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

Percentage Accurate: 85.1% → 92.2%

Time: 24.9s

Alternatives: 24

Speedup: 0.9×

• 50.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (-.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)) < +inf.0

   1. Initial program 94.8%

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

   3. Simplified 94.4%

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

      1. +-commutative 94.4%

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

      2. *-commutative 94.4%

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

      3. fma-def 95.7%

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

      4. fma-udef 95.7%

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

      5. associate-*l* 95.7%

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

      6. associate-*r* 95.7%

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

      7. *-commutative 95.7%

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

      8. fma-def 95.7%

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

      9. *-commutative 95.7%

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

      10. *-commutative 95.7%

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

   5. Applied egg-rr 95.7%

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

   if +inf.0 < (-.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))

   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. associate-*l* 0.0%

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

      2. associate--l+ 0.0%

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

      3. distribute-rgt-out-- 11.1%

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

      4. associate-*l* 22.2%

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

      5. associate-*l* 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in x around inf 77.8%

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

4. Final simplification 93.8%

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

Alternative 2: 91.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: y and z 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[(z * N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision]), $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[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.5%

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

   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. associate-*l* 0.0%

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

      2. associate--l+ 0.0%

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

      3. distribute-rgt-out-- 9.7%

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

      4. associate-*l* 19.4%

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

      5. associate-*l* 19.4%

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

   3. Simplified 19.4%

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

   4. Taylor expanded in x around inf 67.7%

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

4. Final simplification 93.0%

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

Alternative 3: 53.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(k \cdot j\right)\\ t_2 := \left(k \cdot -27\right) \cdot j\\ t_3 := x \cdot \left(i \cdot -4\right) + t_2\\ t_4 := t_2 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -1.25 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -2.45 \cdot 10^{-275}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \cdot c \leq 1.65 \cdot 10^{-292}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot c \leq 6.8 \cdot 10^{-136}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \cdot c \leq 1.42 \cdot 10^{+94}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot c \leq 2.6 \cdot 10^{+120}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 6.2 \cdot 10^{+179}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* k j))))
        (t_2 (* (* k -27.0) j))
        (t_3 (+ (* x (* i -4.0)) t_2))
        (t_4 (+ t_2 (* -4.0 (* t a)))))
   (if (<= (* b c) -1.25e-12)
     t_1
     (if (<= (* b c) -2.45e-275)
       t_4
       (if (<= (* b c) 1.65e-292)
         t_3
         (if (<= (* b c) 6.8e-136)
           t_4
           (if (<= (* b c) 1.42e+94)
             t_3
             (if (<= (* b c) 2.6e+120)
               (* t (* 18.0 (* x (* y z))))
               (if (<= (* b c) 6.2e+179) t_3 t_1)))))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (k * j));
	double t_2 = (k * -27.0) * j;
	double t_3 = (x * (i * -4.0)) + t_2;
	double t_4 = t_2 + (-4.0 * (t * a));
	double tmp;
	if ((b * c) <= -1.25e-12) {
		tmp = t_1;
	} else if ((b * c) <= -2.45e-275) {
		tmp = t_4;
	} else if ((b * c) <= 1.65e-292) {
		tmp = t_3;
	} else if ((b * c) <= 6.8e-136) {
		tmp = t_4;
	} else if ((b * c) <= 1.42e+94) {
		tmp = t_3;
	} else if ((b * c) <= 2.6e+120) {
		tmp = t * (18.0 * (x * (y * z)));
	} else if ((b * c) <= 6.2e+179) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (b * c) - (27.0d0 * (k * j))
    t_2 = (k * (-27.0d0)) * j
    t_3 = (x * (i * (-4.0d0))) + t_2
    t_4 = t_2 + ((-4.0d0) * (t * a))
    if ((b * c) <= (-1.25d-12)) then
        tmp = t_1
    else if ((b * c) <= (-2.45d-275)) then
        tmp = t_4
    else if ((b * c) <= 1.65d-292) then
        tmp = t_3
    else if ((b * c) <= 6.8d-136) then
        tmp = t_4
    else if ((b * c) <= 1.42d+94) then
        tmp = t_3
    else if ((b * c) <= 2.6d+120) then
        tmp = t * (18.0d0 * (x * (y * z)))
    else if ((b * c) <= 6.2d+179) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (k * j));
	double t_2 = (k * -27.0) * j;
	double t_3 = (x * (i * -4.0)) + t_2;
	double t_4 = t_2 + (-4.0 * (t * a));
	double tmp;
	if ((b * c) <= -1.25e-12) {
		tmp = t_1;
	} else if ((b * c) <= -2.45e-275) {
		tmp = t_4;
	} else if ((b * c) <= 1.65e-292) {
		tmp = t_3;
	} else if ((b * c) <= 6.8e-136) {
		tmp = t_4;
	} else if ((b * c) <= 1.42e+94) {
		tmp = t_3;
	} else if ((b * c) <= 2.6e+120) {
		tmp = t * (18.0 * (x * (y * z)));
	} else if ((b * c) <= 6.2e+179) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (27.0 * (k * j))
	t_2 = (k * -27.0) * j
	t_3 = (x * (i * -4.0)) + t_2
	t_4 = t_2 + (-4.0 * (t * a))
	tmp = 0
	if (b * c) <= -1.25e-12:
		tmp = t_1
	elif (b * c) <= -2.45e-275:
		tmp = t_4
	elif (b * c) <= 1.65e-292:
		tmp = t_3
	elif (b * c) <= 6.8e-136:
		tmp = t_4
	elif (b * c) <= 1.42e+94:
		tmp = t_3
	elif (b * c) <= 2.6e+120:
		tmp = t * (18.0 * (x * (y * z)))
	elif (b * c) <= 6.2e+179:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(k * j)))
	t_2 = Float64(Float64(k * -27.0) * j)
	t_3 = Float64(Float64(x * Float64(i * -4.0)) + t_2)
	t_4 = Float64(t_2 + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (Float64(b * c) <= -1.25e-12)
		tmp = t_1;
	elseif (Float64(b * c) <= -2.45e-275)
		tmp = t_4;
	elseif (Float64(b * c) <= 1.65e-292)
		tmp = t_3;
	elseif (Float64(b * c) <= 6.8e-136)
		tmp = t_4;
	elseif (Float64(b * c) <= 1.42e+94)
		tmp = t_3;
	elseif (Float64(b * c) <= 2.6e+120)
		tmp = Float64(t * Float64(18.0 * Float64(x * Float64(y * z))));
	elseif (Float64(b * c) <= 6.2e+179)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (27.0 * (k * j));
	t_2 = (k * -27.0) * j;
	t_3 = (x * (i * -4.0)) + t_2;
	t_4 = t_2 + (-4.0 * (t * a));
	tmp = 0.0;
	if ((b * c) <= -1.25e-12)
		tmp = t_1;
	elseif ((b * c) <= -2.45e-275)
		tmp = t_4;
	elseif ((b * c) <= 1.65e-292)
		tmp = t_3;
	elseif ((b * c) <= 6.8e-136)
		tmp = t_4;
	elseif ((b * c) <= 1.42e+94)
		tmp = t_3;
	elseif ((b * c) <= 2.6e+120)
		tmp = t * (18.0 * (x * (y * z)));
	elseif ((b * c) <= 6.2e+179)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * -27.0), $MachinePrecision] * j), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.25e-12], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -2.45e-275], t$95$4, If[LessEqual[N[(b * c), $MachinePrecision], 1.65e-292], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 6.8e-136], t$95$4, If[LessEqual[N[(b * c), $MachinePrecision], 1.42e+94], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 2.6e+120], N[(t * N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 6.2e+179], t$95$3, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.24999999999999992e-12 or 6.2e179 < (*.f64 b c)

   1. Initial program 80.1%

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

      1. associate-*l* 80.1%

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

      2. associate--l+ 80.1%

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

      3. distribute-rgt-out-- 81.1%

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

      4. associate-*l* 82.9%

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

      5. associate-*l* 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in t around 0 78.8%

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

   5. Taylor expanded in i around 0 73.0%

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

   if -1.24999999999999992e-12 < (*.f64 b c) < -2.44999999999999991e-275 or 1.64999999999999997e-292 < (*.f64 b c) < 6.8000000000000001e-136

   1. Initial program 86.6%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in a around inf 59.0%

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

      1. *-commutative 59.0%

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

   6. Simplified 59.0%

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

   if -2.44999999999999991e-275 < (*.f64 b c) < 1.64999999999999997e-292 or 6.8000000000000001e-136 < (*.f64 b c) < 1.4200000000000001e94 or 2.5999999999999999e120 < (*.f64 b c) < 6.2e179

   1. Initial program 88.3%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in i around inf 66.3%

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

      1. associate-*r* 66.3%

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

      2. *-commutative 66.3%

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

   6. Simplified 66.3%

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

   if 1.4200000000000001e94 < (*.f64 b c) < 2.5999999999999999e120

   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. associate-*l* 99.7%

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

      2. associate--l+ 99.7%

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

      3. distribute-rgt-out-- 99.7%

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

      4. associate-*l* 100.0%

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

      5. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in i around 0 100.0%

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

   5. Taylor expanded in j around 0 100.0%

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

   6. Taylor expanded in b around 0 100.0%

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

   7. Taylor expanded in x around inf 84.2%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.25 \cdot 10^{-12}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;b \cdot c \leq -2.45 \cdot 10^{-275}:\\ \;\;\;\;\left(k \cdot -27\right) \cdot j + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.65 \cdot 10^{-292}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + \left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;b \cdot c \leq 6.8 \cdot 10^{-136}:\\ \;\;\;\;\left(k \cdot -27\right) \cdot j + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.42 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + \left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;b \cdot c \leq 2.6 \cdot 10^{+120}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 6.2 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + \left(k \cdot -27\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \end{array} \]

Alternative 4: 89.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right)\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+78} \lor \neg \left(t \leq 2.4 \cdot 10^{+185}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right) - a \cdot \left(t \cdot 4\right)\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k 27.0))))
   (if (or (<= t -6.2e+78) (not (<= t 2.4e+185)))
     (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) t_1)
     (-
      (+
       (- (* x (* (* y t) (* 18.0 z))) (* a (* t 4.0)))
       (- (* b c) (* x (* 4.0 i))))
      t_1))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * 27.0);
	double tmp;
	if ((t <= -6.2e+78) || !(t <= 2.4e+185)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	} else {
		tmp = (((x * ((y * t) * (18.0 * z))) - (a * (t * 4.0))) + ((b * c) - (x * (4.0 * i)))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * 27.0d0)
    if ((t <= (-6.2d+78)) .or. (.not. (t <= 2.4d+185))) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - t_1
    else
        tmp = (((x * ((y * t) * (18.0d0 * z))) - (a * (t * 4.0d0))) + ((b * c) - (x * (4.0d0 * i)))) - t_1
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * 27.0);
	double tmp;
	if ((t <= -6.2e+78) || !(t <= 2.4e+185)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	} else {
		tmp = (((x * ((y * t) * (18.0 * z))) - (a * (t * 4.0))) + ((b * c) - (x * (4.0 * i)))) - t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * 27.0)
	tmp = 0
	if (t <= -6.2e+78) or not (t <= 2.4e+185):
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1
	else:
		tmp = (((x * ((y * t) * (18.0 * z))) - (a * (t * 4.0))) + ((b * c) - (x * (4.0 * i)))) - t_1
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * 27.0))
	tmp = 0.0
	if ((t <= -6.2e+78) || !(t <= 2.4e+185))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - t_1);
	else
		tmp = Float64(Float64(Float64(Float64(x * Float64(Float64(y * t) * Float64(18.0 * z))) - Float64(a * Float64(t * 4.0))) + Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)))) - t_1);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * 27.0);
	tmp = 0.0;
	if ((t <= -6.2e+78) || ~((t <= 2.4e+185)))
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	else
		tmp = (((x * ((y * t) * (18.0 * z))) - (a * (t * 4.0))) + ((b * c) - (x * (4.0 * i)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -6.2e+78], N[Not[LessEqual[t, 2.4e+185]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(N[(x * N[(N[(y * t), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.2e78 or 2.39999999999999989e185 < t

