253}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-153}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-104}:\\ \;\;\;\;\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-24}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(t \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+179}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 9: 58.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ t_2 := b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: 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)) (* -27.0 (* j k))))
        (t_2 (+ (* b c) (* k (* j -27.0)))))
   (if (<= t -1.15e+72)
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
     (if (<= t -5.2e-85)
       t_2
       (if (<= t -3.5e-123)
         (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))
         (if (<= t 2.45e-211)
           t_1
           (if (<= t 8e-72)
             t_2
             (if (<= t 1.12e+23)
               t_1
               (* 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 = (-4.0 * (x * i)) + (-27.0 * (j * k));
	double t_2 = (b * c) + (k * (j * -27.0));
	double tmp;
	if (t <= -1.15e+72) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -5.2e-85) {
		tmp = t_2;
	} else if (t <= -3.5e-123) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else if (t <= 2.45e-211) {
		tmp = t_1;
	} else if (t <= 8e-72) {
		tmp = t_2;
	} else if (t <= 1.12e+23) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = ((-4.0d0) * (x * i)) + ((-27.0d0) * (j * k))
    t_2 = (b * c) + (k * (j * (-27.0d0)))
    if (t <= (-1.15d+72)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= (-5.2d-85)) then
        tmp = t_2
    else if (t <= (-3.5d-123)) then
        tmp = x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))
    else if (t <= 2.45d-211) then
        tmp = t_1
    else if (t <= 8d-72) then
        tmp = t_2
    else if (t <= 1.12d+23) then
        tmp = t_1
    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 = (-4.0 * (x * i)) + (-27.0 * (j * k));
	double t_2 = (b * c) + (k * (j * -27.0));
	double tmp;
	if (t <= -1.15e+72) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -5.2e-85) {
		tmp = t_2;
	} else if (t <= -3.5e-123) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else if (t <= 2.45e-211) {
		tmp = t_1;
	} else if (t <= 8e-72) {
		tmp = t_2;
	} else if (t <= 1.12e+23) {
		tmp = t_1;
	} 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 = (-4.0 * (x * i)) + (-27.0 * (j * k))
	t_2 = (b * c) + (k * (j * -27.0))
	tmp = 0
	if t <= -1.15e+72:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= -5.2e-85:
		tmp = t_2
	elif t <= -3.5e-123:
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	elif t <= 2.45e-211:
		tmp = t_1
	elif t <= 8e-72:
		tmp = t_2
	elif t <= 1.12e+23:
		tmp = t_1
	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(Float64(-4.0 * Float64(x * i)) + Float64(-27.0 * Float64(j * k)))
	t_2 = Float64(Float64(b * c) + Float64(k * Float64(j * -27.0)))
	tmp = 0.0
	if (t <= -1.15e+72)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= -5.2e-85)
		tmp = t_2;
	elseif (t <= -3.5e-123)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	elseif (t <= 2.45e-211)
		tmp = t_1;
	elseif (t <= 8e-72)
		tmp = t_2;
	elseif (t <= 1.12e+23)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

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)) + (-27.0 * (j * k));
	t_2 = (b * c) + (k * (j * -27.0));
	tmp = 0.0;
	if (t <= -1.15e+72)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= -5.2e-85)
		tmp = t_2;
	elseif (t <= -3.5e-123)
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	elseif (t <= 2.45e-211)
		tmp = t_1;
	elseif (t <= 8e-72)
		tmp = t_2;
	elseif (t <= 1.12e+23)
		tmp = t_1;
	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[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+72], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.2e-85], t$95$2, If[LessEqual[t, -3.5e-123], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.45e-211], t$95$1, If[LessEqual[t, 8e-72], t$95$2, If[LessEqual[t, 1.12e+23], t$95$1, N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.15e72

   1. Initial program 76.8%

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

      1. sub-neg 76.8%

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

      2. associate-+l- 76.8%

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

      3. sub-neg 76.8%

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

      4. sub-neg 76.8%

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

      5. distribute-rgt-out-- 78.8%

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

      6. associate-*l* 78.8%

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

      7. distribute-lft-neg-in 78.8%

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

      8. cancel-sign-sub 78.8%

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

      9. associate-*l* 78.8%

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

      10. associate-*l* 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in t around inf 74.1%

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

      1. pow1 74.1%

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

      2. *-commutative 74.1%

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

   6. Applied egg-rr 74.1%

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

      1. unpow1 74.1%

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

      2. *-commutative 74.1%

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

      3. associate-*l* 74.1%

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

      4. *-commutative 74.1%

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

   8. Simplified 74.1%

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

   if -1.15e72 < t < -5.20000000000000023e-85 or 2.45000000000000016e-211 < t < 7.9999999999999997e-72

   1. Initial program 94.6%

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

      1. sub-neg 94.6%

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

      2. *-commutative 94.6%

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

      3. distribute-rgt-neg-in 94.6%

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

   3. Simplified 94.6%

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

      1. fma-udef 94.6%

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

      2. fma-udef 94.6%

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

      3. associate-*l* 94.6%

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

      4. fma-udef 94.6%

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

   5. Applied egg-rr 94.6%

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

   6. Taylor expanded in b around inf 67.0%

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

   if -5.20000000000000023e-85 < t < -3.4999999999999999e-123

   1. Initial program 82.8%

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

      1. sub-neg 82.8%

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

      2. associate-+l- 82.8%

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

      3. sub-neg 82.8%

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

      4. sub-neg 82.8%

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

      5. distribute-rgt-out-- 82.8%

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

      6. associate-*l* 82.8%

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

      7. distribute-lft-neg-in 82.8%

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

      8. cancel-sign-sub 82.8%

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

      9. associate-*l* 82.8%

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

      10. associate-*l* 82.8%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in x around inf 68.4%

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

   if -3.4999999999999999e-123 < t < 2.45000000000000016e-211 or 7.9999999999999997e-72 < t < 1.12e23

   1. Initial program 86.2%

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

      1. sub-neg 86.2%

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

      2. +-commutative 86.2%

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

      3. associate-*l* 86.2%

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

      4. distribute-rgt-neg-in 86.2%

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

      5. fma-def 89.3%

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

      6. *-commutative 89.3%

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

      7. distribute-rgt-neg-in 89.3%

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

      8. metadata-eval 89.3%

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

      9. sub-neg 89.3%

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

      10. +-commutative 89.3%

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

      11. associate-*l* 89.3%

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

      12. distribute-rgt-neg-in 89.3%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in t around 0 81.3%

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

      1. fma-def 84.4%

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

      2. associate-*r* 84.4%

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

      3. *-commutative 84.4%

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

      4. fma-def 84.4%

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

      5. associate-*r* 84.4%

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

      6. *-commutative 84.4%

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

      7. *-commutative 84.4%

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

      8. *-commutative 84.4%

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

   6. Simplified 84.4%

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

   7. Taylor expanded in c around 0 68.0%

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

   if 1.12e23 < t

   1. Initial program 83.6%

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

      1. sub-neg 83.6%

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

      2. associate-+l- 83.6%

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

      3. sub-neg 83.6%

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

      4. sub-neg 83.6%

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

      5. distribute-rgt-out-- 86.3%

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

      6. associate-*l* 81.2%

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

      7. distribute-lft-neg-in 81.2%

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

      8. cancel-sign-sub 81.2%

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

      9. associate-*l* 81.2%

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

      10. associate-*l* 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in t around inf 72.9%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-85}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-211}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-72}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+23}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 10: 57.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-85}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-86}:\\ \;\;\;\;b \cdot c + \left(18 \cdot y\right) \cdot \left(t \cdot \left(x \cdot z\right)\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: 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)) (* -27.0 (* j k)))))
   (if (<= t -1.45e+71)
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
     (if (<= t -6e-85)
       (+ (* b c) (* k (* j -27.0)))
       (if (<= t -2.4e-123)
         (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))
         (if (<= t 1.9e-172)
           t_1
           (if (<= t 3.2e-86)
             (+ (* b c) (* (* 18.0 y) (* t (* x z))))
             (if (<= t 1.05e+23)
               t_1
               (* 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 = (-4.0 * (x * i)) + (-27.0 * (j * k));
	double tmp;
	if (t <= -1.45e+71) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -6e-85) {
		tmp = (b * c) + (k * (j * -27.0));
	} else if (t <= -2.4e-123) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else if (t <= 1.9e-172) {
		tmp = t_1;
	} else if (t <= 3.2e-86) {
		tmp = (b * c) + ((18.0 * y) * (t * (x * z)));
	} else if (t <= 1.05e+23) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = ((-4.0d0) * (x * i)) + ((-27.0d0) * (j * k))
    if (t <= (-1.45d+71)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= (-6d-85)) then
        tmp = (b * c) + (k * (j * (-27.0d0)))
    else if (t <= (-2.4d-123)) then
        tmp = x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))
    else if (t <= 1.9d-172) then
        tmp = t_1
    else if (t <= 3.2d-86) then
        tmp = (b * c) + ((18.0d0 * y) * (t * (x * z)))
    else if (t <= 1.05d+23) then
        tmp = t_1
    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 = (-4.0 * (x * i)) + (-27.0 * (j * k));
	double tmp;
	if (t <= -1.45e+71) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -6e-85) {
		tmp = (b * c) + (k * (j * -27.0));
	} else if (t <= -2.4e-123) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else if (t <= 1.9e-172) {
		tmp = t_1;
	} else if (t <= 3.2e-86) {
		tmp = (b * c) + ((18.0 * y) * (t * (x * z)));
	} else if (t <= 1.05e+23) {
		tmp = t_1;
	} 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 = (-4.0 * (x * i)) + (-27.0 * (j * k))
	tmp = 0
	if t <= -1.45e+71:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= -6e-85:
		tmp = (b * c) + (k * (j * -27.0))
	elif t <= -2.4e-123:
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	elif t <= 1.9e-172:
		tmp = t_1
	elif t <= 3.2e-86:
		tmp = (b * c) + ((18.0 * y) * (t * (x * z)))
	elif t <= 1.05e+23:
		tmp = t_1
	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(Float64(-4.0 * Float64(x * i)) + Float64(-27.0 * Float64(j * k)))
	tmp = 0.0
	if (t <= -1.45e+71)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= -6e-85)
		tmp = Float64(Float64(b * c) + Float64(k * Float64(j * -27.0)));
	elseif (t <= -2.4e-123)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	elseif (t <= 1.9e-172)
		tmp = t_1;
	elseif (t <= 3.2e-86)
		tmp = Float64(Float64(b * c) + Float64(Float64(18.0 * y) * Float64(t * Float64(x * z))));
	elseif (t <= 1.05e+23)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

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)) + (-27.0 * (j * k));
	tmp = 0.0;
	if (t <= -1.45e+71)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= -6e-85)
		tmp = (b * c) + (k * (j * -27.0));
	elseif (t <= -2.4e-123)
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	elseif (t <= 1.9e-172)
		tmp = t_1;
	elseif (t <= 3.2e-86)
		tmp = (b * c) + ((18.0 * y) * (t * (x * z)));
	elseif (t <= 1.05e+23)
		tmp = t_1;
	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[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e+71], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6e-85], N[(N[(b * c), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.4e-123], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-172], t$95$1, If[LessEqual[t, 3.2e-86], N[(N[(b * c), $MachinePrecision] + N[(N[(18.0 * y), $MachinePrecision] * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+23], t$95$1, N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.45000000000000004e71

   1. Initial program 76.8%

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

      1. sub-neg 76.8%

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

      2. associate-+l- 76.8%

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

      3. sub-neg 76.8%

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

      4. sub-neg 76.8%

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

      5. distribute-rgt-out-- 78.8%

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

      6. associate-*l* 78.8%

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

      7. distribute-lft-neg-in 78.8%

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

      8. cancel-sign-sub 78.8%

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

      9. associate-*l* 78.8%

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

      10. associate-*l* 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in t around inf 74.1%