   1. Initial program 75.3%

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

      1. associate-*l* 75.3%

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

      2. associate--l+ 75.3%

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

      3. distribute-rgt-out-- 79.6%

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

      4. associate-*l* 79.6%

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

      5. associate-*l* 79.6%

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

   3. Simplified 79.6%

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

   4. Taylor expanded in i around 0 91.3%

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

   if -6.2e78 < t < 2.39999999999999989e185

   1. Initial program 88.3%

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

      1. associate-*l* 87.9%

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

      2. associate--l+ 87.9%

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

      3. distribute-rgt-out-- 87.9%

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

      4. associate-*l* 89.4%

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

      5. associate-*l* 89.4%

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

   3. Simplified 89.4%

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

      1. associate-*r* 87.9%

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

      2. distribute-rgt-out-- 87.9%

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

      3. associate-*r* 89.4%

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

      4. *-commutative 89.4%

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

      5. associate-*r* 87.9%

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

      6. *-commutative 87.9%

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

      7. *-commutative 87.9%

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

      8. associate-*l* 87.9%

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

   5. Applied egg-rr 87.9%

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

   6. Taylor expanded in t around 0 89.4%

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

      1. *-commutative 89.4%

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

      2. *-commutative 89.4%

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

      3. *-commutative 89.4%

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

      4. associate-*r* 91.5%

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

      5. associate-*r* 92.8%

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

      6. associate-*r* 92.8%

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

      7. associate-*r* 90.6%

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

      8. associate-*l* 87.9%

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

      9. *-commutative 87.9%

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

      10. associate-*r* 89.4%

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

      11. *-commutative 89.4%

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

      12. associate-*l* 89.4%

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

      13. associate-*l* 91.5%

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

      14. associate-*r* 91.5%

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

      15. *-commutative 91.5%

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

      16. *-commutative 91.5%

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

      17. *-commutative 91.5%

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

      18. associate-*r* 92.5%

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

      19. associate-*l* 92.5%

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

      20. *-commutative 92.5%

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

   8. Simplified 92.5%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+78} \lor \neg \left(t \leq 2.4 \cdot 10^{+185}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right) - a \cdot \left(t \cdot 4\right)\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)\right) - j \cdot \left(k \cdot 27\right)\\ \end{array} \]

Alternative 5: 87.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right)\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+232} \lor \neg \left(x \leq 2.2 \cdot 10^{+135}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - x \cdot \left(4 \cdot i\right)\right) + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k 27.0))))
   (if (or (<= x -1.6e+232) (not (<= x 2.2e+135)))
     (- (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))) t_1)
     (-
      (+
       (- (* b c) (* x (* 4.0 i)))
       (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
      t_1))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * 27.0);
	double tmp;
	if ((x <= -1.6e+232) || !(x <= 2.2e+135)) {
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_1;
	} else {
		tmp = (((b * c) - (x * (4.0 * i))) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * 27.0d0)
    if ((x <= (-1.6d+232)) .or. (.not. (x <= 2.2d+135))) then
        tmp = (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))) - t_1
    else
        tmp = (((b * c) - (x * (4.0d0 * i))) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - t_1
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * 27.0);
	double tmp;
	if ((x <= -1.6e+232) || !(x <= 2.2e+135)) {
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_1;
	} else {
		tmp = (((b * c) - (x * (4.0 * i))) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * 27.0)
	tmp = 0
	if (x <= -1.6e+232) or not (x <= 2.2e+135):
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_1
	else:
		tmp = (((b * c) - (x * (4.0 * i))) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * 27.0))
	tmp = 0.0
	if ((x <= -1.6e+232) || !(x <= 2.2e+135))
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))) - t_1);
	else
		tmp = Float64(Float64(Float64(Float64(b * c) - Float64(x * Float64(4.0 * i))) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - t_1);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * 27.0);
	tmp = 0.0;
	if ((x <= -1.6e+232) || ~((x <= 2.2e+135)))
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_1;
	else
		tmp = (((b * c) - (x * (4.0 * i))) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -1.6e+232], N[Not[LessEqual[x, 2.2e+135]], $MachinePrecision]], N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6000000000000001e232 or 2.1999999999999999e135 < x

   1. Initial program 55.6%

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

      1. associate-*l* 55.6%

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

      2. associate--l+ 55.6%

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

      3. distribute-rgt-out-- 55.6%

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

      4. associate-*l* 60.0%

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

      5. associate-*l* 60.0%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in x around inf 81.2%

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

   if -1.6000000000000001e232 < x < 2.1999999999999999e135

   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. associate-*l* 90.6%

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

      2. associate--l+ 90.6%

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

      3. distribute-rgt-out-- 92.0%

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

      4. associate-*l* 92.5%

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

      5. associate-*l* 92.5%

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

   3. Simplified 92.5%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+232} \lor \neg \left(x \leq 2.2 \cdot 10^{+135}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c - x \cdot \left(4 \cdot i\right)\right) + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - j \cdot \left(k \cdot 27\right)\\ \end{array} \]

Alternative 6: 56.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := b \cdot c - \left(x \cdot 4\right) \cdot i\\ t_2 := b \cdot c - 27 \cdot \left(k \cdot j\right)\\ t_3 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ t_4 := \left(k \cdot -27\right) \cdot j\\ t_5 := t_4 + \left(18 \cdot t\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+125}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-29}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-178}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + t_4\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: y and z 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) (* (* x 4.0) i)))
        (t_2 (- (* b c) (* 27.0 (* k j))))
        (t_3 (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
        (t_4 (* (* k -27.0) j))
        (t_5 (+ t_4 (* (* 18.0 t) (* z (* x y))))))
   (if (<= t -5.5e+125)
     t_3
     (if (<= t -4.4e-29)
       t_5
       (if (<= t -3e-138)
         t_1
         (if (<= t -1.4e-178)
           t_5
           (if (<= t 6e-305)
             t_1
             (if (<= t 5.7e-255)
               t_2
               (if (<= t 1e-157)
                 t_1
                 (if (<= t 1.9e+51)
                   (+ (* x (* i -4.0)) t_4)
                   (if (<= t 4.5e+80) t_2 t_3)))))))))))

C

assert(y < z);
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) - ((x * 4.0) * i);
	double t_2 = (b * c) - (27.0 * (k * j));
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_4 = (k * -27.0) * j;
	double t_5 = t_4 + ((18.0 * t) * (z * (x * y)));
	double tmp;
	if (t <= -5.5e+125) {
		tmp = t_3;
	} else if (t <= -4.4e-29) {
		tmp = t_5;
	} else if (t <= -3e-138) {
		tmp = t_1;
	} else if (t <= -1.4e-178) {
		tmp = t_5;
	} else if (t <= 6e-305) {
		tmp = t_1;
	} else if (t <= 5.7e-255) {
		tmp = t_2;
	} else if (t <= 1e-157) {
		tmp = t_1;
	} else if (t <= 1.9e+51) {
		tmp = (x * (i * -4.0)) + t_4;
	} else if (t <= 4.5e+80) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (b * c) - ((x * 4.0d0) * i)
    t_2 = (b * c) - (27.0d0 * (k * j))
    t_3 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    t_4 = (k * (-27.0d0)) * j
    t_5 = t_4 + ((18.0d0 * t) * (z * (x * y)))
    if (t <= (-5.5d+125)) then
        tmp = t_3
    else if (t <= (-4.4d-29)) then
        tmp = t_5
    else if (t <= (-3d-138)) then
        tmp = t_1
    else if (t <= (-1.4d-178)) then
        tmp = t_5
    else if (t <= 6d-305) then
        tmp = t_1
    else if (t <= 5.7d-255) then
        tmp = t_2
    else if (t <= 1d-157) then
        tmp = t_1
    else if (t <= 1.9d+51) then
        tmp = (x * (i * (-4.0d0))) + t_4
    else if (t <= 4.5d+80) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert y < z;
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) - ((x * 4.0) * i);
	double t_2 = (b * c) - (27.0 * (k * j));
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_4 = (k * -27.0) * j;
	double t_5 = t_4 + ((18.0 * t) * (z * (x * y)));
	double tmp;
	if (t <= -5.5e+125) {
		tmp = t_3;
	} else if (t <= -4.4e-29) {
		tmp = t_5;
	} else if (t <= -3e-138) {
		tmp = t_1;
	} else if (t <= -1.4e-178) {
		tmp = t_5;
	} else if (t <= 6e-305) {
		tmp = t_1;
	} else if (t <= 5.7e-255) {
		tmp = t_2;
	} else if (t <= 1e-157) {
		tmp = t_1;
	} else if (t <= 1.9e+51) {
		tmp = (x * (i * -4.0)) + t_4;
	} else if (t <= 4.5e+80) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - ((x * 4.0) * i)
	t_2 = (b * c) - (27.0 * (k * j))
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	t_4 = (k * -27.0) * j
	t_5 = t_4 + ((18.0 * t) * (z * (x * y)))
	tmp = 0
	if t <= -5.5e+125:
		tmp = t_3
	elif t <= -4.4e-29:
		tmp = t_5
	elif t <= -3e-138:
		tmp = t_1
	elif t <= -1.4e-178:
		tmp = t_5
	elif t <= 6e-305:
		tmp = t_1
	elif t <= 5.7e-255:
		tmp = t_2
	elif t <= 1e-157:
		tmp = t_1
	elif t <= 1.9e+51:
		tmp = (x * (i * -4.0)) + t_4
	elif t <= 4.5e+80:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i))
	t_2 = Float64(Float64(b * c) - Float64(27.0 * Float64(k * j)))
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	t_4 = Float64(Float64(k * -27.0) * j)
	t_5 = Float64(t_4 + Float64(Float64(18.0 * t) * Float64(z * Float64(x * y))))
	tmp = 0.0
	if (t <= -5.5e+125)
		tmp = t_3;
	elseif (t <= -4.4e-29)
		tmp = t_5;
	elseif (t <= -3e-138)
		tmp = t_1;
	elseif (t <= -1.4e-178)
		tmp = t_5;
	elseif (t <= 6e-305)
		tmp = t_1;
	elseif (t <= 5.7e-255)
		tmp = t_2;
	elseif (t <= 1e-157)
		tmp = t_1;
	elseif (t <= 1.9e+51)
		tmp = Float64(Float64(x * Float64(i * -4.0)) + t_4);
	elseif (t <= 4.5e+80)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - ((x * 4.0) * i);
	t_2 = (b * c) - (27.0 * (k * j));
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	t_4 = (k * -27.0) * j;
	t_5 = t_4 + ((18.0 * t) * (z * (x * y)));
	tmp = 0.0;
	if (t <= -5.5e+125)
		tmp = t_3;
	elseif (t <= -4.4e-29)
		tmp = t_5;
	elseif (t <= -3e-138)
		tmp = t_1;
	elseif (t <= -1.4e-178)
		tmp = t_5;
	elseif (t <= 6e-305)
		tmp = t_1;
	elseif (t <= 5.7e-255)
		tmp = t_2;
	elseif (t <= 1e-157)
		tmp = t_1;
	elseif (t <= 1.9e+51)
		tmp = (x * (i * -4.0)) + t_4;
	elseif (t <= 4.5e+80)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z 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[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(k * j), $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]}, Block[{t$95$4 = N[(N[(k * -27.0), $MachinePrecision] * j), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 + N[(N[(18.0 * t), $MachinePrecision] * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e+125], t$95$3, If[LessEqual[t, -4.4e-29], t$95$5, If[LessEqual[t, -3e-138], t$95$1, If[LessEqual[t, -1.4e-178], t$95$5, If[LessEqual[t, 6e-305], t$95$1, If[LessEqual[t, 5.7e-255], t$95$2, If[LessEqual[t, 1e-157], t$95$1, If[LessEqual[t, 1.9e+51], N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision], If[LessEqual[t, 4.5e+80], t$95$2, t$95$3]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.49999999999999996e125 or 4.50000000000000007e80 < t

   1. Initial program 76.6%

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

      1. associate-*l* 76.6%

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

      2. associate--l+ 76.6%

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

      3. distribute-rgt-out-- 80.8%

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

      4. associate-*l* 80.8%

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

      5. associate-*l* 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in i around 0 86.4%

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

   5. Taylor expanded in j around 0 77.5%

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

   6. Taylor expanded in b around 0 73.7%

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

   if -5.49999999999999996e125 < t < -4.39999999999999981e-29 or -3.0000000000000001e-138 < t < -1.4000000000000001e-178

   1. Initial program 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in y around inf 69.9%

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

      1. associate-*r* 69.9%

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

      2. associate-*r* 72.1%

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

   6. Simplified 72.1%

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

   if -4.39999999999999981e-29 < t < -3.0000000000000001e-138 or -1.4000000000000001e-178 < t < 6.0000000000000002e-305 or 5.7000000000000002e-255 < t < 9.99999999999999943e-158

   1. Initial program 85.8%

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

      1. associate-*l* 85.8%

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

      2. associate--l+ 85.7%

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

      3. distribute-rgt-out-- 85.7%

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

      4. associate-*l* 88.4%

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

      5. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in t around 0 87.4%

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

   5. Taylor expanded in i around inf 73.0%

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

      1. *-commutative 73.0%

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

      2. associate-*r* 73.0%

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

   7. Simplified 73.0%

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

   if 6.0000000000000002e-305 < t < 5.7000000000000002e-255 or 1.8999999999999999e51 < t < 4.50000000000000007e80

   1. Initial program 82.4%

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

      1. associate-*l* 78.1%

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

      2. associate--l+ 78.1%

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

      3. distribute-rgt-out-- 78.1%

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

      4. associate-*l* 82.1%

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

      5. associate-*l* 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in t around 0 77.8%

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

   5. Taylor expanded in i around 0 82.3%

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

   if 9.99999999999999943e-158 < t < 1.8999999999999999e51

   1. Initial program 87.5%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in i around inf 64.4%

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

      1. associate-*r* 64.4%

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

      2. *-commutative 64.4%

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

   6. Simplified 64.4%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-29}:\\ \;\;\;\;\left(k \cdot -27\right) \cdot j + \left(18 \cdot t\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-138}:\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-178}:\\ \;\;\;\;\left(k \cdot -27\right) \cdot j + \left(18 \cdot t\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-305}:\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-255}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t \leq 10^{-157}:\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + \left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+80}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 7: 58.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(k \cdot j\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ t_3 := x \cdot \left(i \cdot -4\right) + \left(k \cdot -27\right) \cdot j\\ t_4 := b \cdot c - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{+29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-145}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-157}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* k j))))
        (t_2 (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
        (t_3 (+ (* x (* i -4.0)) (* (* k -27.0) j)))
        (t_4 (- (* b c) (* (* x 4.0) i))))
   (if (<= t -9.5e+81)
     t_2
     (if (<= t -1.4e+29)
       t_3
       (if (<= t -7.4e-6)
         t_2
         (if (<= t -8.2e-145)
           t_4
           (if (<= t 4.2e-257)
             t_1
             (if (<= t 1.1e-157)
               t_4
               (if (<= t 2.15e+49) t_3 (if (<= t 5e+82) t_1 t_2))))))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (k * j));
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_3 = (x * (i * -4.0)) + ((k * -27.0) * j);
	double t_4 = (b * c) - ((x * 4.0) * i);
	double tmp;
	if (t <= -9.5e+81) {
		tmp = t_2;
	} else if (t <= -1.4e+29) {
		tmp = t_3;
	} else if (t <= -7.4e-6) {
		tmp = t_2;
	} else if (t <= -8.2e-145) {
		tmp = t_4;
	} else if (t <= 4.2e-257) {
		tmp = t_1;
	} else if (t <= 1.1e-157) {
		tmp = t_4;
	} else if (t <= 2.15e+49) {
		tmp = t_3;
	} else if (t <= 5e+82) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (b * c) - (27.0d0 * (k * j))
    t_2 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    t_3 = (x * (i * (-4.0d0))) + ((k * (-27.0d0)) * j)
    t_4 = (b * c) - ((x * 4.0d0) * i)
    if (t <= (-9.5d+81)) then
        tmp = t_2
    else if (t <= (-1.4d+29)) then
        tmp = t_3
    else if (t <= (-7.4d-6)) then
        tmp = t_2
    else if (t <= (-8.2d-145)) then
        tmp = t_4
    else if (t <= 4.2d-257) then
        tmp = t_1
    else if (t <= 1.1d-157) then
        tmp = t_4
    else if (t <= 2.15d+49) then
        tmp = t_3
    else if (t <= 5d+82) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (k * j));
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_3 = (x * (i * -4.0)) + ((k * -27.0) * j);
	double t_4 = (b * c) - ((x * 4.0) * i);
	double tmp;
	if (t <= -9.5e+81) {
		tmp = t_2;
	} else if (t <= -1.4e+29) {
		tmp = t_3;
	} else if (t <= -7.4e-6) {
		tmp = t_2;
	} else if (t <= -8.2e-145) {
		tmp = t_4;
	} else if (t <= 4.2e-257) {
		tmp = t_1;
	} else if (t <= 1.1e-157) {
		tmp = t_4;
	} else if (t <= 2.15e+49) {
		tmp = t_3;
	} else if (t <= 5e+82) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (27.0 * (k * j))
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	t_3 = (x * (i * -4.0)) + ((k * -27.0) * j)
	t_4 = (b * c) - ((x * 4.0) * i)
	tmp = 0
	if t <= -9.5e+81:
		tmp = t_2
	elif t <= -1.4e+29:
		tmp = t_3
	elif t <= -7.4e-6:
		tmp = t_2
	elif t <= -8.2e-145:
		tmp = t_4
	elif t <= 4.2e-257:
		tmp = t_1
	elif t <= 1.1e-157:
		tmp = t_4
	elif t <= 2.15e+49:
		tmp = t_3
	elif t <= 5e+82:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(k * j)))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	t_3 = Float64(Float64(x * Float64(i * -4.0)) + Float64(Float64(k * -27.0) * j))
	t_4 = Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if (t <= -9.5e+81)
		tmp = t_2;
	elseif (t <= -1.4e+29)
		tmp = t_3;
	elseif (t <= -7.4e-6)
		tmp = t_2;
	elseif (t <= -8.2e-145)
		tmp = t_4;
	elseif (t <= 4.2e-257)
		tmp = t_1;
	elseif (t <= 1.1e-157)
		tmp = t_4;
	elseif (t <= 2.15e+49)
		tmp = t_3;
	elseif (t <= 5e+82)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (27.0 * (k * j));
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	t_3 = (x * (i * -4.0)) + ((k * -27.0) * j);
	t_4 = (b * c) - ((x * 4.0) * i);
	tmp = 0.0;
	if (t <= -9.5e+81)
		tmp = t_2;
	elseif (t <= -1.4e+29)
		tmp = t_3;
	elseif (t <= -7.4e-6)
		tmp = t_2;
	elseif (t <= -8.2e-145)
		tmp = t_4;
	elseif (t <= 4.2e-257)
		tmp = t_1;
	elseif (t <= 1.1e-157)
		tmp = t_4;
	elseif (t <= 2.15e+49)
		tmp = t_3;
	elseif (t <= 5e+82)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(k * -27.0), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+81], t$95$2, If[LessEqual[t, -1.4e+29], t$95$3, If[LessEqual[t, -7.4e-6], t$95$2, If[LessEqual[t, -8.2e-145], t$95$4, If[LessEqual[t, 4.2e-257], t$95$1, If[LessEqual[t, 1.1e-157], t$95$4, If[LessEqual[t, 2.15e+49], t$95$3, If[LessEqual[t, 5e+82], t$95$1, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.50000000000000083e81 or -1.4e29 < t < -7.4000000000000003e-6 or 5.00000000000000015e82 < t

   1. Initial program 80.1%

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

      1. associate-*l* 80.2%

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

      2. associate--l+ 80.2%

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

      3. distribute-rgt-out-- 83.4%

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

      4. associate-*l* 83.4%

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

      5. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in i around 0 88.4%

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

   5. Taylor expanded in j around 0 79.1%

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

   6. Taylor expanded in b around 0 74.9%

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

   if -9.50000000000000083e81 < t < -1.4e29 or 1.10000000000000005e-157 < t < 2.15e49

   1. Initial program 89.2%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in i around inf 62.9%

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

      1. associate-*r* 62.9%

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

      2. *-commutative 62.9%

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

   6. Simplified 62.9%

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

   if -7.4000000000000003e-6 < t < -8.1999999999999995e-145 or 4.2000000000000002e-257 < t < 1.10000000000000005e-157

   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. associate-*l* 87.7%

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

      2. associate--l+ 87.7%

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

      3. distribute-rgt-out-- 87.7%

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

      4. associate-*l* 87.7%

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

      5. associate-*l* 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in t around 0 81.7%

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

   5. Taylor expanded in i around inf 69.0%

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

      1. *-commutative 69.0%

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

      2. associate-*r* 69.0%

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

   7. Simplified 69.0%

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

   if -8.1999999999999995e-145 < t < 4.2000000000000002e-257 or 2.15e49 < t < 5.00000000000000015e82

   1. Initial program 85.3%

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

      1. associate-*l* 83.5%

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

      2. associate--l+ 83.5%

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

      3. distribute-rgt-out-- 83.5%

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

      4. associate-*l* 87.0%

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

      5. associate-*l* 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in t around 0 86.4%