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

      1. pow1 74.1%

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

      2. *-commutative 74.1%

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

   6. Applied egg-rr 74.1%

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

      1. unpow1 74.1%

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

      2. *-commutative 74.1%

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

      3. associate-*l* 74.1%

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

      4. *-commutative 74.1%

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

   8. Simplified 74.1%

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

   if -1.45000000000000004e71 < t < -6.00000000000000044e-85

   1. Initial program 97.2%

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

      1. sub-neg 97.2%

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

      2. *-commutative 97.2%

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

      3. distribute-rgt-neg-in 97.2%

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

   3. Simplified 97.1%

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

      1. fma-udef 97.1%

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

      2. fma-udef 97.1%

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

      3. associate-*l* 97.1%

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

      4. fma-udef 97.1%

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

   5. Applied egg-rr 97.1%

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

   6. Taylor expanded in b around inf 66.5%

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

   if -6.00000000000000044e-85 < t < -2.4e-123

   1. Initial program 82.8%

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

      1. sub-neg 82.8%

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

      2. associate-+l- 82.8%

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

      3. sub-neg 82.8%

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

      4. sub-neg 82.8%

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

      5. distribute-rgt-out-- 82.8%

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

      6. associate-*l* 82.8%

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

      7. distribute-lft-neg-in 82.8%

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

      8. cancel-sign-sub 82.8%

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

      9. associate-*l* 82.8%

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

      10. associate-*l* 82.8%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in x around inf 68.4%

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

   if -2.4e-123 < t < 1.89999999999999993e-172 or 3.20000000000000006e-86 < t < 1.0500000000000001e23

   1. Initial program 87.9%

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

      1. sub-neg 87.9%

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

      2. +-commutative 87.9%

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

      3. associate-*l* 87.9%

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

      4. distribute-rgt-neg-in 87.9%

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

      5. fma-def 90.6%

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

      6. *-commutative 90.6%

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

      7. distribute-rgt-neg-in 90.6%

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

      8. metadata-eval 90.6%

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

      9. sub-neg 90.6%

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

      10. +-commutative 90.6%

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

      11. associate-*l* 90.6%

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

      12. distribute-rgt-neg-in 90.6%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in t around 0 82.2%

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

      1. fma-def 84.9%

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

      2. associate-*r* 84.9%

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

      3. *-commutative 84.9%

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

      4. fma-def 84.9%

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

      5. associate-*r* 85.0%

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

      6. *-commutative 85.0%

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

      7. *-commutative 85.0%

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

      8. *-commutative 85.0%

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

   6. Simplified 85.0%

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

   7. Taylor expanded in c around 0 66.6%

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

   if 1.89999999999999993e-172 < t < 3.20000000000000006e-86

   1. Initial program 78.9%

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

      1. sub-neg 78.9%

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

      2. associate-+l- 78.9%

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

      3. sub-neg 78.9%

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

      4. sub-neg 78.9%

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

      5. distribute-rgt-out-- 78.9%

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

      6. associate-*l* 78.9%

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

      7. distribute-lft-neg-in 78.9%

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

      8. cancel-sign-sub 78.9%

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

      9. associate-*l* 78.9%

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

      10. associate-*l* 78.9%

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

   3. Simplified 78.9%

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

   4. Taylor expanded in j around 0 67.8%

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

   5. Taylor expanded in i around 0 67.8%

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

   6. Taylor expanded in y around inf 88.7%

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

      1. associate-*r* 88.7%

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

   8. Simplified 88.7%

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

   if 1.0500000000000001e23 < t

   1. Initial program 83.6%

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

      1. sub-neg 83.6%

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

      2. associate-+l- 83.6%

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

      3. sub-neg 83.6%

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

      4. sub-neg 83.6%

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

      5. distribute-rgt-out-- 86.3%

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

      6. associate-*l* 81.2%

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

      7. distribute-lft-neg-in 81.2%

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

      8. cancel-sign-sub 81.2%

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

      9. associate-*l* 81.2%

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

      10. associate-*l* 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in t around inf 72.9%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-85}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-172}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-86}:\\ \;\;\;\;b \cdot c + \left(18 \cdot y\right) \cdot \left(t \cdot \left(x \cdot z\right)\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+23}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 11: 74.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-85}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 280:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (- (* b c) (* t (- (* a 4.0) (* 18.0 (* y (* x z))))))))
   (if (<= t -3.3e+96)
     t_1
     (if (<= t -2.45e-85)
       (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))
       (if (<= t -9.2e-116)
         (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))
         (if (<= t 280.0)
           (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
           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 = (b * c) - (t * ((a * 4.0) - (18.0 * (y * (x * z)))));
	double tmp;
	if (t <= -3.3e+96) {
		tmp = t_1;
	} else if (t <= -2.45e-85) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if (t <= -9.2e-116) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else if (t <= 280.0) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} 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 = (b * c) - (t * ((a * 4.0d0) - (18.0d0 * (y * (x * z)))))
    if (t <= (-3.3d+96)) then
        tmp = t_1
    else if (t <= (-2.45d-85)) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    else if (t <= (-9.2d-116)) then
        tmp = x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))
    else if (t <= 280.0d0) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    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 = (b * c) - (t * ((a * 4.0) - (18.0 * (y * (x * z)))));
	double tmp;
	if (t <= -3.3e+96) {
		tmp = t_1;
	} else if (t <= -2.45e-85) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if (t <= -9.2e-116) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else if (t <= 280.0) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} 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 = (b * c) - (t * ((a * 4.0) - (18.0 * (y * (x * z)))))
	tmp = 0
	if t <= -3.3e+96:
		tmp = t_1
	elif t <= -2.45e-85:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	elif t <= -9.2e-116:
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	elif t <= 280.0:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	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(Float64(b * c) - Float64(t * Float64(Float64(a * 4.0) - Float64(18.0 * Float64(y * Float64(x * z))))))
	tmp = 0.0
	if (t <= -3.3e+96)
		tmp = t_1;
	elseif (t <= -2.45e-85)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	elseif (t <= -9.2e-116)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	elseif (t <= 280.0)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	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 = (b * c) - (t * ((a * 4.0) - (18.0 * (y * (x * z)))));
	tmp = 0.0;
	if (t <= -3.3e+96)
		tmp = t_1;
	elseif (t <= -2.45e-85)
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	elseif (t <= -9.2e-116)
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	elseif (t <= 280.0)
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	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[(N[(b * c), $MachinePrecision] - N[(t * N[(N[(a * 4.0), $MachinePrecision] - N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e+96], t$95$1, If[LessEqual[t, -2.45e-85], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.2e-116], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 280.0], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.29999999999999984e96 or 280 < t

   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-- 82.6%

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

      6. associate-*l* 79.7%

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

      7. distribute-lft-neg-in 79.7%

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

      8. cancel-sign-sub 79.7%

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

      9. associate-*l* 79.7%

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

      10. associate-*l* 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in j around 0 76.8%

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

   5. Taylor expanded in i around 0 76.8%

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

   if -3.29999999999999984e96 < t < -2.45000000000000007e-85

   1. Initial program 94.9%

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

   2. Taylor expanded in x around 0 78.6%

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

   if -2.45000000000000007e-85 < t < -9.20000000000000006e-116

   1. Initial program 89.5%

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

      1. sub-neg 89.5%

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

      2. associate-+l- 89.5%

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

      3. sub-neg 89.5%

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

      4. sub-neg 89.5%

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

      5. distribute-rgt-out-- 89.5%

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

      6. associate-*l* 89.5%

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

      7. distribute-lft-neg-in 89.5%

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

      8. cancel-sign-sub 89.5%

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

      9. associate-*l* 89.5%

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

      10. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in x around inf 72.5%

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

   if -9.20000000000000006e-116 < t < 280

   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* 87.7%

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

      7. distribute-lft-neg-in 87.7%

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

      8. cancel-sign-sub 87.7%

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

      9. associate-*l* 87.7%

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

      10. associate-*l* 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in t around 0 80.1%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+96}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-85}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;t \leq 280:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - t \cdot \left(a \cdot 4 - 18 \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 12: 32.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-46}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-127}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-308}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;y \leq 0.0145:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* t (* a -4.0))) (t_2 (* 18.0 (* y (* t (* x z))))))
   (if (<= y -4.2e+232)
     t_2
     (if (<= y -9e+223)
       t_1
       (if (<= y -4e+74)
         t_2
         (if (<= y -2.9e-46)
           (* k (* j -27.0))
           (if (<= y -1.75e-127)
             (* x (* i -4.0))
             (if (<= y 8.5e-308)
               (* j (* k -27.0))
               (if (<= y 0.0145) 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 = t * (a * -4.0);
	double t_2 = 18.0 * (y * (t * (x * z)));
	double tmp;
	if (y <= -4.2e+232) {
		tmp = t_2;
	} else if (y <= -9e+223) {
		tmp = t_1;
	} else if (y <= -4e+74) {
		tmp = t_2;
	} else if (y <= -2.9e-46) {
		tmp = k * (j * -27.0);
	} else if (y <= -1.75e-127) {
		tmp = x * (i * -4.0);
	} else if (y <= 8.5e-308) {
		tmp = j * (k * -27.0);
	} else if (y <= 0.0145) {
		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 = t * (a * (-4.0d0))
    t_2 = 18.0d0 * (y * (t * (x * z)))
    if (y <= (-4.2d+232)) then
        tmp = t_2
    else if (y <= (-9d+223)) then
        tmp = t_1
    else if (y <= (-4d+74)) then
        tmp = t_2
    else if (y <= (-2.9d-46)) then
        tmp = k * (j * (-27.0d0))
    else if (y <= (-1.75d-127)) then
        tmp = x * (i * (-4.0d0))
    else if (y <= 8.5d-308) then
        tmp = j * (k * (-27.0d0))
    else if (y <= 0.0145d0) 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 = t * (a * -4.0);
	double t_2 = 18.0 * (y * (t * (x * z)));
	double tmp;
	if (y <= -4.2e+232) {
		tmp = t_2;
	} else if (y <= -9e+223) {
		tmp = t_1;
	} else if (y <= -4e+74) {
		tmp = t_2;
	} else if (y <= -2.9e-46) {
		tmp = k * (j * -27.0);
	} else if (y <= -1.75e-127) {
		tmp = x * (i * -4.0);
	} else if (y <= 8.5e-308) {
		tmp = j * (k * -27.0);
	} else if (y <= 0.0145) {
		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 = t * (a * -4.0)
	t_2 = 18.0 * (y * (t * (x * z)))
	tmp = 0
	if y <= -4.2e+232:
		tmp = t_2
	elif y <= -9e+223:
		tmp = t_1
	elif y <= -4e+74:
		tmp = t_2
	elif y <= -2.9e-46:
		tmp = k * (j * -27.0)
	elif y <= -1.75e-127:
		tmp = x * (i * -4.0)
	elif y <= 8.5e-308:
		tmp = j * (k * -27.0)
	elif y <= 0.0145:
		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(t * Float64(a * -4.0))
	t_2 = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))))
	tmp = 0.0
	if (y <= -4.2e+232)
		tmp = t_2;
	elseif (y <= -9e+223)
		tmp = t_1;
	elseif (y <= -4e+74)
		tmp = t_2;
	elseif (y <= -2.9e-46)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (y <= -1.75e-127)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (y <= 8.5e-308)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (y <= 0.0145)
		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 = t * (a * -4.0);
	t_2 = 18.0 * (y * (t * (x * z)));
	tmp = 0.0;
	if (y <= -4.2e+232)
		tmp = t_2;
	elseif (y <= -9e+223)
		tmp = t_1;
	elseif (y <= -4e+74)
		tmp = t_2;
	elseif (y <= -2.9e-46)
		tmp = k * (j * -27.0);
	elseif (y <= -1.75e-127)
		tmp = x * (i * -4.0);
	elseif (y <= 8.5e-308)
		tmp = j * (k * -27.0);
	elseif (y <= 0.0145)
		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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+232], t$95$2, If[LessEqual[y, -9e+223], t$95$1, If[LessEqual[y, -4e+74], t$95$2, If[LessEqual[y, -2.9e-46], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.75e-127], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-308], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0145], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.19999999999999982e232 or -9e223 < y < -3.99999999999999981e74 or 0.0145000000000000007 < y

   1. Initial program 77.3%

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

      1. sub-neg 77.3%

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

      2. associate-+l- 77.3%

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

      3. sub-neg 77.3%

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

      4. sub-neg 77.3%

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

      5. distribute-rgt-out-- 79.2%

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

      6. associate-*l* 76.5%

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

      7. distribute-lft-neg-in 76.5%

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

      8. cancel-sign-sub 76.5%

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

      9. associate-*l* 76.5%

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

      10. associate-*l* 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in t around inf 57.1%

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

   5. Taylor expanded in y around inf 55.1%

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

   if -4.19999999999999982e232 < y < -9e223 or 8.49999999999999972e-308 < y < 0.0145000000000000007

   1. Initial program 88.0%

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

      1. sub-neg 88.0%

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

      2. associate-+l- 88.0%

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

      3. sub-neg 88.0%

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

      4. sub-neg 88.0%

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

      5. distribute-rgt-out-- 88.0%

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

      6. associate-*l* 88.0%

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

      7. distribute-lft-neg-in 88.0%

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

      8. cancel-sign-sub 88.0%

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

      9. associate-*l* 88.0%

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

      10. associate-*l* 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in t around inf 39.3%

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

   5. Taylor expanded in y around 0 30.8%

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

   if -3.99999999999999981e74 < y < -2.90000000000000005e-46

   1. Initial program 91.7%

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

      1. sub-neg 91.7%

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

      2. +-commutative 91.7%

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

      3. associate-*l* 91.7%

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

      4. distribute-rgt-neg-in 91.7%

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

      5. fma-def 91.7%

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

      6. *-commutative 91.7%

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

      7. distribute-rgt-neg-in 91.7%

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

      8. metadata-eval 91.7%

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

      9. sub-neg 91.7%

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

      10. +-commutative 91.7%

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

      11. associate-*l* 91.7%

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

      12. distribute-rgt-neg-in 91.7%

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

   3. Simplified 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 j around inf 30.7%

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

      1. associate-*r* 30.7%

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

      2. *-commutative 30.7%

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

      3. *-commutative 30.7%

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

      4. *-commutative 30.7%

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

   6. Simplified 30.7%

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

   7. Taylor expanded in j around 0 30.7%

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

      1. *-commutative 30.7%

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

      2. associate-*r* 30.7%

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

   9. Simplified 30.7%

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

   if -2.90000000000000005e-46 < y < -1.74999999999999995e-127

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. associate-+l- 99.9%

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

      3. sub-neg 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-out-- 99.9%

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

      6. associate-*l* 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 x around inf 41.7%

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

   5. Taylor expanded in y around 0 18.3%

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

   if -1.74999999999999995e-127 < y < 8.49999999999999972e-308

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. +-commutative 96.1%

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

      3. associate-*l* 96.1%

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

      4. distribute-rgt-neg-in 96.1%

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

      5. fma-def 96.1%

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

      6. *-commutative 96.1%

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

      7. distribute-rgt-neg-in 96.1%

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

      8. metadata-eval 96.1%

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

      9. sub-neg 96.1%

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

      10. +-commutative 96.1%

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

      11. associate-*l* 96.1%

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

      12. distribute-rgt-neg-in 96.1%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in j around inf 42.0%

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

      1. associate-*r* 42.0%

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

      2. *-commutative 42.0%

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

      3. *-commutative 42.0%

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

      4. *-commutative 42.0%

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

   6. Simplified 42.0%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+232}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+223}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+74}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-46}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-127}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-308}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;y \leq 0.0145:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 13: 49.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := b \cdot c + t_1\\ \mathbf{if}\;k \leq -3.8 \cdot 10^{-59}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 7 \cdot 10^{-174}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{-130}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;k \leq 1.09 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1700000:\\ \;\;\;\;x \cdot \left(\left(z \cdot t\right) \cdot \left(18 \cdot y\right)\right)\\ \mathbf{elif}\;k \leq 3600000:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_1 - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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 (* -4.0 (* t a))) (t_2 (+ (* b c) t_1)))
   (if (<= k -3.8e-59)
     (+ (* -4.0 (* x i)) (* -27.0 (* j k)))
     (if (<= k 7e-174)
       t_2
       (if (<= k 4.6e-130)
         (* x (* 18.0 (* y (* z t))))
         (if (<= k 1.09e-44)
           t_2
           (if (<= k 1700000.0)
             (* x (* (* z t) (* 18.0 y)))
             (if (<= k 3600000.0) (* b c) (- t_1 (* 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 t_1 = -4.0 * (t * a);
	double t_2 = (b * c) + t_1;
	double tmp;
	if (k <= -3.8e-59) {
		tmp = (-4.0 * (x * i)) + (-27.0 * (j * k));
	} else if (k <= 7e-174) {
		tmp = t_2;
	} else if (k <= 4.6e-130) {
		tmp = x * (18.0 * (y * (z * t)));
	} else if (k <= 1.09e-44) {
		tmp = t_2;
	} else if (k <= 1700000.0) {
		tmp = x * ((z * t) * (18.0 * y));
	} else if (k <= 3600000.0) {
		tmp = b * c;
	} else {
		tmp = t_1 - (27.0 * (j * k));
	}
	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 = (-4.0d0) * (t * a)
    t_2 = (b * c) + t_1
    if (k <= (-3.8d-59)) then
        tmp = ((-4.0d0) * (x * i)) + ((-27.0d0) * (j * k))
    else if (k <= 7d-174) then
        tmp = t_2
    else if (k <= 4.6d-130) then
        tmp = x * (18.0d0 * (y * (z * t)))
    else if (k <= 1.09d-44) then
        tmp = t_2
    else if (k <= 1700000.0d0) then
        tmp = x * ((z * t) * (18.0d0 * y))
    else if (k <= 3600000.0d0) then
        tmp = b * c
    else
        tmp = t_1 - (27.0d0 * (j * k))
    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 * (t * a);
	double t_2 = (b * c) + t_1;
	double tmp;
	if (k <= -3.8e-59) {
		tmp = (-4.0 * (x * i)) + (-27.0 * (j * k));
	} else if (k <= 7e-174) {
		tmp = t_2;
	} else if (k <= 4.6e-130) {
		tmp = x * (18.0 * (y * (z * t)));
	} else if (k <= 1.09e-44) {
		tmp = t_2;
	} else if (k <= 1700000.0) {
		tmp = x * ((z * t) * (18.0 * y));
	} else if (k <= 3600000.0) {
		tmp = b * c;
	} else {
		tmp = t_1 - (27.0 * (j * k));
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (t * a)
	t_2 = (b * c) + t_1
	tmp = 0
	if k <= -3.8e-59:
		tmp = (-4.0 * (x * i)) + (-27.0 * (j * k))
	elif k <= 7e-174:
		tmp = t_2
	elif k <= 4.6e-130:
		tmp = x * (18.0 * (y * (z * t)))
	elif k <= 1.09e-44:
		tmp = t_2
	elif k <= 1700000.0:
		tmp = x * ((z * t) * (18.0 * y))
	elif k <= 3600000.0:
		tmp = b * c
	else:
		tmp = t_1 - (27.0 * (j * k))
	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(t * a))
	t_2 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (k <= -3.8e-59)
		tmp = Float64(Float64(-4.0 * Float64(x * i)) + Float64(-27.0 * Float64(j * k)));
	elseif (k <= 7e-174)
		tmp = t_2;
	elseif (k <= 4.6e-130)
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))));
	elseif (k <= 1.09e-44)
		tmp = t_2;
	elseif (k <= 1700000.0)
		tmp = Float64(x * Float64(Float64(z * t) * Float64(18.0 * y)));
	elseif (k <= 3600000.0)
		tmp = Float64(b * c);
	else
		tmp = Float64(t_1 - Float64(27.0 * Float64(j * k)));
	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 * (t * a);
	t_2 = (b * c) + t_1;
	tmp = 0.0;
	if (k <= -3.8e-59)
		tmp = (-4.0 * (x * i)) + (-27.0 * (j * k));
	elseif (k <= 7e-174)
		tmp = t_2;
	elseif (k <= 4.6e-130)
		tmp = x * (18.0 * (y * (z * t)));
	elseif (k <= 1.09e-44)
		tmp = t_2;
	elseif (k <= 1700000.0)
		tmp = x * ((z * t) * (18.0 * y));
	elseif (k <= 3600000.0)
		tmp = b * c;
	else
		tmp = t_1 - (27.0 * (j * k));
	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[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[k, -3.8e-59], N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 7e-174], t$95$2, If[LessEqual[k, 4.6e-130], N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.09e-44], t$95$2, If[LessEqual[k, 1700000.0], N[(x * N[(N[(z * t), $MachinePrecision] * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3600000.0], N[(b * c), $MachinePrecision], N[(t$95$1 - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if k < -3.79999999999999983e-59

   1. Initial program 84.7%

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

      1. sub-neg 84.7%

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

      2. +-commutative 84.7%

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

      3. associate-*l* 84.8%

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

      4. distribute-rgt-neg-in 84.8%

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

      5. fma-def 89.5%

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

      6. *-commutative 89.5%

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

      7. distribute-rgt-neg-in 89.5%

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

      8. metadata-eval 89.5%

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

      9. sub-neg 89.5%

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

      10. +-commutative 89.5%

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

      11. associate-*l* 89.5%

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

      12. distribute-rgt-neg-in 89.5%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in t around 0 58.1%

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

      1. fma-def 60.4%

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

      2. associate-*r* 60.4%

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

      3. *-commutative 60.4%

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

      4. fma-def 60.4%

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

      5. associate-*r* 60.4%

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

      6. *-commutative 60.4%

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

      7. *-commutative 60.4%

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

      8. *-commutative 60.4%

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

   6. Simplified 60.4%

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

   7. Taylor expanded in c around 0 49.7%

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

   if -3.79999999999999983e-59 < k < 6.99999999999999975e-174 or 4.6000000000000002e-130 < k < 1.09e-44

   1. Initial program 88.5%

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

      1. sub-neg 88.5%

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

      2. associate-+l- 88.5%

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

      3. sub-neg 88.5%

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

      4. sub-neg 88.5%

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

      5. distribute-rgt-out-- 88.5%

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

      6. associate-*l* 87.5%

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

      7. distribute-lft-neg-in 87.5%

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

      8. cancel-sign-sub 87.5%

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

      9. associate-*l* 87.5%

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

      10. associate-*l* 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in j around 0 84.8%

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

   5. Taylor expanded in x around 0 53.0%

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

   if 6.99999999999999975e-174 < k < 4.6000000000000002e-130

   1. Initial program 56.7%

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

      1. sub-neg 56.7%

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

      2. associate-+l- 56.7%

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

      3. sub-neg 56.7%

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

      4. sub-neg 56.7%

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

      5. distribute-rgt-out-- 56.7%

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

      6. associate-*l* 56.7%

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

      7. distribute-lft-neg-in 56.7%

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

      8. cancel-sign-sub 56.7%

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

      9. associate-*l* 56.7%

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

      10. associate-*l* 56.7%

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

   3. Simplified 56.7%

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

   4. Taylor expanded in x around inf 93.8%

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

   5. Taylor expanded in y around inf 78.3%

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

   if 1.09e-44 < k < 1.7e6

   1. Initial program 93.2%

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

      1. sub-neg 93.2%

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

      2. associate-+l- 93.2%

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

      3. sub-neg 93.2%

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

      4. sub-neg 93.2%

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

      5. distribute-rgt-out-- 93.2%

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

      6. associate-*l* 87.1%

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

      7. distribute-lft-neg-in 87.1%

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

      8. cancel-sign-sub 87.1%

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

      9. associate-*l* 87.1%

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

      10. associate-*l* 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in x around inf 61.0%