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

   5. Taylor expanded in i around 0 72.3%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + \left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-6}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-145}:\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-257}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-157}:\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + \left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+82}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 8: 58.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := \left(k \cdot -27\right) \cdot j\\ t_2 := b \cdot c - \left(x \cdot 4\right) \cdot i\\ t_3 := x \cdot \left(y \cdot z\right)\\ t_4 := t \cdot \left(18 \cdot t_3 - a \cdot 4\right)\\ t_5 := b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+125}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -0.00036:\\ \;\;\;\;18 \cdot \left(t \cdot t_3\right) + t_1\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-258}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+83}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* k -27.0) j))
        (t_2 (- (* b c) (* (* x 4.0) i)))
        (t_3 (* x (* y z)))
        (t_4 (* t (- (* 18.0 t_3) (* a 4.0))))
        (t_5 (- (* b c) (* 27.0 (* k j)))))
   (if (<= t -2.8e+125)
     t_4
     (if (<= t -0.00036)
       (+ (* 18.0 (* t t_3)) t_1)
       (if (<= t -3.1e-145)
         t_2
         (if (<= t 3e-258)
           t_5
           (if (<= t 1.3e-158)
             t_2
             (if (<= t 3.5e+49)
               (+ (* x (* i -4.0)) t_1)
               (if (<= t 1.05e+83) t_5 t_4)))))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (k * -27.0) * j;
	double t_2 = (b * c) - ((x * 4.0) * i);
	double t_3 = x * (y * z);
	double t_4 = t * ((18.0 * t_3) - (a * 4.0));
	double t_5 = (b * c) - (27.0 * (k * j));
	double tmp;
	if (t <= -2.8e+125) {
		tmp = t_4;
	} else if (t <= -0.00036) {
		tmp = (18.0 * (t * t_3)) + t_1;
	} else if (t <= -3.1e-145) {
		tmp = t_2;
	} else if (t <= 3e-258) {
		tmp = t_5;
	} else if (t <= 1.3e-158) {
		tmp = t_2;
	} else if (t <= 3.5e+49) {
		tmp = (x * (i * -4.0)) + t_1;
	} else if (t <= 1.05e+83) {
		tmp = t_5;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = (k * (-27.0d0)) * j
    t_2 = (b * c) - ((x * 4.0d0) * i)
    t_3 = x * (y * z)
    t_4 = t * ((18.0d0 * t_3) - (a * 4.0d0))
    t_5 = (b * c) - (27.0d0 * (k * j))
    if (t <= (-2.8d+125)) then
        tmp = t_4
    else if (t <= (-0.00036d0)) then
        tmp = (18.0d0 * (t * t_3)) + t_1
    else if (t <= (-3.1d-145)) then
        tmp = t_2
    else if (t <= 3d-258) then
        tmp = t_5
    else if (t <= 1.3d-158) then
        tmp = t_2
    else if (t <= 3.5d+49) then
        tmp = (x * (i * (-4.0d0))) + t_1
    else if (t <= 1.05d+83) then
        tmp = t_5
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (k * -27.0) * j;
	double t_2 = (b * c) - ((x * 4.0) * i);
	double t_3 = x * (y * z);
	double t_4 = t * ((18.0 * t_3) - (a * 4.0));
	double t_5 = (b * c) - (27.0 * (k * j));
	double tmp;
	if (t <= -2.8e+125) {
		tmp = t_4;
	} else if (t <= -0.00036) {
		tmp = (18.0 * (t * t_3)) + t_1;
	} else if (t <= -3.1e-145) {
		tmp = t_2;
	} else if (t <= 3e-258) {
		tmp = t_5;
	} else if (t <= 1.3e-158) {
		tmp = t_2;
	} else if (t <= 3.5e+49) {
		tmp = (x * (i * -4.0)) + t_1;
	} else if (t <= 1.05e+83) {
		tmp = t_5;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (k * -27.0) * j
	t_2 = (b * c) - ((x * 4.0) * i)
	t_3 = x * (y * z)
	t_4 = t * ((18.0 * t_3) - (a * 4.0))
	t_5 = (b * c) - (27.0 * (k * j))
	tmp = 0
	if t <= -2.8e+125:
		tmp = t_4
	elif t <= -0.00036:
		tmp = (18.0 * (t * t_3)) + t_1
	elif t <= -3.1e-145:
		tmp = t_2
	elif t <= 3e-258:
		tmp = t_5
	elif t <= 1.3e-158:
		tmp = t_2
	elif t <= 3.5e+49:
		tmp = (x * (i * -4.0)) + t_1
	elif t <= 1.05e+83:
		tmp = t_5
	else:
		tmp = t_4
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(k * -27.0) * j)
	t_2 = Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i))
	t_3 = Float64(x * Float64(y * z))
	t_4 = Float64(t * Float64(Float64(18.0 * t_3) - Float64(a * 4.0)))
	t_5 = Float64(Float64(b * c) - Float64(27.0 * Float64(k * j)))
	tmp = 0.0
	if (t <= -2.8e+125)
		tmp = t_4;
	elseif (t <= -0.00036)
		tmp = Float64(Float64(18.0 * Float64(t * t_3)) + t_1);
	elseif (t <= -3.1e-145)
		tmp = t_2;
	elseif (t <= 3e-258)
		tmp = t_5;
	elseif (t <= 1.3e-158)
		tmp = t_2;
	elseif (t <= 3.5e+49)
		tmp = Float64(Float64(x * Float64(i * -4.0)) + t_1);
	elseif (t <= 1.05e+83)
		tmp = t_5;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (k * -27.0) * j;
	t_2 = (b * c) - ((x * 4.0) * i);
	t_3 = x * (y * z);
	t_4 = t * ((18.0 * t_3) - (a * 4.0));
	t_5 = (b * c) - (27.0 * (k * j));
	tmp = 0.0;
	if (t <= -2.8e+125)
		tmp = t_4;
	elseif (t <= -0.00036)
		tmp = (18.0 * (t * t_3)) + t_1;
	elseif (t <= -3.1e-145)
		tmp = t_2;
	elseif (t <= 3e-258)
		tmp = t_5;
	elseif (t <= 1.3e-158)
		tmp = t_2;
	elseif (t <= 3.5e+49)
		tmp = (x * (i * -4.0)) + t_1;
	elseif (t <= 1.05e+83)
		tmp = t_5;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z 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[(k * -27.0), $MachinePrecision] * j), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(18.0 * t$95$3), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+125], t$95$4, If[LessEqual[t, -0.00036], N[(N[(18.0 * N[(t * t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, -3.1e-145], t$95$2, If[LessEqual[t, 3e-258], t$95$5, If[LessEqual[t, 1.3e-158], t$95$2, If[LessEqual[t, 3.5e+49], N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 1.05e+83], t$95$5, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.8000000000000001e125 or 1.05000000000000001e83 < t

   1. Initial program 76.6%

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

      1. associate-*l* 76.6%

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

      2. associate--l+ 76.6%

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

      3. distribute-rgt-out-- 80.8%

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

      4. associate-*l* 80.8%

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

      5. associate-*l* 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in i around 0 86.4%

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

   5. Taylor expanded in j around 0 77.5%

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

   6. Taylor expanded in b around 0 73.7%

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

   if -2.8000000000000001e125 < t < -3.60000000000000023e-4

   1. Initial program 93.7%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in y around inf 74.0%

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

   if -3.60000000000000023e-4 < t < -3.1e-145 or 3.00000000000000021e-258 < t < 1.3e-158

   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. associate-*l* 87.9%

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

      2. associate--l+ 87.9%

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

      3. distribute-rgt-out-- 87.9%

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

      4. associate-*l* 88.0%

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

      5. associate-*l* 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in t around 0 80.3%

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

   5. Taylor expanded in i around inf 67.8%

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

      1. *-commutative 67.8%

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

      2. associate-*r* 67.8%

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

   7. Simplified 67.8%

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

   if -3.1e-145 < t < 3.00000000000000021e-258 or 3.49999999999999975e49 < t < 1.05000000000000001e83

   1. Initial program 85.3%

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

      1. associate-*l* 83.5%

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

      2. associate--l+ 83.5%

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

      3. distribute-rgt-out-- 83.5%

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

      4. associate-*l* 87.0%

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

      5. associate-*l* 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in t around 0 86.4%

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

   5. Taylor expanded in i around 0 72.3%

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

   if 1.3e-158 < t < 3.49999999999999975e49

   1. Initial program 87.5%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in i around inf 64.4%

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

      1. associate-*r* 64.4%

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

      2. *-commutative 64.4%

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

   6. Simplified 64.4%

      \[\leadsto \color{blue}{x \cdot \left(-4 \cdot i\right)} + j \cdot \left(k \cdot -27\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -0.00036:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + \left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-145}:\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-258}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-158}:\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) + \left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+83}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 9: 74.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ t_3 := j \cdot \left(k \cdot 27\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{+126}:\\ \;\;\;\;b \cdot c + t_2\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - t_3\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-8}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c - \left(t_1 + 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 - t_3\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i)))
        (t_2 (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
        (t_3 (* j (* k 27.0))))
   (if (<= t -7e+126)
     (+ (* b c) t_2)
     (if (<= t -1.25e+31)
       (- (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))) t_3)
       (if (<= t -4.4e-8)
         (- t_2 t_1)
         (if (<= t 1.1e+88)
           (- (* b c) (+ t_1 (* 27.0 (* k j))))
           (- t_2 t_3)))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_3 = j * (k * 27.0);
	double tmp;
	if (t <= -7e+126) {
		tmp = (b * c) + t_2;
	} else if (t <= -1.25e+31) {
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_3;
	} else if (t <= -4.4e-8) {
		tmp = t_2 - t_1;
	} else if (t <= 1.1e+88) {
		tmp = (b * c) - (t_1 + (27.0 * (k * j)));
	} else {
		tmp = t_2 - t_3;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 4.0d0 * (x * i)
    t_2 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    t_3 = j * (k * 27.0d0)
    if (t <= (-7d+126)) then
        tmp = (b * c) + t_2
    else if (t <= (-1.25d+31)) then
        tmp = (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))) - t_3
    else if (t <= (-4.4d-8)) then
        tmp = t_2 - t_1
    else if (t <= 1.1d+88) then
        tmp = (b * c) - (t_1 + (27.0d0 * (k * j)))
    else
        tmp = t_2 - t_3
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 4.0 * (x * i);
	double t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_3 = j * (k * 27.0);
	double tmp;
	if (t <= -7e+126) {
		tmp = (b * c) + t_2;
	} else if (t <= -1.25e+31) {
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_3;
	} else if (t <= -4.4e-8) {
		tmp = t_2 - t_1;
	} else if (t <= 1.1e+88) {
		tmp = (b * c) - (t_1 + (27.0 * (k * j)));
	} else {
		tmp = t_2 - t_3;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	t_3 = j * (k * 27.0)
	tmp = 0
	if t <= -7e+126:
		tmp = (b * c) + t_2
	elif t <= -1.25e+31:
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_3
	elif t <= -4.4e-8:
		tmp = t_2 - t_1
	elif t <= 1.1e+88:
		tmp = (b * c) - (t_1 + (27.0 * (k * j)))
	else:
		tmp = t_2 - t_3
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	t_3 = Float64(j * Float64(k * 27.0))
	tmp = 0.0
	if (t <= -7e+126)
		tmp = Float64(Float64(b * c) + t_2);
	elseif (t <= -1.25e+31)
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))) - t_3);
	elseif (t <= -4.4e-8)
		tmp = Float64(t_2 - t_1);
	elseif (t <= 1.1e+88)
		tmp = Float64(Float64(b * c) - Float64(t_1 + Float64(27.0 * Float64(k * j))));
	else
		tmp = Float64(t_2 - t_3);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	t_3 = j * (k * 27.0);
	tmp = 0.0;
	if (t <= -7e+126)
		tmp = (b * c) + t_2;
	elseif (t <= -1.25e+31)
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_3;
	elseif (t <= -4.4e-8)
		tmp = t_2 - t_1;
	elseif (t <= 1.1e+88)
		tmp = (b * c) - (t_1 + (27.0 * (k * j)));
	else
		tmp = t_2 - t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+126], N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[t, -1.25e+31], N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[t, -4.4e-8], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[t, 1.1e+88], N[(N[(b * c), $MachinePrecision] - N[(t$95$1 + N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - t$95$3), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.0000000000000005e126

   1. Initial program 61.2%

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

      1. associate-*l* 61.2%

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

      2. associate--l+ 61.2%

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

      3. distribute-rgt-out-- 70.9%

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

      4. associate-*l* 71.0%

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

      5. associate-*l* 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in i around 0 83.9%

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

   5. Taylor expanded in j around 0 80.9%

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

   if -7.0000000000000005e126 < t < -1.25000000000000007e31

   1. Initial program 92.0%

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

      1. associate-*l* 92.2%

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

      2. associate--l+ 92.2%

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

      3. distribute-rgt-out-- 92.2%

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

      4. associate-*l* 92.2%

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

      5. associate-*l* 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in x around inf 86.2%

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

   if -1.25000000000000007e31 < t < -4.3999999999999997e-8

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. distribute-rgt-out-- 100.0%

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

      4. associate-*l* 99.8%

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

      5. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in b around 0 98.7%

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

   5. Taylor expanded in j around 0 98.7%

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

   if -4.3999999999999997e-8 < t < 1.10000000000000004e88

   1. Initial program 86.9%

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

      1. associate-*l* 86.2%

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

      2. associate--l+ 86.2%

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

      3. distribute-rgt-out-- 86.2%

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

      4. associate-*l* 88.2%

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

      5. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in t around 0 83.7%

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

   if 1.10000000000000004e88 < t

   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. associate-*l* 87.7%

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

      2. associate--l+ 87.7%

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

      3. distribute-rgt-out-- 87.7%

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

      4. associate-*l* 87.7%

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

      5. associate-*l* 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in t around inf 88.1%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} - j \cdot \left(27 \cdot k\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+126}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - j \cdot \left(k \cdot 27\right)\\ \end{array} \]

Alternative 10: 74.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ t_3 := t \cdot \left(18 \cdot t_2 - a \cdot 4\right)\\ t_4 := 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+148}:\\ \;\;\;\;b \cdot c + t_3\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{+31}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot t_2\right)\right) - t_1\\ \mathbf{elif}\;t \leq -0.000255:\\ \;\;\;\;t_3 - t_4\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+89}:\\ \;\;\;\;b \cdot c - \left(t_4 + 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3 - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k 27.0)))
        (t_2 (* x (* y z)))
        (t_3 (* t (- (* 18.0 t_2) (* a 4.0))))
        (t_4 (* 4.0 (* x i))))
   (if (<= t -1.6e+148)
     (+ (* b c) t_3)
     (if (<= t -1.16e+31)
       (- (+ (* b c) (* 18.0 (* t t_2))) t_1)
       (if (<= t -0.000255)
         (- t_3 t_4)
         (if (<= t 1.9e+89)
           (- (* b c) (+ t_4 (* 27.0 (* k j))))
           (- t_3 t_1)))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * 27.0);
	double t_2 = x * (y * z);
	double t_3 = t * ((18.0 * t_2) - (a * 4.0));
	double t_4 = 4.0 * (x * i);
	double tmp;
	if (t <= -1.6e+148) {
		tmp = (b * c) + t_3;
	} else if (t <= -1.16e+31) {
		tmp = ((b * c) + (18.0 * (t * t_2))) - t_1;
	} else if (t <= -0.000255) {
		tmp = t_3 - t_4;
	} else if (t <= 1.9e+89) {
		tmp = (b * c) - (t_4 + (27.0 * (k * j)));
	} else {
		tmp = t_3 - t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * (k * 27.0d0)
    t_2 = x * (y * z)
    t_3 = t * ((18.0d0 * t_2) - (a * 4.0d0))
    t_4 = 4.0d0 * (x * i)
    if (t <= (-1.6d+148)) then
        tmp = (b * c) + t_3
    else if (t <= (-1.16d+31)) then
        tmp = ((b * c) + (18.0d0 * (t * t_2))) - t_1
    else if (t <= (-0.000255d0)) then
        tmp = t_3 - t_4
    else if (t <= 1.9d+89) then
        tmp = (b * c) - (t_4 + (27.0d0 * (k * j)))
    else
        tmp = t_3 - t_1
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * 27.0);
	double t_2 = x * (y * z);
	double t_3 = t * ((18.0 * t_2) - (a * 4.0));
	double t_4 = 4.0 * (x * i);
	double tmp;
	if (t <= -1.6e+148) {
		tmp = (b * c) + t_3;
	} else if (t <= -1.16e+31) {
		tmp = ((b * c) + (18.0 * (t * t_2))) - t_1;
	} else if (t <= -0.000255) {
		tmp = t_3 - t_4;
	} else if (t <= 1.9e+89) {
		tmp = (b * c) - (t_4 + (27.0 * (k * j)));
	} else {
		tmp = t_3 - t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * 27.0)
	t_2 = x * (y * z)
	t_3 = t * ((18.0 * t_2) - (a * 4.0))
	t_4 = 4.0 * (x * i)
	tmp = 0
	if t <= -1.6e+148:
		tmp = (b * c) + t_3
	elif t <= -1.16e+31:
		tmp = ((b * c) + (18.0 * (t * t_2))) - t_1
	elif t <= -0.000255:
		tmp = t_3 - t_4
	elif t <= 1.9e+89:
		tmp = (b * c) - (t_4 + (27.0 * (k * j)))
	else:
		tmp = t_3 - t_1
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * 27.0))
	t_2 = Float64(x * Float64(y * z))
	t_3 = Float64(t * Float64(Float64(18.0 * t_2) - Float64(a * 4.0)))
	t_4 = Float64(4.0 * Float64(x * i))
	tmp = 0.0
	if (t <= -1.6e+148)
		tmp = Float64(Float64(b * c) + t_3);
	elseif (t <= -1.16e+31)
		tmp = Float64(Float64(Float64(b * c) + Float64(18.0 * Float64(t * t_2))) - t_1);
	elseif (t <= -0.000255)
		tmp = Float64(t_3 - t_4);
	elseif (t <= 1.9e+89)
		tmp = Float64(Float64(b * c) - Float64(t_4 + Float64(27.0 * Float64(k * j))));
	else
		tmp = Float64(t_3 - t_1);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * 27.0);
	t_2 = x * (y * z);
	t_3 = t * ((18.0 * t_2) - (a * 4.0));
	t_4 = 4.0 * (x * i);
	tmp = 0.0;
	if (t <= -1.6e+148)
		tmp = (b * c) + t_3;
	elseif (t <= -1.16e+31)
		tmp = ((b * c) + (18.0 * (t * t_2))) - t_1;
	elseif (t <= -0.000255)
		tmp = t_3 - t_4;
	elseif (t <= 1.9e+89)
		tmp = (b * c) - (t_4 + (27.0 * (k * j)));
	else
		tmp = t_3 - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * t$95$2), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+148], N[(N[(b * c), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[t, -1.16e+31], N[(N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, -0.000255], N[(t$95$3 - t$95$4), $MachinePrecision], If[LessEqual[t, 1.9e+89], N[(N[(b * c), $MachinePrecision] - N[(t$95$4 + N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$3 - t$95$1), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.6e148

   1. Initial program 59.2%

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

      1. associate-*l* 59.2%

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

      2. associate--l+ 59.2%

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

      3. distribute-rgt-out-- 70.3%

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

      4. associate-*l* 70.4%

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

      5. associate-*l* 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in i around 0 81.5%

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

   5. Taylor expanded in j around 0 81.6%

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

   if -1.6e148 < t < -1.1599999999999999e31

   1. Initial program 89.8%

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

      1. associate-*l* 89.9%

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

      2. associate--l+ 89.9%

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

      3. distribute-rgt-out-- 89.9%

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

      4. associate-*l* 89.9%

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

      5. associate-*l* 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in i around 0 90.4%

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

   5. Taylor expanded in a around 0 87.4%

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

   if -1.1599999999999999e31 < t < -2.55e-4

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. distribute-rgt-out-- 100.0%

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

      4. associate-*l* 99.8%

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

      5. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in b around 0 98.7%

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

   5. Taylor expanded in j around 0 98.7%

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

   if -2.55e-4 < t < 1.90000000000000012e89

   1. Initial program 86.9%

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

      1. associate-*l* 86.2%

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

      2. associate--l+ 86.2%

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

      3. distribute-rgt-out-- 86.2%

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

      4. associate-*l* 88.2%

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

      5. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in t around 0 83.7%

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

   if 1.90000000000000012e89 < t

   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. associate-*l* 87.7%

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

      2. associate--l+ 87.7%

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

      3. distribute-rgt-out-- 87.7%

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

      4. associate-*l* 87.7%

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

      5. associate-*l* 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in t around inf 88.1%

      \[\leadsto \color{blue}{t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - 4 \cdot a\right)} - j \cdot \left(27 \cdot k\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+148}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{+31}:\\ \;\;\;\;\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t \leq -0.000255:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+89}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - j \cdot \left(k \cdot 27\right)\\ \end{array} \]

Alternative 11: 83.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right)\\ \mathbf{if}\;t \leq -0.00062 \lor \neg \left(t \leq 1.38 \cdot 10^{+85}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k 27.0))))
   (if (or (<= t -0.00062) (not (<= t 1.38e+85)))
     (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) t_1)
     (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) t_1))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * 27.0);
	double tmp;
	if ((t <= -0.00062) || !(t <= 1.38e+85)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * 27.0d0)
    if ((t <= (-0.00062d0)) .or. (.not. (t <= 1.38d+85))) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - t_1
    else
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - t_1
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * 27.0);
	double tmp;
	if ((t <= -0.00062) || !(t <= 1.38e+85)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * 27.0)
	tmp = 0
	if (t <= -0.00062) or not (t <= 1.38e+85):
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1
	else:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * 27.0))
	tmp = 0.0
	if ((t <= -0.00062) || !(t <= 1.38e+85))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - t_1);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * 27.0);
	tmp = 0.0;
	if ((t <= -0.00062) || ~((t <= 1.38e+85)))
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	else
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -0.00062], N[Not[LessEqual[t, 1.38e+85]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.2e-4 or 1.3799999999999999e85 < t

   1. Initial program 81.8%

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

      1. associate-*l* 81.8%

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

      2. associate--l+ 81.8%

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

      3. distribute-rgt-out-- 84.7%

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

      4. associate-*l* 84.7%

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

      5. associate-*l* 84.7%

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

   3. Simplified 84.7%

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

   4. Taylor expanded in i around 0 87.2%

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

   if -6.2e-4 < t < 1.3799999999999999e85

   1. Initial program 86.9%

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

      1. associate-*l* 86.3%

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

      2. associate--l+ 86.3%

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

      3. distribute-rgt-out-- 86.3%

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

      4. associate-*l* 88.2%

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

      5. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

      1. associate-*r* 86.3%

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

      2. distribute-rgt-out-- 86.3%

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

      3. associate-*r* 88.2%

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

      4. *-commutative 88.2%

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

      5. associate-*r* 86.3%

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

      6. *-commutative 86.3%

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

      7. *-commutative 86.3%

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

      8. associate-*l* 86.3%

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

   5. Applied egg-rr 86.3%

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

   6. Taylor expanded in z around 0 89.6%

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

      1. distribute-lft-out 89.6%

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

      2. *-commutative 89.6%

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

      3. *-commutative 89.6%

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

   8. Simplified 89.6%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.00062 \lor \neg \left(t \leq 1.38 \cdot 10^{+85}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - j \cdot \left(k \cdot 27\right)\\ \end{array} \]

Alternative 12: 74.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+86} \lor \neg \left(t \leq -2.9 \cdot 10^{+29}\right) \land \left(t \leq -9 \cdot 10^{-5} \lor \neg \left(t \leq 5.8 \cdot 10^{+87}\right)\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(k \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -9.2e+86)
         (and (not (<= t -2.9e+29)) (or (<= t -9e-5) (not (<= t 5.8e+87)))))
   (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
   (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* k j))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -9.2e+86) || (!(t <= -2.9e+29) && ((t <= -9e-5) || !(t <= 5.8e+87)))) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (k * j)));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-9.2d+86)) .or. (.not. (t <= (-2.9d+29))) .and. (t <= (-9d-5)) .or. (.not. (t <= 5.8d+87))) then
        tmp = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    else
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (k * j)))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -9.2e+86) || (!(t <= -2.9e+29) && ((t <= -9e-5) || !(t <= 5.8e+87)))) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (k * j)));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -9.2e+86) or (not (t <= -2.9e+29) and ((t <= -9e-5) or not (t <= 5.8e+87))):
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	else:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (k * j)))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -9.2e+86) || (!(t <= -2.9e+29) && ((t <= -9e-5) || !(t <= 5.8e+87))))
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(k * j))));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -9.2e+86) || (~((t <= -2.9e+29)) && ((t <= -9e-5) || ~((t <= 5.8e+87)))))
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	else
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (k * j)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -9.2e+86], And[N[Not[LessEqual[t, -2.9e+29]], $MachinePrecision], Or[LessEqual[t, -9e-5], N[Not[LessEqual[t, 5.8e+87]], $MachinePrecision]]]], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.19999999999999958e86 or -2.8999999999999999e29 < t < -9.00000000000000057e-5 or 5.7999999999999996e87 < t

   1. Initial program 79.5%

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

      1. associate-*l* 79.5%

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

      2. associate--l+ 79.5%

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

      3. distribute-rgt-out-- 82.9%

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

      4. associate-*l* 82.9%

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

      5. associate-*l* 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in i around 0 89.1%

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

   5. Taylor expanded in j around 0 80.6%

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

   if -9.19999999999999958e86 < t < -2.8999999999999999e29 or -9.00000000000000057e-5 < t < 5.7999999999999996e87