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

   5. Taylor expanded in y around inf 54.7%

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

      1. associate-*r* 54.8%

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

      2. *-commutative 54.8%

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

   7. Simplified 54.8%

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

   if 1.7e6 < k < 3.6e6

   1. Initial program 85.2%

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

      1. sub-neg 85.2%

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

      2. associate-+l- 85.2%

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

      3. sub-neg 85.2%

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

      4. sub-neg 85.2%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 86.4%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 84.9%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 84.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 84.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 84.9%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 84.9%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 84.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 68.6%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in c around inf 20.4%

      \[\leadsto \color{blue}{c \cdot b} \]

   if 3.6e6 < k

   1. Initial program 83.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around -inf 77.0%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(-18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - -4 \cdot a\right) \cdot t\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in y around 0 67.1%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t\right) - 27 \cdot \left(k \cdot j\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.8 \cdot 10^{-59}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 7 \cdot 10^{-174}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{-130}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;k \leq 1.09 \cdot 10^{-44}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;k \leq 1700000:\\ \;\;\;\;x \cdot \left(\left(z \cdot t\right) \cdot \left(18 \cdot y\right)\right)\\ \mathbf{elif}\;k \leq 3600000:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 14: 58.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ t_2 := b \cdot c + k \cdot \left(j \cdot -27\right)\\ t_3 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

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)) (* -27.0 (* j k))))
        (t_2 (+ (* b c) (* k (* j -27.0))))
        (t_3 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -2.2e+71)
     t_3
     (if (<= t -1.7e-77)
       t_2
       (if (<= t 4.4e-211)
         t_1
         (if (<= t 3.3e-69) t_2 (if (<= t 9.6e+22) t_1 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)) + (-27.0 * (j * k));
	double t_2 = (b * c) + (k * (j * -27.0));
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -2.2e+71) {
		tmp = t_3;
	} else if (t <= -1.7e-77) {
		tmp = t_2;
	} else if (t <= 4.4e-211) {
		tmp = t_1;
	} else if (t <= 3.3e-69) {
		tmp = t_2;
	} else if (t <= 9.6e+22) {
		tmp = t_1;
	} 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)) + ((-27.0d0) * (j * k))
    t_2 = (b * c) + (k * (j * (-27.0d0)))
    t_3 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-2.2d+71)) then
        tmp = t_3
    else if (t <= (-1.7d-77)) then
        tmp = t_2
    else if (t <= 4.4d-211) then
        tmp = t_1
    else if (t <= 3.3d-69) then
        tmp = t_2
    else if (t <= 9.6d+22) then
        tmp = t_1
    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)) + (-27.0 * (j * k));
	double t_2 = (b * c) + (k * (j * -27.0));
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -2.2e+71) {
		tmp = t_3;
	} else if (t <= -1.7e-77) {
		tmp = t_2;
	} else if (t <= 4.4e-211) {
		tmp = t_1;
	} else if (t <= 3.3e-69) {
		tmp = t_2;
	} else if (t <= 9.6e+22) {
		tmp = t_1;
	} 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)) + (-27.0 * (j * k))
	t_2 = (b * c) + (k * (j * -27.0))
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -2.2e+71:
		tmp = t_3
	elif t <= -1.7e-77:
		tmp = t_2
	elif t <= 4.4e-211:
		tmp = t_1
	elif t <= 3.3e-69:
		tmp = t_2
	elif t <= 9.6e+22:
		tmp = t_1
	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(Float64(-4.0 * Float64(x * i)) + Float64(-27.0 * Float64(j * k)))
	t_2 = Float64(Float64(b * c) + Float64(k * Float64(j * -27.0)))
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -2.2e+71)
		tmp = t_3;
	elseif (t <= -1.7e-77)
		tmp = t_2;
	elseif (t <= 4.4e-211)
		tmp = t_1;
	elseif (t <= 3.3e-69)
		tmp = t_2;
	elseif (t <= 9.6e+22)
		tmp = t_1;
	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)) + (-27.0 * (j * k));
	t_2 = (b * c) + (k * (j * -27.0));
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -2.2e+71)
		tmp = t_3;
	elseif (t <= -1.7e-77)
		tmp = t_2;
	elseif (t <= 4.4e-211)
		tmp = t_1;
	elseif (t <= 3.3e-69)
		tmp = t_2;
	elseif (t <= 9.6e+22)
		tmp = t_1;
	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[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e+71], t$95$3, If[LessEqual[t, -1.7e-77], t$95$2, If[LessEqual[t, 4.4e-211], t$95$1, If[LessEqual[t, 3.3e-69], t$95$2, If[LessEqual[t, 9.6e+22], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.19999999999999995e71 or 9.6e22 < t

   1. Initial program 80.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 80.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 80.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 80.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 80.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 83.2%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 80.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 80.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 80.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 80.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 80.2%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 80.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 73.4%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]
   5. Step-by-step derivation

      1. pow1 73.4%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{{\left(y \cdot \left(z \cdot x\right)\right)}^{1}} - 4 \cdot a\right) \]

      2. *-commutative 73.4%

         \[\leadsto t \cdot \left(18 \cdot {\left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)}^{1} - 4 \cdot a\right) \]

   6. Applied egg-rr 73.4%

      \[\leadsto t \cdot \left(18 \cdot \color{blue}{{\left(y \cdot \left(x \cdot z\right)\right)}^{1}} - 4 \cdot a\right) \]
   7. Step-by-step derivation

      1. unpow1 73.4%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(y \cdot \left(x \cdot z\right)\right)} - 4 \cdot a\right) \]

      2. *-commutative 73.4%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(x \cdot z\right) \cdot y\right)} - 4 \cdot a\right) \]

      3. associate-*l* 71.9%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(z \cdot y\right)\right)} - 4 \cdot a\right) \]

      4. *-commutative 71.9%

         \[\leadsto t \cdot \left(18 \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right) - 4 \cdot a\right) \]

   8. Simplified 71.9%

      \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)} - 4 \cdot a\right) \]

   if -2.19999999999999995e71 < t < -1.69999999999999991e-77 or 4.39999999999999996e-211 < t < 3.3e-69

   1. Initial program 94.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 94.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. *-commutative 94.4%

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\color{blue}{k \cdot \left(j \cdot 27\right)}\right) \]

      3. distribute-rgt-neg-in 94.4%

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \color{blue}{k \cdot \left(-j \cdot 27\right)} \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x \cdot 18, y \cdot z, a \cdot -4\right), \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right) + k \cdot \left(j \cdot -27\right)} \]
   4. Step-by-step derivation

      1. fma-udef 96.3%

         \[\leadsto \color{blue}{\left(t \cdot \mathsf{fma}\left(x \cdot 18, y \cdot z, a \cdot -4\right) + \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right)} + k \cdot \left(j \cdot -27\right) \]

      2. fma-udef 96.3%

         \[\leadsto \left(t \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)} + \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right) + k \cdot \left(j \cdot -27\right) \]

      3. associate-*l* 96.3%

         \[\leadsto \left(t \cdot \left(\color{blue}{x \cdot \left(18 \cdot \left(y \cdot z\right)\right)} + a \cdot -4\right) + \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right) + k \cdot \left(j \cdot -27\right) \]

      4. fma-udef 96.3%

         \[\leadsto \left(t \cdot \color{blue}{\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right)} + \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right) + k \cdot \left(j \cdot -27\right) \]

   5. Applied egg-rr 96.3%

      \[\leadsto \color{blue}{\left(t \cdot \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right) + \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right)} + k \cdot \left(j \cdot -27\right) \]

   6. Taylor expanded in b around inf 65.7%

      \[\leadsto \color{blue}{c \cdot b} + k \cdot \left(j \cdot -27\right) \]

   if -1.69999999999999991e-77 < t < 4.39999999999999996e-211 or 3.3e-69 < t < 9.6e22

   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. +-commutative 86.1%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 86.1%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 86.1%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 88.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 88.6%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 88.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 88.6%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 88.6%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 88.6%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 88.6%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 88.6%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in t around 0 75.8%

      \[\leadsto \color{blue}{c \cdot b + \left(-4 \cdot \left(i \cdot x\right) + -27 \cdot \left(k \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 78.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, -4 \cdot \left(i \cdot x\right) + -27 \cdot \left(k \cdot j\right)\right)} \]

      2. associate-*r* 78.4%

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-4 \cdot i\right) \cdot x} + -27 \cdot \left(k \cdot j\right)\right) \]

      3. *-commutative 78.4%

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{x \cdot \left(-4 \cdot i\right)} + -27 \cdot \left(k \cdot j\right)\right) \]

      4. fma-def 78.4%

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(x, -4 \cdot i, -27 \cdot \left(k \cdot j\right)\right)}\right) \]

      5. associate-*r* 78.4%

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(x, -4 \cdot i, \color{blue}{\left(-27 \cdot k\right) \cdot j}\right)\right) \]

      6. *-commutative 78.4%

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(x, -4 \cdot i, \color{blue}{\left(k \cdot -27\right)} \cdot j\right)\right) \]

      7. *-commutative 78.4%

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(x, -4 \cdot i, \color{blue}{j \cdot \left(k \cdot -27\right)}\right)\right) \]

      8. *-commutative 78.4%

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(x, -4 \cdot i, j \cdot \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

   6. Simplified 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(x, -4 \cdot i, j \cdot \left(-27 \cdot k\right)\right)\right)} \]

   7. Taylor expanded in c around 0 62.2%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + -27 \cdot \left(k \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-77}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-211}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-69}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+22}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 15: 58.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ t_2 := b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;t \leq -4.25 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: 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)) (* -27.0 (* j k))))
        (t_2 (+ (* b c) (* k (* j -27.0)))))
   (if (<= t -4.25e+74)
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
     (if (<= t -1e-76)
       t_2
       (if (<= t 2.75e-211)
         t_1
         (if (<= t 2.6e-79)
           t_2
           (if (<= t 1.26e+23)
             t_1
             (* 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 = (-4.0 * (x * i)) + (-27.0 * (j * k));
	double t_2 = (b * c) + (k * (j * -27.0));
	double tmp;
	if (t <= -4.25e+74) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -1e-76) {
		tmp = t_2;
	} else if (t <= 2.75e-211) {
		tmp = t_1;
	} else if (t <= 2.6e-79) {
		tmp = t_2;
	} else if (t <= 1.26e+23) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = ((-4.0d0) * (x * i)) + ((-27.0d0) * (j * k))
    t_2 = (b * c) + (k * (j * (-27.0d0)))
    if (t <= (-4.25d+74)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= (-1d-76)) then
        tmp = t_2
    else if (t <= 2.75d-211) then
        tmp = t_1
    else if (t <= 2.6d-79) then
        tmp = t_2
    else if (t <= 1.26d+23) then
        tmp = t_1
    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 = (-4.0 * (x * i)) + (-27.0 * (j * k));
	double t_2 = (b * c) + (k * (j * -27.0));
	double tmp;
	if (t <= -4.25e+74) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -1e-76) {
		tmp = t_2;
	} else if (t <= 2.75e-211) {
		tmp = t_1;
	} else if (t <= 2.6e-79) {
		tmp = t_2;
	} else if (t <= 1.26e+23) {
		tmp = t_1;
	} 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 = (-4.0 * (x * i)) + (-27.0 * (j * k))
	t_2 = (b * c) + (k * (j * -27.0))
	tmp = 0
	if t <= -4.25e+74:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= -1e-76:
		tmp = t_2
	elif t <= 2.75e-211:
		tmp = t_1
	elif t <= 2.6e-79:
		tmp = t_2
	elif t <= 1.26e+23:
		tmp = t_1
	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(Float64(-4.0 * Float64(x * i)) + Float64(-27.0 * Float64(j * k)))
	t_2 = Float64(Float64(b * c) + Float64(k * Float64(j * -27.0)))
	tmp = 0.0
	if (t <= -4.25e+74)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= -1e-76)
		tmp = t_2;
	elseif (t <= 2.75e-211)
		tmp = t_1;
	elseif (t <= 2.6e-79)
		tmp = t_2;
	elseif (t <= 1.26e+23)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