   1. Initial program 87.6%

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

      1. associate-*l* 87.1%

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

      2. associate--l+ 87.1%

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

      3. distribute-rgt-out-- 87.1%

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

      4. associate-*l* 88.8%

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

      5. associate-*l* 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in t around 0 82.2%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+86} \lor \neg \left(t \leq -2.9 \cdot 10^{+29}\right) \land \left(t \leq -9 \cdot 10^{-5} \lor \neg \left(t \leq 5.8 \cdot 10^{+87}\right)\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(k \cdot j\right)\right)\\ \end{array} \]

Alternative 13: 73.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := t \cdot \left(18 \cdot t_1 - a \cdot 4\right)\\ t_3 := 4 \cdot \left(x \cdot i\right)\\ t_4 := b \cdot c + t_2\\ \mathbf{if}\;t \leq -2.65 \cdot 10^{+125}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+31}:\\ \;\;\;\;18 \cdot \left(t \cdot t_1\right) + \left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-5}:\\ \;\;\;\;t_2 - t_3\\ \mathbf{elif}\;t \leq 1.38 \cdot 10^{+85}:\\ \;\;\;\;b \cdot c - \left(t_3 + 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* y z)))
        (t_2 (* t (- (* 18.0 t_1) (* a 4.0))))
        (t_3 (* 4.0 (* x i)))
        (t_4 (+ (* b c) t_2)))
   (if (<= t -2.65e+125)
     t_4
     (if (<= t -1.5e+31)
       (+ (* 18.0 (* t t_1)) (* (* k -27.0) j))
       (if (<= t -1.12e-5)
         (- t_2 t_3)
         (if (<= t 1.38e+85) (- (* b c) (+ t_3 (* 27.0 (* k j)))) t_4))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (y * z);
	double t_2 = t * ((18.0 * t_1) - (a * 4.0));
	double t_3 = 4.0 * (x * i);
	double t_4 = (b * c) + t_2;
	double tmp;
	if (t <= -2.65e+125) {
		tmp = t_4;
	} else if (t <= -1.5e+31) {
		tmp = (18.0 * (t * t_1)) + ((k * -27.0) * j);
	} else if (t <= -1.12e-5) {
		tmp = t_2 - t_3;
	} else if (t <= 1.38e+85) {
		tmp = (b * c) - (t_3 + (27.0 * (k * j)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = t * ((18.0d0 * t_1) - (a * 4.0d0))
    t_3 = 4.0d0 * (x * i)
    t_4 = (b * c) + t_2
    if (t <= (-2.65d+125)) then
        tmp = t_4
    else if (t <= (-1.5d+31)) then
        tmp = (18.0d0 * (t * t_1)) + ((k * (-27.0d0)) * j)
    else if (t <= (-1.12d-5)) then
        tmp = t_2 - t_3
    else if (t <= 1.38d+85) then
        tmp = (b * c) - (t_3 + (27.0d0 * (k * j)))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (y * z);
	double t_2 = t * ((18.0 * t_1) - (a * 4.0));
	double t_3 = 4.0 * (x * i);
	double t_4 = (b * c) + t_2;
	double tmp;
	if (t <= -2.65e+125) {
		tmp = t_4;
	} else if (t <= -1.5e+31) {
		tmp = (18.0 * (t * t_1)) + ((k * -27.0) * j);
	} else if (t <= -1.12e-5) {
		tmp = t_2 - t_3;
	} else if (t <= 1.38e+85) {
		tmp = (b * c) - (t_3 + (27.0 * (k * j)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (y * z)
	t_2 = t * ((18.0 * t_1) - (a * 4.0))
	t_3 = 4.0 * (x * i)
	t_4 = (b * c) + t_2
	tmp = 0
	if t <= -2.65e+125:
		tmp = t_4
	elif t <= -1.5e+31:
		tmp = (18.0 * (t * t_1)) + ((k * -27.0) * j)
	elif t <= -1.12e-5:
		tmp = t_2 - t_3
	elif t <= 1.38e+85:
		tmp = (b * c) - (t_3 + (27.0 * (k * j)))
	else:
		tmp = t_4
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(t * Float64(Float64(18.0 * t_1) - Float64(a * 4.0)))
	t_3 = Float64(4.0 * Float64(x * i))
	t_4 = Float64(Float64(b * c) + t_2)
	tmp = 0.0
	if (t <= -2.65e+125)
		tmp = t_4;
	elseif (t <= -1.5e+31)
		tmp = Float64(Float64(18.0 * Float64(t * t_1)) + Float64(Float64(k * -27.0) * j));
	elseif (t <= -1.12e-5)
		tmp = Float64(t_2 - t_3);
	elseif (t <= 1.38e+85)
		tmp = Float64(Float64(b * c) - Float64(t_3 + Float64(27.0 * Float64(k * j))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (y * z);
	t_2 = t * ((18.0 * t_1) - (a * 4.0));
	t_3 = 4.0 * (x * i);
	t_4 = (b * c) + t_2;
	tmp = 0.0;
	if (t <= -2.65e+125)
		tmp = t_4;
	elseif (t <= -1.5e+31)
		tmp = (18.0 * (t * t_1)) + ((k * -27.0) * j);
	elseif (t <= -1.12e-5)
		tmp = t_2 - t_3;
	elseif (t <= 1.38e+85)
		tmp = (b * c) - (t_3 + (27.0 * (k * j)));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * t$95$1), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t, -2.65e+125], t$95$4, If[LessEqual[t, -1.5e+31], N[(N[(18.0 * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(k * -27.0), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.12e-5], N[(t$95$2 - t$95$3), $MachinePrecision], If[LessEqual[t, 1.38e+85], N[(N[(b * c), $MachinePrecision] - N[(t$95$3 + N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.6500000000000001e125 or 1.3799999999999999e85 < t

   1. Initial program 76.3%

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

      1. associate-*l* 76.3%

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

      2. associate--l+ 76.3%

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

      3. distribute-rgt-out-- 80.5%

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

      4. associate-*l* 80.5%

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

      5. associate-*l* 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in i around 0 87.6%

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

   5. Taylor expanded in j around 0 78.5%

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

   if -2.6500000000000001e125 < t < -1.49999999999999995e31

   1. Initial program 92.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in y around inf 77.5%

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

   if -1.49999999999999995e31 < t < -1.11999999999999995e-5

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. distribute-rgt-out-- 100.0%

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

      4. associate-*l* 99.8%

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

      5. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in b around 0 98.7%

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

   5. Taylor expanded in j around 0 98.7%

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

   if -1.11999999999999995e-5 < t < 1.3799999999999999e85

   1. Initial program 86.9%

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

      1. associate-*l* 86.2%

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

      2. associate--l+ 86.2%

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

      3. distribute-rgt-out-- 86.2%

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

      4. associate-*l* 88.2%

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

      5. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in t around 0 83.7%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+125}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+31}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + \left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 1.38 \cdot 10^{+85}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 14: 79.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ t_2 := j \cdot \left(k \cdot 27\right)\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+127}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;t \leq -0.0052:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - t_2\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+94}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 - t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z 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 (- (* 18.0 (* x (* y z))) (* a 4.0))))
        (t_2 (* j (* k 27.0))))
   (if (<= t -1.65e+127)
     (+ (* b c) t_1)
     (if (<= t -0.0052)
       (- (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))) t_2)
       (if (<= t 4e+94)
         (- (- (* b c) (* 4.0 (+ (* t a) (* x i)))) t_2)
         (- t_1 t_2))))))

C

assert(y < z);
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 * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_2 = j * (k * 27.0);
	double tmp;
	if (t <= -1.65e+127) {
		tmp = (b * c) + t_1;
	} else if (t <= -0.0052) {
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_2;
	} else if (t <= 4e+94) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_2;
	} else {
		tmp = t_1 - t_2;
	}
	return tmp;
}

Fortran

NOTE: y and z 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 * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    t_2 = j * (k * 27.0d0)
    if (t <= (-1.65d+127)) then
        tmp = (b * c) + t_1
    else if (t <= (-0.0052d0)) then
        tmp = (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))) - t_2
    else if (t <= 4d+94) then
        tmp = ((b * c) - (4.0d0 * ((t * a) + (x * i)))) - t_2
    else
        tmp = t_1 - t_2
    end if
    code = tmp
end function

Java

assert y < z;
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 * ((18.0 * (x * (y * z))) - (a * 4.0));
	double t_2 = j * (k * 27.0);
	double tmp;
	if (t <= -1.65e+127) {
		tmp = (b * c) + t_1;
	} else if (t <= -0.0052) {
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_2;
	} else if (t <= 4e+94) {
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_2;
	} else {
		tmp = t_1 - t_2;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	t_2 = j * (k * 27.0)
	tmp = 0
	if t <= -1.65e+127:
		tmp = (b * c) + t_1
	elif t <= -0.0052:
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_2
	elif t <= 4e+94:
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_2
	else:
		tmp = t_1 - t_2
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	t_2 = Float64(j * Float64(k * 27.0))
	tmp = 0.0
	if (t <= -1.65e+127)
		tmp = Float64(Float64(b * c) + t_1);
	elseif (t <= -0.0052)
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))) - t_2);
	elseif (t <= 4e+94)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(Float64(t * a) + Float64(x * i)))) - t_2);
	else
		tmp = Float64(t_1 - t_2);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	t_2 = j * (k * 27.0);
	tmp = 0.0;
	if (t <= -1.65e+127)
		tmp = (b * c) + t_1;
	elseif (t <= -0.0052)
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_2;
	elseif (t <= 4e+94)
		tmp = ((b * c) - (4.0 * ((t * a) + (x * i)))) - t_2;
	else
		tmp = t_1 - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z 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[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.65e+127], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, -0.0052], N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t, 4e+94], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(t$95$1 - t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.64999999999999988e127

   1. Initial program 61.2%

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

      1. associate-*l* 61.2%

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

      2. associate--l+ 61.2%

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

      3. distribute-rgt-out-- 70.9%

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

      4. associate-*l* 71.0%

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

      5. associate-*l* 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in i around 0 83.9%

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

   5. Taylor expanded in j around 0 80.9%

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

   if -1.64999999999999988e127 < t < -0.0051999999999999998

   1. Initial program 93.7%

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

      1. associate-*l* 93.8%

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

      2. associate--l+ 93.8%

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

      3. distribute-rgt-out-- 93.8%

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

      4. associate-*l* 93.8%

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

      5. associate-*l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in x around inf 85.1%

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

   if -0.0051999999999999998 < t < 4.0000000000000001e94

   1. Initial program 86.9%

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

      1. associate-*l* 86.3%

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

      2. associate--l+ 86.3%

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

      3. distribute-rgt-out-- 86.3%

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

      4. associate-*l* 88.2%

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

      5. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

      1. associate-*r* 86.3%

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

      2. distribute-rgt-out-- 86.3%

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

      3. associate-*r* 88.2%

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

      4. *-commutative 88.2%

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

      5. associate-*r* 86.3%

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

      6. *-commutative 86.3%

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

      7. *-commutative 86.3%

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

      8. associate-*l* 86.3%

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

   5. Applied egg-rr 86.3%

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

   6. Taylor expanded in z around 0 89.6%

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

      1. distribute-lft-out 89.6%

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

      2. *-commutative 89.6%

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

      3. *-commutative 89.6%

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

   8. Simplified 89.6%

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

   if 4.0000000000000001e94 < t

   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. associate-*l* 87.7%

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

      2. associate--l+ 87.7%

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

      3. distribute-rgt-out-- 87.7%

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

      4. associate-*l* 87.7%

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

      5. associate-*l* 87.7%

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

   3. Simplified 87.7%

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

   4. Taylor expanded in t around inf 88.1%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+127}:\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -0.0052:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+94}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a + x \cdot i\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - j \cdot \left(k \cdot 27\right)\\ \end{array} \]

Alternative 15: 74.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-8} \lor \neg \left(t \leq 1.1 \cdot 10^{+85}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(k \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.1e-8) (not (<= t 1.1e+85)))
   (- (* t (- (* 18.0 (* x (* y z))) (* a 4.0))) (* j (* k 27.0)))
   (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* k j))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.1e-8) || !(t <= 1.1e+85)) {
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - (j * (k * 27.0));
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (k * j)));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-1.1d-8)) .or. (.not. (t <= 1.1d+85))) then
        tmp = (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))) - (j * (k * 27.0d0))
    else
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (k * j)))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.1e-8) || !(t <= 1.1e+85)) {
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - (j * (k * 27.0));
	} else {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (k * j)));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.1e-8) or not (t <= 1.1e+85):
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - (j * (k * 27.0))
	else:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (k * j)))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.1e-8) || !(t <= 1.1e+85))
		tmp = Float64(Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))) - Float64(j * Float64(k * 27.0)));
	else
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(k * j))));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1.1e-8) || ~((t <= 1.1e+85)))
		tmp = (t * ((18.0 * (x * (y * z))) - (a * 4.0))) - (j * (k * 27.0));
	else
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (k * j)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.1e-8], N[Not[LessEqual[t, 1.1e+85]], $MachinePrecision]], N[(N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0999999999999999e-8 or 1.1000000000000001e85 < t

   1. Initial program 81.9%

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

      1. associate-*l* 82.0%

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

      2. associate--l+ 82.0%

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

      3. distribute-rgt-out-- 84.8%

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

      4. associate-*l* 84.8%

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

      5. associate-*l* 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in t around inf 80.8%

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

   if -1.0999999999999999e-8 < t < 1.1000000000000001e85

   1. Initial program 86.9%

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

      1. associate-*l* 86.2%

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

      2. associate--l+ 86.2%

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

      3. distribute-rgt-out-- 86.2%

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

      4. associate-*l* 88.2%

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

      5. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in t around 0 83.7%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-8} \lor \neg \left(t \leq 1.1 \cdot 10^{+85}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(k \cdot j\right)\right)\\ \end{array} \]

Alternative 16: 70.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := t \cdot \left(18 \cdot t_1 - a \cdot 4\right)\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -0.0026:\\ \;\;\;\;18 \cdot \left(t \cdot t_1\right) + \left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+91}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* t (- (* 18.0 t_1) (* a 4.0)))))
   (if (<= t -2.4e+126)
     t_2
     (if (<= t -0.0026)
       (+ (* 18.0 (* t t_1)) (* (* k -27.0) j))
       (if (<= t 3e+91)
         (- (* b c) (+ (* 4.0 (* x i)) (* 27.0 (* k j))))
         t_2)))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (y * z);
	double t_2 = t * ((18.0 * t_1) - (a * 4.0));
	double tmp;
	if (t <= -2.4e+126) {
		tmp = t_2;
	} else if (t <= -0.0026) {
		tmp = (18.0 * (t * t_1)) + ((k * -27.0) * j);
	} else if (t <= 3e+91) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = t * ((18.0d0 * t_1) - (a * 4.0d0))
    if (t <= (-2.4d+126)) then
        tmp = t_2
    else if (t <= (-0.0026d0)) then
        tmp = (18.0d0 * (t * t_1)) + ((k * (-27.0d0)) * j)
    else if (t <= 3d+91) then
        tmp = (b * c) - ((4.0d0 * (x * i)) + (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * (y * z);
	double t_2 = t * ((18.0 * t_1) - (a * 4.0));
	double tmp;
	if (t <= -2.4e+126) {
		tmp = t_2;
	} else if (t <= -0.0026) {
		tmp = (18.0 * (t * t_1)) + ((k * -27.0) * j);
	} else if (t <= 3e+91) {
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * (y * z)
	t_2 = t * ((18.0 * t_1) - (a * 4.0))
	tmp = 0
	if t <= -2.4e+126:
		tmp = t_2
	elif t <= -0.0026:
		tmp = (18.0 * (t * t_1)) + ((k * -27.0) * j)
	elif t <= 3e+91:
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(t * Float64(Float64(18.0 * t_1) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -2.4e+126)
		tmp = t_2;
	elseif (t <= -0.0026)
		tmp = Float64(Float64(18.0 * Float64(t * t_1)) + Float64(Float64(k * -27.0) * j));
	elseif (t <= 3e+91)
		tmp = Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(x * i)) + Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * (y * z);
	t_2 = t * ((18.0 * t_1) - (a * 4.0));
	tmp = 0.0;
	if (t <= -2.4e+126)
		tmp = t_2;
	elseif (t <= -0.0026)
		tmp = (18.0 * (t * t_1)) + ((k * -27.0) * j);
	elseif (t <= 3e+91)
		tmp = (b * c) - ((4.0 * (x * i)) + (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * t$95$1), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e+126], t$95$2, If[LessEqual[t, -0.0026], N[(N[(18.0 * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(k * -27.0), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+91], N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.40000000000000012e126 or 3.00000000000000006e91 < t

   1. Initial program 76.3%

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

      1. associate-*l* 76.3%

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

      2. associate--l+ 76.3%

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

      3. distribute-rgt-out-- 80.5%

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

      4. associate-*l* 80.5%

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

      5. associate-*l* 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in i around 0 87.6%

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

   5. Taylor expanded in j around 0 78.5%

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

   6. Taylor expanded in b around 0 74.6%

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

   if -2.40000000000000012e126 < t < -0.0025999999999999999

   1. Initial program 93.7%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in y around inf 74.0%

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

   if -0.0025999999999999999 < t < 3.00000000000000006e91

   1. Initial program 86.9%

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

      1. associate-*l* 86.3%

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

      2. associate--l+ 86.3%

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

      3. distribute-rgt-out-- 86.3%

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

      4. associate-*l* 88.2%

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

      5. associate-*l* 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in t around 0 83.2%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+126}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -0.0026:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + \left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+91}:\\ \;\;\;\;b \cdot c - \left(4 \cdot \left(x \cdot i\right) + 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 17: 53.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.2 \cdot 10^{-14} \lor \neg \left(b \cdot c \leq 3.2 \cdot 10^{+21}\right):\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot -27\right) \cdot j + -4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -3.2e-14) (not (<= (* b c) 3.2e+21)))
   (- (* b c) (* 27.0 (* k j)))
   (+ (* (* k -27.0) j) (* -4.0 (* t a)))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -3.2e-14) || !((b * c) <= 3.2e+21)) {
		tmp = (b * c) - (27.0 * (k * j));
	} else {
		tmp = ((k * -27.0) * j) + (-4.0 * (t * a));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-3.2d-14)) .or. (.not. ((b * c) <= 3.2d+21))) then
        tmp = (b * c) - (27.0d0 * (k * j))
    else
        tmp = ((k * (-27.0d0)) * j) + ((-4.0d0) * (t * a))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -3.2e-14) || !((b * c) <= 3.2e+21)) {
		tmp = (b * c) - (27.0 * (k * j));
	} else {
		tmp = ((k * -27.0) * j) + (-4.0 * (t * a));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -3.2e-14) or not ((b * c) <= 3.2e+21):
		tmp = (b * c) - (27.0 * (k * j))
	else:
		tmp = ((k * -27.0) * j) + (-4.0 * (t * a))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -3.2e-14) || !(Float64(b * c) <= 3.2e+21))
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(k * j)));
	else
		tmp = Float64(Float64(Float64(k * -27.0) * j) + Float64(-4.0 * Float64(t * a)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -3.2e-14) || ~(((b * c) <= 3.2e+21)))
		tmp = (b * c) - (27.0 * (k * j));
	else
		tmp = ((k * -27.0) * j) + (-4.0 * (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -3.2e-14], N[Not[LessEqual[N[(b * c), $MachinePrecision], 3.2e+21]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(k * -27.0), $MachinePrecision] * j), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -3.2000000000000002e-14 or 3.2e21 < (*.f64 b c)

   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. associate-*l* 82.0%

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

      2. associate--l+ 82.0%

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

      3. distribute-rgt-out-- 82.7%

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

      4. associate-*l* 84.9%

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

      5. associate-*l* 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in t around 0 76.1%

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

   5. Taylor expanded in i around 0 66.5%

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

   if -3.2000000000000002e-14 < (*.f64 b c) < 3.2e21

   1. Initial program 87.1%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in a around inf 53.5%

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

      1. *-commutative 53.5%

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

   6. Simplified 53.5%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.2 \cdot 10^{-14} \lor \neg \left(b \cdot c \leq 3.2 \cdot 10^{+21}\right):\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(k \cdot -27\right) \cdot j + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 18: 51.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := b \cdot c - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+23}:\\ \;\;\;\;b \cdot c + \left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-16} \lor \neg \left(x \leq 1.85 \cdot 10^{+28}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z 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) (* (* x 4.0) i))))
   (if (<= x -5.5e+93)
     t_1
     (if (<= x -3.6e+23)
       (+ (* b c) (* (* k -27.0) j))
       (if (or (<= x -1.4e-16) (not (<= x 1.85e+28)))
         t_1
         (- (* b c) (* 27.0 (* k j))))))))

C

assert(y < z);
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) - ((x * 4.0) * i);
	double tmp;
	if (x <= -5.5e+93) {
		tmp = t_1;
	} else if (x <= -3.6e+23) {
		tmp = (b * c) + ((k * -27.0) * j);
	} else if ((x <= -1.4e-16) || !(x <= 1.85e+28)) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (27.0 * (k * j));
	}
	return tmp;
}

Fortran

NOTE: y and z 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) - ((x * 4.0d0) * i)
    if (x <= (-5.5d+93)) then
        tmp = t_1
    else if (x <= (-3.6d+23)) then
        tmp = (b * c) + ((k * (-27.0d0)) * j)
    else if ((x <= (-1.4d-16)) .or. (.not. (x <= 1.85d+28))) then
        tmp = t_1
    else
        tmp = (b * c) - (27.0d0 * (k * j))
    end if
    code = tmp
end function

Java

assert y < z;
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) - ((x * 4.0) * i);
	double tmp;
	if (x <= -5.5e+93) {
		tmp = t_1;
	} else if (x <= -3.6e+23) {
		tmp = (b * c) + ((k * -27.0) * j);
	} else if ((x <= -1.4e-16) || !(x <= 1.85e+28)) {
		tmp = t_1;
	} else {
		tmp = (b * c) - (27.0 * (k * j));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - ((x * 4.0) * i)
	tmp = 0
	if x <= -5.5e+93:
		tmp = t_1
	elif x <= -3.6e+23:
		tmp = (b * c) + ((k * -27.0) * j)
	elif (x <= -1.4e-16) or not (x <= 1.85e+28):
		tmp = t_1
	else:
		tmp = (b * c) - (27.0 * (k * j))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if (x <= -5.5e+93)
		tmp = t_1;
	elseif (x <= -3.6e+23)
		tmp = Float64(Float64(b * c) + Float64(Float64(k * -27.0) * j));
	elseif ((x <= -1.4e-16) || !(x <= 1.85e+28))
		tmp = t_1;
	else
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(k * j)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - ((x * 4.0) * i);
	tmp = 0.0;
	if (x <= -5.5e+93)
		tmp = t_1;
	elseif (x <= -3.6e+23)
		tmp = (b * c) + ((k * -27.0) * j);
	elseif ((x <= -1.4e-16) || ~((x <= 1.85e+28)))
		tmp = t_1;
	else
		tmp = (b * c) - (27.0 * (k * j));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z 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[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5e+93], t$95$1, If[LessEqual[x, -3.6e+23], N[(N[(b * c), $MachinePrecision] + N[(N[(k * -27.0), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.4e-16], N[Not[LessEqual[x, 1.85e+28]], $MachinePrecision]], t$95$1, N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5000000000000003e93 or -3.5999999999999998e23 < x < -1.4000000000000001e-16 or 1.85e28 < x

   1. Initial program 72.1%

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

      1. associate-*l* 72.2%

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

      2. associate--l+ 72.2%

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

      3. distribute-rgt-out-- 74.1%

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

      4. associate-*l* 77.9%

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

      5. associate-*l* 77.9%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in t around 0 58.0%