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)) + (-27.0 * (j * k));
	t_2 = (b * c) + (k * (j * -27.0));
	tmp = 0.0;
	if (t <= -4.25e+74)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= -1e-76)
		tmp = t_2;
	elseif (t <= 2.75e-211)
		tmp = t_1;
	elseif (t <= 2.6e-79)
		tmp = t_2;
	elseif (t <= 1.26e+23)
		tmp = t_1;
	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[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.25e+74], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1e-76], t$95$2, If[LessEqual[t, 2.75e-211], t$95$1, If[LessEqual[t, 2.6e-79], t$95$2, If[LessEqual[t, 1.26e+23], t$95$1, N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.25000000000000014e74

   1. Initial program 76.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 76.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 76.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 76.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 76.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 78.8%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 78.8%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 78.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 78.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 78.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 78.8%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 74.1%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]
   5. Step-by-step derivation

      1. pow1 74.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{{\left(y \cdot \left(z \cdot x\right)\right)}^{1}} - 4 \cdot a\right) \]

      2. *-commutative 74.1%

         \[\leadsto t \cdot \left(18 \cdot {\left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)}^{1} - 4 \cdot a\right) \]

   6. Applied egg-rr 74.1%

      \[\leadsto t \cdot \left(18 \cdot \color{blue}{{\left(y \cdot \left(x \cdot z\right)\right)}^{1}} - 4 \cdot a\right) \]
   7. Step-by-step derivation

      1. unpow1 74.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(y \cdot \left(x \cdot z\right)\right)} - 4 \cdot a\right) \]

      2. *-commutative 74.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(x \cdot z\right) \cdot y\right)} - 4 \cdot a\right) \]

      3. associate-*l* 74.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(z \cdot y\right)\right)} - 4 \cdot a\right) \]

      4. *-commutative 74.1%

         \[\leadsto t \cdot \left(18 \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right) - 4 \cdot a\right) \]

   8. Simplified 74.1%

      \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)} - 4 \cdot a\right) \]

   if -4.25000000000000014e74 < t < -9.99999999999999927e-77 or 2.74999999999999987e-211 < t < 2.59999999999999994e-79

   1. Initial program 94.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 94.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. *-commutative 94.4%

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\color{blue}{k \cdot \left(j \cdot 27\right)}\right) \]

      3. distribute-rgt-neg-in 94.4%

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \color{blue}{k \cdot \left(-j \cdot 27\right)} \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x \cdot 18, y \cdot z, a \cdot -4\right), \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right) + k \cdot \left(j \cdot -27\right)} \]
   4. Step-by-step derivation

      1. fma-udef 96.3%

         \[\leadsto \color{blue}{\left(t \cdot \mathsf{fma}\left(x \cdot 18, y \cdot z, a \cdot -4\right) + \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right)} + k \cdot \left(j \cdot -27\right) \]

      2. fma-udef 96.3%

         \[\leadsto \left(t \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)} + \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right) + k \cdot \left(j \cdot -27\right) \]

      3. associate-*l* 96.3%

         \[\leadsto \left(t \cdot \left(\color{blue}{x \cdot \left(18 \cdot \left(y \cdot z\right)\right)} + a \cdot -4\right) + \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right) + k \cdot \left(j \cdot -27\right) \]

      4. fma-udef 96.3%

         \[\leadsto \left(t \cdot \color{blue}{\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right)} + \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right) + k \cdot \left(j \cdot -27\right) \]

   5. Applied egg-rr 96.3%

      \[\leadsto \color{blue}{\left(t \cdot \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right) + \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right)} + k \cdot \left(j \cdot -27\right) \]

   6. Taylor expanded in b around inf 65.7%

      \[\leadsto \color{blue}{c \cdot b} + k \cdot \left(j \cdot -27\right) \]

   if -9.99999999999999927e-77 < t < 2.74999999999999987e-211 or 2.59999999999999994e-79 < t < 1.26000000000000004e23

   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. +-commutative 86.1%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 86.1%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 86.1%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 88.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 88.6%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 88.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 88.6%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 88.6%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 88.6%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 88.6%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 88.6%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in t around 0 75.8%

      \[\leadsto \color{blue}{c \cdot b + \left(-4 \cdot \left(i \cdot x\right) + -27 \cdot \left(k \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 78.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, -4 \cdot \left(i \cdot x\right) + -27 \cdot \left(k \cdot j\right)\right)} \]

      2. associate-*r* 78.4%

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\left(-4 \cdot i\right) \cdot x} + -27 \cdot \left(k \cdot j\right)\right) \]

      3. *-commutative 78.4%

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{x \cdot \left(-4 \cdot i\right)} + -27 \cdot \left(k \cdot j\right)\right) \]

      4. fma-def 78.4%

         \[\leadsto \mathsf{fma}\left(c, b, \color{blue}{\mathsf{fma}\left(x, -4 \cdot i, -27 \cdot \left(k \cdot j\right)\right)}\right) \]

      5. associate-*r* 78.4%

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(x, -4 \cdot i, \color{blue}{\left(-27 \cdot k\right) \cdot j}\right)\right) \]

      6. *-commutative 78.4%

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(x, -4 \cdot i, \color{blue}{\left(k \cdot -27\right)} \cdot j\right)\right) \]

      7. *-commutative 78.4%

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(x, -4 \cdot i, \color{blue}{j \cdot \left(k \cdot -27\right)}\right)\right) \]

      8. *-commutative 78.4%

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{fma}\left(x, -4 \cdot i, j \cdot \color{blue}{\left(-27 \cdot k\right)}\right)\right) \]

   6. Simplified 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(x, -4 \cdot i, j \cdot \left(-27 \cdot k\right)\right)\right)} \]

   7. Taylor expanded in c around 0 62.2%

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right) + -27 \cdot \left(k \cdot j\right)} \]

   if 1.26000000000000004e23 < t

   1. Initial program 83.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 83.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 83.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 83.6%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 83.6%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 86.3%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 81.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 81.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 81.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 81.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 81.2%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 72.9%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.25 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-76}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-211}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-79}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{+23}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 16: 71.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-122}:\\ \;\;\;\;b \cdot c + \left(18 \cdot y\right) \cdot \left(t \cdot \left(x \cdot z\right)\right)\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))))
   (if (<= t -1.26e+78)
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
     (if (<= t -3.2e-89)
       t_1
       (if (<= t -1.25e-122)
         (+ (* b c) (* (* 18.0 y) (* t (* x z))))
         (if (<= t 1.32e+23)
           t_1
           (* 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 = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	double tmp;
	if (t <= -1.26e+78) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -3.2e-89) {
		tmp = t_1;
	} else if (t <= -1.25e-122) {
		tmp = (b * c) + ((18.0 * y) * (t * (x * z)));
	} else if (t <= 1.32e+23) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    if (t <= (-1.26d+78)) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (t <= (-3.2d-89)) then
        tmp = t_1
    else if (t <= (-1.25d-122)) then
        tmp = (b * c) + ((18.0d0 * y) * (t * (x * z)))
    else if (t <= 1.32d+23) then
        tmp = t_1
    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 = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	double tmp;
	if (t <= -1.26e+78) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (t <= -3.2e-89) {
		tmp = t_1;
	} else if (t <= -1.25e-122) {
		tmp = (b * c) + ((18.0 * y) * (t * (x * z)));
	} else if (t <= 1.32e+23) {
		tmp = t_1;
	} 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 = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	tmp = 0
	if t <= -1.26e+78:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif t <= -3.2e-89:
		tmp = t_1
	elif t <= -1.25e-122:
		tmp = (b * c) + ((18.0 * y) * (t * (x * z)))
	elif t <= 1.32e+23:
		tmp = t_1
	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(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))))
	tmp = 0.0
	if (t <= -1.26e+78)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (t <= -3.2e-89)
		tmp = t_1;
	elseif (t <= -1.25e-122)
		tmp = Float64(Float64(b * c) + Float64(Float64(18.0 * y) * Float64(t * Float64(x * z))));
	elseif (t <= 1.32e+23)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	tmp = 0.0;
	if (t <= -1.26e+78)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (t <= -3.2e-89)
		tmp = t_1;
	elseif (t <= -1.25e-122)
		tmp = (b * c) + ((18.0 * y) * (t * (x * z)));
	elseif (t <= 1.32e+23)
		tmp = t_1;
	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[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e+78], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.2e-89], t$95$1, If[LessEqual[t, -1.25e-122], N[(N[(b * c), $MachinePrecision] + N[(N[(18.0 * y), $MachinePrecision] * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.32e+23], t$95$1, N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.25999999999999992e78

   1. Initial program 76.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 76.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 76.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 76.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 76.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 78.8%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 78.8%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 78.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 78.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 78.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 78.8%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 74.1%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]
   5. Step-by-step derivation

      1. pow1 74.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{{\left(y \cdot \left(z \cdot x\right)\right)}^{1}} - 4 \cdot a\right) \]

      2. *-commutative 74.1%

         \[\leadsto t \cdot \left(18 \cdot {\left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)}^{1} - 4 \cdot a\right) \]

   6. Applied egg-rr 74.1%

      \[\leadsto t \cdot \left(18 \cdot \color{blue}{{\left(y \cdot \left(x \cdot z\right)\right)}^{1}} - 4 \cdot a\right) \]
   7. Step-by-step derivation

      1. unpow1 74.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(y \cdot \left(x \cdot z\right)\right)} - 4 \cdot a\right) \]

      2. *-commutative 74.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(x \cdot z\right) \cdot y\right)} - 4 \cdot a\right) \]

      3. associate-*l* 74.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(z \cdot y\right)\right)} - 4 \cdot a\right) \]

      4. *-commutative 74.1%

         \[\leadsto t \cdot \left(18 \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right) - 4 \cdot a\right) \]

   8. Simplified 74.1%

      \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)} - 4 \cdot a\right) \]

   if -1.25999999999999992e78 < t < -3.19999999999999998e-89 or -1.25e-122 < t < 1.3199999999999999e23

   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. Step-by-step derivation

      1. sub-neg 90.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 90.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 90.2%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 90.2%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 90.2%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 90.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 90.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 90.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 90.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 90.2%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 90.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around 0 78.2%

      \[\leadsto \color{blue}{c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]

   if -3.19999999999999998e-89 < t < -1.25e-122

   1. Initial program 79.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 79.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 79.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 79.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 79.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 79.0%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 79.0%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 79.0%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 79.0%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 79.0%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 79.0%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 79.0%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in i around 0 78.5%

      \[\leadsto \color{blue}{c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   6. Taylor expanded in y around inf 77.8%

      \[\leadsto c \cdot b + \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 77.7%

         \[\leadsto c \cdot b + \color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} \]

   8. Simplified 77.7%

      \[\leadsto c \cdot b + \color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} \]

   if 1.3199999999999999e23 < t

   1. Initial program 83.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 83.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 83.6%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 83.6%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 83.6%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 86.3%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 81.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 81.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 81.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 81.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 81.2%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 72.9%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-89}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-122}:\\ \;\;\;\;b \cdot c + \left(18 \cdot y\right) \cdot \left(t \cdot \left(x \cdot z\right)\right)\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+23}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 17: 71.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{if}\;x \leq -5.1 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+19}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+160}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))))
   (if (<= x -5.1e+51)
     t_1
     (if (<= x 1.3e+19)
       (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))
       (if (<= x 1.3e+136)
         (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
         (if (<= x 7.5e+160)
           (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* j k))))
           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 = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	double tmp;
	if (x <= -5.1e+51) {
		tmp = t_1;
	} else if (x <= 1.3e+19) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if (x <= 1.3e+136) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (x <= 7.5e+160) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} 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 = x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))
    if (x <= (-5.1d+51)) then
        tmp = t_1
    else if (x <= 1.3d+19) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    else if (x <= 1.3d+136) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else if (x <= 7.5d+160) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (j * k)))
    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 = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	double tmp;
	if (x <= -5.1e+51) {
		tmp = t_1;
	} else if (x <= 1.3e+19) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if (x <= 1.3e+136) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else if (x <= 7.5e+160) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	} 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 = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	tmp = 0
	if x <= -5.1e+51:
		tmp = t_1
	elif x <= 1.3e+19:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	elif x <= 1.3e+136:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	elif x <= 7.5e+160:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)))
	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(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)))
	tmp = 0.0
	if (x <= -5.1e+51)
		tmp = t_1;
	elseif (x <= 1.3e+19)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	elseif (x <= 1.3e+136)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	elseif (x <= 7.5e+160)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(j * k))));
	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 = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	tmp = 0.0;
	if (x <= -5.1e+51)
		tmp = t_1;
	elseif (x <= 1.3e+19)
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	elseif (x <= 1.3e+136)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	elseif (x <= 7.5e+160)
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (j * k)));
	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[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.1e+51], t$95$1, If[LessEqual[x, 1.3e+19], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+136], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+160], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.1000000000000001e51 or 7.50000000000000028e160 < x

   1. Initial program 72.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 72.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 72.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 72.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 72.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 74.2%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 76.8%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 76.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 76.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 76.8%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 76.8%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 76.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 79.6%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

   if -5.1000000000000001e51 < x < 1.3e19

   1. Initial program 91.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 74.7%

      \[\leadsto \color{blue}{\left(c \cdot b - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if 1.3e19 < x < 1.3000000000000001e136

   1. Initial program 90.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 90.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 90.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 90.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 90.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 90.3%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 90.3%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 90.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 90.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 90.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 85.6%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 72.7%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]
   5. Step-by-step derivation

      1. pow1 72.7%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{{\left(y \cdot \left(z \cdot x\right)\right)}^{1}} - 4 \cdot a\right) \]

      2. *-commutative 72.7%

         \[\leadsto t \cdot \left(18 \cdot {\left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)}^{1} - 4 \cdot a\right) \]

   6. Applied egg-rr 72.7%

      \[\leadsto t \cdot \left(18 \cdot \color{blue}{{\left(y \cdot \left(x \cdot z\right)\right)}^{1}} - 4 \cdot a\right) \]
   7. Step-by-step derivation

      1. unpow1 72.7%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(y \cdot \left(x \cdot z\right)\right)} - 4 \cdot a\right) \]

      2. *-commutative 72.7%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(x \cdot z\right) \cdot y\right)} - 4 \cdot a\right) \]

      3. associate-*l* 81.7%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(z \cdot y\right)\right)} - 4 \cdot a\right) \]

      4. *-commutative 81.7%

         \[\leadsto t \cdot \left(18 \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right) - 4 \cdot a\right) \]

   8. Simplified 81.7%

      \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)} - 4 \cdot a\right) \]

   if 1.3000000000000001e136 < x < 7.50000000000000028e160

   1. Initial program 81.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 81.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 81.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 81.7%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 81.7%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 90.8%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 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* 90.6%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around 0 73.8%

      \[\leadsto \color{blue}{c \cdot b - \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.1 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+19}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+160}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 18: 41.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+238}:\\ \;\;\;\;\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{+126}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-307}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

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) (* -4.0 (* t a)))))
   (if (<= y -1.8e+238)
     (* (* (* (* x 18.0) y) z) t)
     (if (<= y -9e+223)
       t_1
       (if (<= y -5.1e+126)
         (* 18.0 (* y (* t (* x z))))
         (if (<= y -2.7e-205)
           t_1
           (if (<= y -4e-307)
             (* j (* k -27.0))
             (if (<= y 4e-62) t_1 (* x (* 18.0 (* y (* z t))))))))))))

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) + (-4.0 * (t * a));
	double tmp;
	if (y <= -1.8e+238) {
		tmp = (((x * 18.0) * y) * z) * t;
	} else if (y <= -9e+223) {
		tmp = t_1;
	} else if (y <= -5.1e+126) {
		tmp = 18.0 * (y * (t * (x * z)));
	} else if (y <= -2.7e-205) {
		tmp = t_1;
	} else if (y <= -4e-307) {
		tmp = j * (k * -27.0);
	} else if (y <= 4e-62) {
		tmp = t_1;
	} else {
		tmp = x * (18.0 * (y * (z * t)));
	}
	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) + ((-4.0d0) * (t * a))
    if (y <= (-1.8d+238)) then
        tmp = (((x * 18.0d0) * y) * z) * t
    else if (y <= (-9d+223)) then
        tmp = t_1
    else if (y <= (-5.1d+126)) then
        tmp = 18.0d0 * (y * (t * (x * z)))
    else if (y <= (-2.7d-205)) then
        tmp = t_1
    else if (y <= (-4d-307)) then
        tmp = j * (k * (-27.0d0))
    else if (y <= 4d-62) then
        tmp = t_1
    else
        tmp = x * (18.0d0 * (y * (z * t)))
    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) + (-4.0 * (t * a));
	double tmp;
	if (y <= -1.8e+238) {
		tmp = (((x * 18.0) * y) * z) * t;
	} else if (y <= -9e+223) {
		tmp = t_1;
	} else if (y <= -5.1e+126) {
		tmp = 18.0 * (y * (t * (x * z)));
	} else if (y <= -2.7e-205) {
		tmp = t_1;
	} else if (y <= -4e-307) {
		tmp = j * (k * -27.0);
	} else if (y <= 4e-62) {
		tmp = t_1;
	} else {
		tmp = x * (18.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	tmp = 0
	if y <= -1.8e+238:
		tmp = (((x * 18.0) * y) * z) * t
	elif y <= -9e+223:
		tmp = t_1
	elif y <= -5.1e+126:
		tmp = 18.0 * (y * (t * (x * z)))
	elif y <= -2.7e-205:
		tmp = t_1
	elif y <= -4e-307:
		tmp = j * (k * -27.0)
	elif y <= 4e-62:
		tmp = t_1
	else:
		tmp = x * (18.0 * (y * (z * t)))
	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(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (y <= -1.8e+238)
		tmp = Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t);
	elseif (y <= -9e+223)
		tmp = t_1;
	elseif (y <= -5.1e+126)
		tmp = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))));
	elseif (y <= -2.7e-205)
		tmp = t_1;
	elseif (y <= -4e-307)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (y <= 4e-62)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))));
	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) + (-4.0 * (t * a));
	tmp = 0.0;
	if (y <= -1.8e+238)
		tmp = (((x * 18.0) * y) * z) * t;
	elseif (y <= -9e+223)
		tmp = t_1;
	elseif (y <= -5.1e+126)
		tmp = 18.0 * (y * (t * (x * z)));
	elseif (y <= -2.7e-205)
		tmp = t_1;
	elseif (y <= -4e-307)
		tmp = j * (k * -27.0);
	elseif (y <= 4e-62)
		tmp = t_1;
	else
		tmp = x * (18.0 * (y * (z * t)));
	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[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+238], N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, -9e+223], t$95$1, If[LessEqual[y, -5.1e+126], N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.7e-205], t$95$1, If[LessEqual[y, -4e-307], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-62], t$95$1, N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.79999999999999986e238

   1. Initial program 80.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 80.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 80.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 80.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 80.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 80.5%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 80.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 80.5%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 80.5%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 80.5%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 80.5%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 80.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 52.1%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]
   5. Step-by-step derivation

      1. pow1 52.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{{\left(y \cdot \left(z \cdot x\right)\right)}^{1}} - 4 \cdot a\right) \]

      2. *-commutative 52.1%

         \[\leadsto t \cdot \left(18 \cdot {\left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)}^{1} - 4 \cdot a\right) \]

   6. Applied egg-rr 52.1%

      \[\leadsto t \cdot \left(18 \cdot \color{blue}{{\left(y \cdot \left(x \cdot z\right)\right)}^{1}} - 4 \cdot a\right) \]
   7. Step-by-step derivation

      1. unpow1 52.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(y \cdot \left(x \cdot z\right)\right)} - 4 \cdot a\right) \]

      2. *-commutative 52.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(x \cdot z\right) \cdot y\right)} - 4 \cdot a\right) \]

      3. associate-*l* 52.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(z \cdot y\right)\right)} - 4 \cdot a\right) \]

      4. *-commutative 52.1%

         \[\leadsto t \cdot \left(18 \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right) - 4 \cdot a\right) \]

   8. Simplified 52.1%

      \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)} - 4 \cdot a\right) \]

   9. Taylor expanded in x around inf 61.0%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 61.0%

          \[\leadsto \color{blue}{\left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) \cdot 18} \]

       2. *-commutative 61.0%

          \[\leadsto \color{blue}{\left(\left(t \cdot \left(z \cdot x\right)\right) \cdot y\right)} \cdot 18 \]

       3. associate-*l* 51.7%

          \[\leadsto \color{blue}{\left(t \cdot \left(\left(z \cdot x\right) \cdot y\right)\right)} \cdot 18 \]

       4. *-commutative 51.7%

          \[\leadsto \left(t \cdot \color{blue}{\left(y \cdot \left(z \cdot x\right)\right)}\right) \cdot 18 \]

       5. associate-*r* 51.7%

          \[\leadsto \left(t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) \cdot 18 \]

       6. *-commutative 51.7%

          \[\leadsto \left(t \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \cdot 18 \]

       7. associate-*r* 51.7%

          \[\leadsto \color{blue}{t \cdot \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18\right)} \]

       8. *-commutative 51.7%

          \[\leadsto t \cdot \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \cdot 18\right) \]

       9. associate-*r* 51.7%

          \[\leadsto t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)} \]

       10. *-commutative 51.7%

           \[\leadsto t \cdot \left(\color{blue}{\left(z \cdot y\right)} \cdot \left(x \cdot 18\right)\right) \]

       11. associate-*l* 61.4%

           \[\leadsto t \cdot \color{blue}{\left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)} \]

   11. Simplified 61.4%

       \[\leadsto \color{blue}{t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)} \]

   if -1.79999999999999986e238 < y < -9e223 or -5.1000000000000001e126 < y < -2.7000000000000001e-205 or -3.99999999999999964e-307 < y < 4.0000000000000002e-62

   1. Initial program 91.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 91.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 91.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 91.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 91.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 92.1%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 91.4%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      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* 91.3%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   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 j around 0 70.9%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in x around 0 51.3%

      \[\leadsto \color{blue}{c \cdot b + -4 \cdot \left(a \cdot t\right)} \]

   if -9e223 < y < -5.1000000000000001e126

   1. Initial program 67.3%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 67.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 67.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 67.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 67.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 71.4%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 71.3%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 71.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 71.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 71.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 71.3%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 71.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 59.4%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around inf 59.2%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]

   if -2.7000000000000001e-205 < y < -3.99999999999999964e-307

   1. Initial program 99.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 99.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 99.7%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 99.7%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 99.7%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 99.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 99.7%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 99.7%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 99.7%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 99.7%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 47.5%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 47.5%

         \[\leadsto \color{blue}{\left(-27 \cdot k\right) \cdot j} \]

      2. *-commutative 47.5%

         \[\leadsto \color{blue}{\left(k \cdot -27\right)} \cdot j \]

      3. *-commutative 47.5%

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

      4. *-commutative 47.5%

         \[\leadsto j \cdot \color{blue}{\left(-27 \cdot k\right)} \]

   6. Simplified 47.5%

      \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} \]

   if 4.0000000000000002e-62 < y

   1. Initial program 78.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 78.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 78.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 78.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 78.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 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* 77.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 77.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 77.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 77.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 77.7%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 77.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 50.5%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

   5. Taylor expanded in y around inf 42.5%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \cdot x \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+238}:\\ \;\;\;\;\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+223}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{+126}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-205}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-307}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-62}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 19: 42.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+238}:\\ \;\;\;\;\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(t \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-307}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

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) (* -4.0 (* t a)))))
   (if (<= y -1.75e+238)
     (* (* (* (* x 18.0) y) z) t)
     (if (<= y -9e+223)
       t_1
       (if (<= y -6e+80)
         (* x (* t (* y (* 18.0 z))))
         (if (<= y -1.22e-307)
           (+ (* b c) (* k (* j -27.0)))
           (if (<= y 4.2e-62) t_1 (* x (* 18.0 (* y (* z t)))))))))))

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) + (-4.0 * (t * a));
	double tmp;
	if (y <= -1.75e+238) {
		tmp = (((x * 18.0) * y) * z) * t;
	} else if (y <= -9e+223) {
		tmp = t_1;
	} else if (y <= -6e+80) {
		tmp = x * (t * (y * (18.0 * z)));
	} else if (y <= -1.22e-307) {
		tmp = (b * c) + (k * (j * -27.0));
	} else if (y <= 4.2e-62) {
		tmp = t_1;
	} else {
		tmp = x * (18.0 * (y * (z * t)));
	}
	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) + ((-4.0d0) * (t * a))
    if (y <= (-1.75d+238)) then
        tmp = (((x * 18.0d0) * y) * z) * t
    else if (y <= (-9d+223)) then
        tmp = t_1
    else if (y <= (-6d+80)) then
        tmp = x * (t * (y * (18.0d0 * z)))
    else if (y <= (-1.22d-307)) then
        tmp = (b * c) + (k * (j * (-27.0d0)))
    else if (y <= 4.2d-62) then
        tmp = t_1
    else
        tmp = x * (18.0d0 * (y * (z * t)))
    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) + (-4.0 * (t * a));
	double tmp;
	if (y <= -1.75e+238) {
		tmp = (((x * 18.0) * y) * z) * t;
	} else if (y <= -9e+223) {
		tmp = t_1;
	} else if (y <= -6e+80) {
		tmp = x * (t * (y * (18.0 * z)));
	} else if (y <= -1.22e-307) {
		tmp = (b * c) + (k * (j * -27.0));
	} else if (y <= 4.2e-62) {
		tmp = t_1;
	} else {
		tmp = x * (18.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	tmp = 0
	if y <= -1.75e+238:
		tmp = (((x * 18.0) * y) * z) * t
	elif y <= -9e+223:
		tmp = t_1
	elif y <= -6e+80:
		tmp = x * (t * (y * (18.0 * z)))
	elif y <= -1.22e-307:
		tmp = (b * c) + (k * (j * -27.0))
	elif y <= 4.2e-62:
		tmp = t_1
	else:
		tmp = x * (18.0 * (y * (z * t)))
	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(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (y <= -1.75e+238)
		tmp = Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t);
	elseif (y <= -9e+223)
		tmp = t_1;
	elseif (y <= -6e+80)
		tmp = Float64(x * Float64(t * Float64(y * Float64(18.0 * z))));
	elseif (y <= -1.22e-307)
		tmp = Float64(Float64(b * c) + Float64(k * Float64(j * -27.0)));
	elseif (y <= 4.2e-62)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))));
	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) + (-4.0 * (t * a));
	tmp = 0.0;
	if (y <= -1.75e+238)
		tmp = (((x * 18.0) * y) * z) * t;
	elseif (y <= -9e+223)
		tmp = t_1;
	elseif (y <= -6e+80)
		tmp = x * (t * (y * (18.0 * z)));
	elseif (y <= -1.22e-307)
		tmp = (b * c) + (k * (j * -27.0));
	elseif (y <= 4.2e-62)
		tmp = t_1;
	else
		tmp = x * (18.0 * (y * (z * t)));
	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[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e+238], N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, -9e+223], t$95$1, If[LessEqual[y, -6e+80], N[(x * N[(t * N[(y * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.22e-307], N[(N[(b * c), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-62], t$95$1, N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.75000000000000001e238

   1. Initial program 80.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 80.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 80.5%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 80.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 80.5%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 80.5%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 80.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 80.5%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 80.5%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 80.5%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 80.5%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 80.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 52.1%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]
   5. Step-by-step derivation

      1. pow1 52.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{{\left(y \cdot \left(z \cdot x\right)\right)}^{1}} - 4 \cdot a\right) \]

      2. *-commutative 52.1%

         \[\leadsto t \cdot \left(18 \cdot {\left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)}^{1} - 4 \cdot a\right) \]

   6. Applied egg-rr 52.1%

      \[\leadsto t \cdot \left(18 \cdot \color{blue}{{\left(y \cdot \left(x \cdot z\right)\right)}^{1}} - 4 \cdot a\right) \]
   7. Step-by-step derivation

      1. unpow1 52.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(y \cdot \left(x \cdot z\right)\right)} - 4 \cdot a\right) \]

      2. *-commutative 52.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(\left(x \cdot z\right) \cdot y\right)} - 4 \cdot a\right) \]

      3. associate-*l* 52.1%

         \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(z \cdot y\right)\right)} - 4 \cdot a\right) \]

      4. *-commutative 52.1%

         \[\leadsto t \cdot \left(18 \cdot \left(x \cdot \color{blue}{\left(y \cdot z\right)}\right) - 4 \cdot a\right) \]

   8. Simplified 52.1%

      \[\leadsto t \cdot \left(18 \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)} - 4 \cdot a\right) \]

   9. Taylor expanded in x around inf 61.0%

      \[\leadsto \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 61.0%

          \[\leadsto \color{blue}{\left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) \cdot 18} \]

       2. *-commutative 61.0%

          \[\leadsto \color{blue}{\left(\left(t \cdot \left(z \cdot x\right)\right) \cdot y\right)} \cdot 18 \]

       3. associate-*l* 51.7%

          \[\leadsto \color{blue}{\left(t \cdot \left(\left(z \cdot x\right) \cdot y\right)\right)} \cdot 18 \]

       4. *-commutative 51.7%

          \[\leadsto \left(t \cdot \color{blue}{\left(y \cdot \left(z \cdot x\right)\right)}\right) \cdot 18 \]

       5. associate-*r* 51.7%

          \[\leadsto \left(t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) \cdot 18 \]

       6. *-commutative 51.7%

          \[\leadsto \left(t \cdot \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \cdot 18 \]

       7. associate-*r* 51.7%

          \[\leadsto \color{blue}{t \cdot \left(\left(x \cdot \left(y \cdot z\right)\right) \cdot 18\right)} \]

       8. *-commutative 51.7%

          \[\leadsto t \cdot \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x\right)} \cdot 18\right) \]

       9. associate-*r* 51.7%

          \[\leadsto t \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot \left(x \cdot 18\right)\right)} \]

       10. *-commutative 51.7%

           \[\leadsto t \cdot \left(\color{blue}{\left(z \cdot y\right)} \cdot \left(x \cdot 18\right)\right) \]

       11. associate-*l* 61.4%

           \[\leadsto t \cdot \color{blue}{\left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)} \]

   11. Simplified 61.4%

       \[\leadsto \color{blue}{t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right)} \]

   if -1.75000000000000001e238 < y < -9e223 or -1.22e-307 < y < 4.1999999999999998e-62

   1. Initial program 91.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 91.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 91.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 91.1%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 91.1%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 91.1%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 91.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      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* 91.1%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   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. Taylor expanded in j around 0 64.2%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in x around 0 45.7%

      \[\leadsto \color{blue}{c \cdot b + -4 \cdot \left(a \cdot t\right)} \]

   if -9e223 < y < -5.99999999999999974e80

   1. Initial program 68.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 68.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 68.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 68.2%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 68.2%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 71.4%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 68.3%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 68.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 68.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 68.3%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 68.3%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 68.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 71.9%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

   5. Taylor expanded in y around inf 56.0%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \cdot x \]
   6. Step-by-step derivation

      1. associate-*r* 56.1%

         \[\leadsto \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(t \cdot z\right)\right)} \cdot x \]

      2. *-commutative 56.1%

         \[\leadsto \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(z \cdot t\right)}\right) \cdot x \]

      3. associate-*r* 56.1%

         \[\leadsto \color{blue}{\left(\left(\left(18 \cdot y\right) \cdot z\right) \cdot t\right)} \cdot x \]

      4. associate-*r* 56.0%

         \[\leadsto \left(\color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)} \cdot t\right) \cdot x \]

      5. *-commutative 56.0%

         \[\leadsto \left(\left(18 \cdot \color{blue}{\left(z \cdot y\right)}\right) \cdot t\right) \cdot x \]

      6. associate-*r* 56.1%

         \[\leadsto \left(\color{blue}{\left(\left(18 \cdot z\right) \cdot y\right)} \cdot t\right) \cdot x \]

   7. Simplified 56.1%

      \[\leadsto \color{blue}{\left(\left(\left(18 \cdot z\right) \cdot y\right) \cdot t\right)} \cdot x \]

   if -5.99999999999999974e80 < y < -1.22e-307

   1. Initial program 95.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 95.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. *-commutative 95.4%

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\color{blue}{k \cdot \left(j \cdot 27\right)}\right) \]

      3. distribute-rgt-neg-in 95.4%

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \color{blue}{k \cdot \left(-j \cdot 27\right)} \]

   3. Simplified 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x \cdot 18, y \cdot z, a \cdot -4\right), \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right) + k \cdot \left(j \cdot -27\right)} \]
   4. Step-by-step derivation

      1. fma-udef 95.5%

         \[\leadsto \color{blue}{\left(t \cdot \mathsf{fma}\left(x \cdot 18, y \cdot z, a \cdot -4\right) + \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right)} + k \cdot \left(j \cdot -27\right) \]

      2. fma-udef 95.5%

         \[\leadsto \left(t \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)} + \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right) + k \cdot \left(j \cdot -27\right) \]

      3. associate-*l* 95.5%

         \[\leadsto \left(t \cdot \left(\color{blue}{x \cdot \left(18 \cdot \left(y \cdot z\right)\right)} + a \cdot -4\right) + \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right) + k \cdot \left(j \cdot -27\right) \]

      4. fma-udef 95.5%

         \[\leadsto \left(t \cdot \color{blue}{\mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right)} + \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right) + k \cdot \left(j \cdot -27\right) \]

   5. Applied egg-rr 95.5%

      \[\leadsto \color{blue}{\left(t \cdot \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right) + \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right)} + k \cdot \left(j \cdot -27\right) \]

   6. Taylor expanded in b around inf 51.4%

      \[\leadsto \color{blue}{c \cdot b} + k \cdot \left(j \cdot -27\right) \]

   if 4.1999999999999998e-62 < y

   1. Initial program 78.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 78.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 78.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 78.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 78.8%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 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* 77.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 77.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 77.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 77.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 77.7%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 77.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 50.5%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - 4 \cdot i\right) \cdot x} \]

   5. Taylor expanded in y around inf 42.5%

      \[\leadsto \color{blue}{\left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)} \cdot x \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+238}:\\ \;\;\;\;\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+223}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(t \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-307}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-62}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 20: 32.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1650000:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 9 \cdot 10^{-271}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

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
 (if (<= k -1650000.0)
   (* -27.0 (* j k))
   (if (<= k 9e-271)
     (* b c)
     (if (<= k 2.7e+69) (* t (* a -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 <= -1650000.0) {
		tmp = -27.0 * (j * k);
	} else if (k <= 9e-271) {
		tmp = b * c;
	} else if (k <= 2.7e+69) {
		tmp = t * (a * -4.0);
	} 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) :: tmp
    if (k <= (-1650000.0d0)) then
        tmp = (-27.0d0) * (j * k)
    else if (k <= 9d-271) then
        tmp = b * c
    else if (k <= 2.7d+69) then
        tmp = t * (a * (-4.0d0))
    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 tmp;
	if (k <= -1650000.0) {
		tmp = -27.0 * (j * k);
	} else if (k <= 9e-271) {
		tmp = b * c;
	} else if (k <= 2.7e+69) {
		tmp = t * (a * -4.0);
	} 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):
	tmp = 0
	if k <= -1650000.0:
		tmp = -27.0 * (j * k)
	elif k <= 9e-271:
		tmp = b * c
	elif k <= 2.7e+69:
		tmp = t * (a * -4.0)
	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)
	tmp = 0.0
	if (k <= -1650000.0)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (k <= 9e-271)
		tmp = Float64(b * c);
	elseif (k <= 2.7e+69)
		tmp = Float64(t * Float64(a * -4.0));
	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)
	tmp = 0.0;
	if (k <= -1650000.0)
		tmp = -27.0 * (j * k);
	elseif (k <= 9e-271)
		tmp = b * c;
	elseif (k <= 2.7e+69)
		tmp = t * (a * -4.0);
	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_] := If[LessEqual[k, -1650000.0], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 9e-271], N[(b * c), $MachinePrecision], If[LessEqual[k, 2.7e+69], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if k < -1.65e6

   1. Initial program 84.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 84.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. +-commutative 84.1%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 84.2%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 84.2%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 90.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 90.0%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 90.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 90.0%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 90.0%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 90.0%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 90.0%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 90.0%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 92.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 36.8%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -1.65e6 < k < 8.9999999999999995e-271

   1. Initial program 89.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 89.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 89.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 89.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 89.9%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 89.9%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 91.4%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      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* 92.8%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 92.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 85.4%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in c around inf 33.7%

      \[\leadsto \color{blue}{c \cdot b} \]

   if 8.9999999999999995e-271 < k < 2.6999999999999998e69

   1. Initial program 83.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 83.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 83.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 83.4%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 83.4%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 83.4%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 76.2%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 76.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 76.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 76.2%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 76.2%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 76.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in t around inf 53.0%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)} \]

   5. Taylor expanded in y around 0 32.3%

      \[\leadsto t \cdot \color{blue}{\left(-4 \cdot a\right)} \]

   if 2.6999999999999998e69 < k

   1. Initial program 82.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 82.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. +-commutative 82.7%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 80.8%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 80.8%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 84.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 84.6%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 84.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 84.6%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 84.6%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 84.6%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 84.6%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 84.6%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 90.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 50.5%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 50.6%

         \[\leadsto \color{blue}{\left(-27 \cdot k\right) \cdot j} \]

      2. *-commutative 50.6%

         \[\leadsto \color{blue}{\left(k \cdot -27\right)} \cdot j \]

      3. *-commutative 50.6%

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

      4. *-commutative 50.6%

         \[\leadsto j \cdot \color{blue}{\left(-27 \cdot k\right)} \]

   6. Simplified 50.6%

      \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} \]

   7. Taylor expanded in j around 0 50.5%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 50.5%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. associate-*r* 50.7%

         \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   9. Simplified 50.7%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1650000:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 9 \cdot 10^{-271}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 21: 34.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -4.6 \cdot 10^{+17} \lor \neg \left(k \leq 1.1 \cdot 10^{+19}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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 (or (<= k -4.6e+17) (not (<= k 1.1e+19))) (* -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 ((k <= -4.6e+17) || !(k <= 1.1e+19)) {
		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 ((k <= (-4.6d+17)) .or. (.not. (k <= 1.1d+19))) 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 ((k <= -4.6e+17) || !(k <= 1.1e+19)) {
		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 (k <= -4.6e+17) or not (k <= 1.1e+19):
		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 ((k <= -4.6e+17) || !(k <= 1.1e+19))
		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 ((k <= -4.6e+17) || ~((k <= 1.1e+19)))
		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[Or[LessEqual[k, -4.6e+17], N[Not[LessEqual[k, 1.1e+19]], $MachinePrecision]], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -4.6e17 or 1.1e19 < k

   1. Initial program 84.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 84.1%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. +-commutative 84.1%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 83.3%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 83.3%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 88.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 88.1%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 88.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 88.1%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 88.1%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 88.1%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 88.1%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 88.1%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 42.1%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -4.6e17 < k < 1.1e19

   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. associate-+l- 86.3%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 86.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 86.3%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 87.1%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 85.7%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 85.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 85.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 85.7%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 86.5%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 86.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 81.4%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in c around inf 29.7%

      \[\leadsto \color{blue}{c \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -4.6 \cdot 10^{+17} \lor \neg \left(k \leq 1.1 \cdot 10^{+19}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 22: 34.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -41000000:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+19}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

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
 (if (<= k -41000000.0)
   (* -27.0 (* j k))
   (if (<= k 2.1e+19) (* 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 tmp;
	if (k <= -41000000.0) {
		tmp = -27.0 * (j * k);
	} else if (k <= 2.1e+19) {
		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) :: tmp
    if (k <= (-41000000.0d0)) then
        tmp = (-27.0d0) * (j * k)
    else if (k <= 2.1d+19) 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 tmp;
	if (k <= -41000000.0) {
		tmp = -27.0 * (j * k);
	} else if (k <= 2.1e+19) {
		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):
	tmp = 0
	if k <= -41000000.0:
		tmp = -27.0 * (j * k)
	elif k <= 2.1e+19:
		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)
	tmp = 0.0
	if (k <= -41000000.0)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (k <= 2.1e+19)
		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)
	tmp = 0.0;
	if (k <= -41000000.0)
		tmp = -27.0 * (j * k);
	elseif (k <= 2.1e+19)
		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_] := If[LessEqual[k, -41000000.0], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.1e+19], N[(b * c), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -4.1e7

   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 89.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 89.8%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 89.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 89.8%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 89.8%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 89.8%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 89.8%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 89.8%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 92.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 37.3%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -4.1e7 < k < 2.1e19

   1. Initial program 87.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 87.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 87.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 87.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 87.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 87.0%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 85.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 85.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 85.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 85.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 86.4%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 81.2%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in c around inf 29.9%

      \[\leadsto \color{blue}{c \cdot b} \]

   if 2.1e19 < k

   1. Initial program 82.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 82.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. +-commutative 82.8%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 81.0%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 81.0%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 84.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 84.5%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 84.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 84.5%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 84.5%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 84.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 84.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 84.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 47.1%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 47.2%

         \[\leadsto \color{blue}{\left(-27 \cdot k\right) \cdot j} \]

      2. *-commutative 47.2%

         \[\leadsto \color{blue}{\left(k \cdot -27\right)} \cdot j \]

      3. *-commutative 47.2%

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

      4. *-commutative 47.2%

         \[\leadsto j \cdot \color{blue}{\left(-27 \cdot k\right)} \]

   6. Simplified 47.2%

      \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -41000000:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{+19}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 23: 34.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -6800000000:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 4.7 \cdot 10^{+19}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

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
 (if (<= k -6800000000.0)
   (* -27.0 (* j k))
   (if (<= k 4.7e+19) (* 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 tmp;
	if (k <= -6800000000.0) {
		tmp = -27.0 * (j * k);
	} else if (k <= 4.7e+19) {
		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) :: tmp
    if (k <= (-6800000000.0d0)) then
        tmp = (-27.0d0) * (j * k)
    else if (k <= 4.7d+19) 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 tmp;
	if (k <= -6800000000.0) {
		tmp = -27.0 * (j * k);
	} else if (k <= 4.7e+19) {
		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):
	tmp = 0
	if k <= -6800000000.0:
		tmp = -27.0 * (j * k)
	elif k <= 4.7e+19:
		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)
	tmp = 0.0
	if (k <= -6800000000.0)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (k <= 4.7e+19)
		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)
	tmp = 0.0;
	if (k <= -6800000000.0)
		tmp = -27.0 * (j * k);
	elseif (k <= 4.7e+19)
		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_] := If[LessEqual[k, -6800000000.0], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 4.7e+19], N[(b * c), $MachinePrecision], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -6.8e9

   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 89.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 89.8%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 89.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 89.8%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 89.8%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 89.8%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 89.8%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 89.8%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 92.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 37.3%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]

   if -6.8e9 < k < 4.7e19

   1. Initial program 87.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 87.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 87.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

      3. sub-neg 87.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      4. sub-neg 87.0%

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      5. distribute-rgt-out-- 87.0%

         \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 85.6%

         \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

      7. distribute-lft-neg-in 85.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

      8. cancel-sign-sub 85.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      9. associate-*l* 85.6%

         \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

      10. associate-*l* 86.4%

          \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in j around 0 81.2%

      \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   5. Taylor expanded in c around inf 29.9%

      \[\leadsto \color{blue}{c \cdot b} \]

   if 4.7e19 < k

   1. Initial program 82.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. sub-neg 82.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

      2. +-commutative 82.8%

         \[\leadsto \color{blue}{\left(-\left(j \cdot 27\right) \cdot k\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      3. associate-*l* 81.0%

         \[\leadsto \left(-\color{blue}{j \cdot \left(27 \cdot k\right)}\right) + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      4. distribute-rgt-neg-in 81.0%

         \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} + \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      5. fma-def 84.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, -27 \cdot k, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right)} \]

      6. *-commutative 84.5%

         \[\leadsto \mathsf{fma}\left(j, -\color{blue}{k \cdot 27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      7. distribute-rgt-neg-in 84.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{k \cdot \left(-27\right)}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      8. metadata-eval 84.5%

         \[\leadsto \mathsf{fma}\left(j, k \cdot \color{blue}{-27}, \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) \]

      9. sub-neg 84.5%

         \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) + \left(-\left(x \cdot 4\right) \cdot i\right)}\right) \]

      10. +-commutative 84.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{\left(-\left(x \cdot 4\right) \cdot i\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)}\right) \]

      11. associate-*l* 84.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \left(-\color{blue}{x \cdot \left(4 \cdot i\right)}\right) + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

      12. distribute-rgt-neg-in 84.5%

          \[\leadsto \mathsf{fma}\left(j, k \cdot -27, \color{blue}{x \cdot \left(-4 \cdot i\right)} + \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)\right) \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(x, i \cdot -4, \mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), b \cdot c\right)\right)\right)} \]

   4. Taylor expanded in j around inf 47.1%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 47.2%

         \[\leadsto \color{blue}{\left(-27 \cdot k\right) \cdot j} \]

      2. *-commutative 47.2%

         \[\leadsto \color{blue}{\left(k \cdot -27\right)} \cdot j \]

      3. *-commutative 47.2%

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

      4. *-commutative 47.2%

         \[\leadsto j \cdot \color{blue}{\left(-27 \cdot k\right)} \]

   6. Simplified 47.2%

      \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} \]

   7. Taylor expanded in j around 0 47.1%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 47.1%

         \[\leadsto \color{blue}{\left(k \cdot j\right) \cdot -27} \]

      2. associate-*r* 47.3%

         \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]

   9. Simplified 47.3%

      \[\leadsto \color{blue}{k \cdot \left(j \cdot -27\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -6800000000:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 4.7 \cdot 10^{+19}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 24: 23.7% 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 85.2%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
2. Step-by-step derivation

   1. sub-neg 85.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]

   2. associate-+l- 85.2%

      \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right)} \]

   3. sub-neg 85.2%

      \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + \left(-\left(a \cdot 4\right) \cdot t\right)\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

   4. sub-neg 85.2%

      \[\leadsto \left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

   5. distribute-rgt-out-- 86.4%

      \[\leadsto \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

   6. associate-*l* 84.9%

      \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \left(-\left(j \cdot 27\right) \cdot k\right)\right) \]

   7. distribute-lft-neg-in 84.9%

      \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i - \color{blue}{\left(-j \cdot 27\right) \cdot k}\right) \]

   8. cancel-sign-sub 84.9%

      \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

   9. associate-*l* 84.9%

      \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]

   10. associate-*l* 84.9%

       \[\leadsto \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

3. Simplified 84.9%

   \[\leadsto \color{blue}{\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

4. Taylor expanded in j around 0 68.6%

   \[\leadsto \color{blue}{\left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) - 4 \cdot a\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

5. Taylor expanded in c around inf 20.4%

   \[\leadsto \color{blue}{c \cdot b} \]

6. Final simplification 20.4%

   \[\leadsto b \cdot c \]

Developer target: 89.3% 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 2023173 
(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)))