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

   5. Taylor expanded in i around inf 54.3%

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

      1. *-commutative 54.3%

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

      2. associate-*r* 54.3%

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

   7. Simplified 54.3%

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

   if -5.5000000000000003e93 < x < -3.5999999999999998e23

   1. Initial program 80.1%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in b around inf 74.6%

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

   if -1.4000000000000001e-16 < x < 1.85e28

   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. associate-*l* 94.7%

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

      2. associate--l+ 94.7%

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

      3. distribute-rgt-out-- 95.5%

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

      4. associate-*l* 93.3%

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

      5. associate-*l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in t around 0 69.9%

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

   5. Taylor expanded in i around 0 62.7%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+93}:\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+23}:\\ \;\;\;\;b \cdot c + \left(k \cdot -27\right) \cdot j\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-16} \lor \neg \left(x \leq 1.85 \cdot 10^{+28}\right):\\ \;\;\;\;b \cdot c - \left(x \cdot 4\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \end{array} \]

Alternative 19: 33.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -35000 \lor \neg \left(x \leq 2.7 \cdot 10^{+17}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -35000.0) (not (<= x 2.7e+17)))
   (* t (* 18.0 (* x (* y z))))
   (* -27.0 (* k j))))

C

assert(y < z);
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 <= -35000.0) || !(x <= 2.7e+17)) {
		tmp = t * (18.0 * (x * (y * z)));
	} else {
		tmp = -27.0 * (k * j);
	}
	return tmp;
}

Fortran

NOTE: y and z 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 <= (-35000.0d0)) .or. (.not. (x <= 2.7d+17))) then
        tmp = t * (18.0d0 * (x * (y * z)))
    else
        tmp = (-27.0d0) * (k * j)
    end if
    code = tmp
end function

Java

assert y < z;
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 <= -35000.0) || !(x <= 2.7e+17)) {
		tmp = t * (18.0 * (x * (y * z)));
	} else {
		tmp = -27.0 * (k * j);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -35000.0) or not (x <= 2.7e+17):
		tmp = t * (18.0 * (x * (y * z)))
	else:
		tmp = -27.0 * (k * j)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -35000.0) || !(x <= 2.7e+17))
		tmp = Float64(t * Float64(18.0 * Float64(x * Float64(y * z))));
	else
		tmp = Float64(-27.0 * Float64(k * j));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -35000.0) || ~((x <= 2.7e+17)))
		tmp = t * (18.0 * (x * (y * z)));
	else
		tmp = -27.0 * (k * j);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -35000.0], N[Not[LessEqual[x, 2.7e+17]], $MachinePrecision]], N[(t * N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -35000 or 2.7e17 < x

   1. Initial program 72.6%

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

      1. associate-*l* 72.6%

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

      2. associate--l+ 72.6%

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

      3. distribute-rgt-out-- 74.2%

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

      4. associate-*l* 79.0%

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

      5. associate-*l* 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in i around 0 67.4%

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

   5. Taylor expanded in j around 0 58.7%

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

   6. Taylor expanded in b around 0 46.7%

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

   7. Taylor expanded in x around inf 38.5%

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

   if -35000 < x < 2.7e17

   1. Initial program 96.1%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in j around inf 36.5%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -35000 \lor \neg \left(x \leq 2.7 \cdot 10^{+17}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \]

Alternative 20: 33.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -35000000000 \lor \neg \left(x \leq 3.2 \cdot 10^{+16}\right):\\ \;\;\;\;t \cdot \left(y \cdot \left(\left(x \cdot 18\right) \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -35000000000.0) (not (<= x 3.2e+16)))
   (* t (* y (* (* x 18.0) z)))
   (* -27.0 (* k j))))

C

assert(y < z);
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 <= -35000000000.0) || !(x <= 3.2e+16)) {
		tmp = t * (y * ((x * 18.0) * z));
	} else {
		tmp = -27.0 * (k * j);
	}
	return tmp;
}

Fortran

NOTE: y and z 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 <= (-35000000000.0d0)) .or. (.not. (x <= 3.2d+16))) then
        tmp = t * (y * ((x * 18.0d0) * z))
    else
        tmp = (-27.0d0) * (k * j)
    end if
    code = tmp
end function

Java

assert y < z;
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 <= -35000000000.0) || !(x <= 3.2e+16)) {
		tmp = t * (y * ((x * 18.0) * z));
	} else {
		tmp = -27.0 * (k * j);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -35000000000.0) or not (x <= 3.2e+16):
		tmp = t * (y * ((x * 18.0) * z))
	else:
		tmp = -27.0 * (k * j)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -35000000000.0) || !(x <= 3.2e+16))
		tmp = Float64(t * Float64(y * Float64(Float64(x * 18.0) * z)));
	else
		tmp = Float64(-27.0 * Float64(k * j));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -35000000000.0) || ~((x <= 3.2e+16)))
		tmp = t * (y * ((x * 18.0) * z));
	else
		tmp = -27.0 * (k * j);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -35000000000.0], N[Not[LessEqual[x, 3.2e+16]], $MachinePrecision]], N[(t * N[(y * N[(N[(x * 18.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5e10 or 3.2e16 < x

   1. Initial program 72.6%

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

      1. associate-*l* 72.6%

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

      2. associate--l+ 72.6%

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

      3. distribute-rgt-out-- 74.2%

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

      4. associate-*l* 79.0%

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

      5. associate-*l* 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in i around 0 67.4%

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

   5. Taylor expanded in j around 0 58.7%

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

   6. Taylor expanded in b around 0 46.7%

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

   7. Taylor expanded in x around inf 38.5%

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

      1. associate-*r* 38.5%

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

      2. *-commutative 38.5%

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

      3. associate-*l* 40.8%

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

   9. Simplified 40.8%

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

   if -3.5e10 < x < 3.2e16

   1. Initial program 96.1%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in j around inf 36.5%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -35000000000 \lor \neg \left(x \leq 3.2 \cdot 10^{+16}\right):\\ \;\;\;\;t \cdot \left(y \cdot \left(\left(x \cdot 18\right) \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \]

Alternative 21: 45.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 7.8 \cdot 10^{+17}:\\ \;\;\;\;b \cdot c + \left(k \cdot -27\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(\left(x \cdot 18\right) \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x 7.8e+17)
   (+ (* b c) (* (* k -27.0) j))
   (* t (* y (* (* x 18.0) z)))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= 7.8e+17) {
		tmp = (b * c) + ((k * -27.0) * j);
	} else {
		tmp = t * (y * ((x * 18.0) * z));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= 7.8d+17) then
        tmp = (b * c) + ((k * (-27.0d0)) * j)
    else
        tmp = t * (y * ((x * 18.0d0) * z))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= 7.8e+17) {
		tmp = (b * c) + ((k * -27.0) * j);
	} else {
		tmp = t * (y * ((x * 18.0) * z));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= 7.8e+17:
		tmp = (b * c) + ((k * -27.0) * j)
	else:
		tmp = t * (y * ((x * 18.0) * z))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= 7.8e+17)
		tmp = Float64(Float64(b * c) + Float64(Float64(k * -27.0) * j));
	else
		tmp = Float64(t * Float64(y * Float64(Float64(x * 18.0) * z)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= 7.8e+17)
		tmp = (b * c) + ((k * -27.0) * j);
	else
		tmp = t * (y * ((x * 18.0) * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, 7.8e+17], N[(N[(b * c), $MachinePrecision] + N[(N[(k * -27.0), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * N[(N[(x * 18.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.8e17

   1. Initial program 88.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in b around inf 56.8%

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

   if 7.8e17 < x

   1. Initial program 73.5%

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

      1. associate-*l* 73.5%

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

      2. associate--l+ 73.5%

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

      3. distribute-rgt-out-- 75.2%

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

      4. associate-*l* 78.5%

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

      5. associate-*l* 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in i around 0 60.9%

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

   5. Taylor expanded in j around 0 53.0%

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

   6. Taylor expanded in b around 0 48.0%

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

   7. Taylor expanded in x around inf 39.7%

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

      1. associate-*r* 39.7%

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

      2. *-commutative 39.7%

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

      3. associate-*l* 41.3%

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

   9. Simplified 41.3%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.8 \cdot 10^{+17}:\\ \;\;\;\;b \cdot c + \left(k \cdot -27\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(\left(x \cdot 18\right) \cdot z\right)\right)\\ \end{array} \]

Alternative 22: 45.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 7.8 \cdot 10^{+17}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(\left(x \cdot 18\right) \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x 7.8e+17) (- (* b c) (* 27.0 (* k j))) (* t (* y (* (* x 18.0) z)))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= 7.8e+17) {
		tmp = (b * c) - (27.0 * (k * j));
	} else {
		tmp = t * (y * ((x * 18.0) * z));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= 7.8d+17) then
        tmp = (b * c) - (27.0d0 * (k * j))
    else
        tmp = t * (y * ((x * 18.0d0) * z))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= 7.8e+17) {
		tmp = (b * c) - (27.0 * (k * j));
	} else {
		tmp = t * (y * ((x * 18.0) * z));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= 7.8e+17:
		tmp = (b * c) - (27.0 * (k * j))
	else:
		tmp = t * (y * ((x * 18.0) * z))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= 7.8e+17)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(k * j)));
	else
		tmp = Float64(t * Float64(y * Float64(Float64(x * 18.0) * z)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= 7.8e+17)
		tmp = (b * c) - (27.0 * (k * j));
	else
		tmp = t * (y * ((x * 18.0) * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, 7.8e+17], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y * N[(N[(x * 18.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.8e17

   1. Initial program 88.3%

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

      1. associate-*l* 87.8%

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

      2. associate--l+ 87.8%

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

      3. distribute-rgt-out-- 88.8%

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

      4. associate-*l* 89.3%

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

      5. associate-*l* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in t around 0 69.3%

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

   5. Taylor expanded in i around 0 57.3%

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

   if 7.8e17 < x

   1. Initial program 73.5%

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

      1. associate-*l* 73.5%

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

      2. associate--l+ 73.5%

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

      3. distribute-rgt-out-- 75.2%

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

      4. associate-*l* 78.5%

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

      5. associate-*l* 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in i around 0 60.9%

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

   5. Taylor expanded in j around 0 53.0%

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

   6. Taylor expanded in b around 0 48.0%

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

   7. Taylor expanded in x around inf 39.7%

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

      1. associate-*r* 39.7%

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

      2. *-commutative 39.7%

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

      3. associate-*l* 41.3%

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

   9. Simplified 41.3%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.8 \cdot 10^{+17}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(\left(x \cdot 18\right) \cdot z\right)\right)\\ \end{array} \]

Alternative 23: 30.8% accurate, 3.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+125} \lor \neg \left(t \leq 9.6 \cdot 10^{+154}\right):\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -7.5e+125) (not (<= t 9.6e+154)))
   (* t (* a -4.0))
   (* -27.0 (* k j))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -7.5e+125) || !(t <= 9.6e+154)) {
		tmp = t * (a * -4.0);
	} else {
		tmp = -27.0 * (k * j);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-7.5d+125)) .or. (.not. (t <= 9.6d+154))) then
        tmp = t * (a * (-4.0d0))
    else
        tmp = (-27.0d0) * (k * j)
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -7.5e+125) || !(t <= 9.6e+154)) {
		tmp = t * (a * -4.0);
	} else {
		tmp = -27.0 * (k * j);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -7.5e+125) or not (t <= 9.6e+154):
		tmp = t * (a * -4.0)
	else:
		tmp = -27.0 * (k * j)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -7.5e+125) || !(t <= 9.6e+154))
		tmp = Float64(t * Float64(a * -4.0));
	else
		tmp = Float64(-27.0 * Float64(k * j));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -7.5e+125) || ~((t <= 9.6e+154)))
		tmp = t * (a * -4.0);
	else
		tmp = -27.0 * (k * j);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -7.5e+125], N[Not[LessEqual[t, 9.6e+154]], $MachinePrecision]], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.5000000000000006e125 or 9.60000000000000059e154 < t

   1. Initial program 73.7%

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

      1. associate-*l* 73.7%

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

      2. associate--l+ 73.7%

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

      3. distribute-rgt-out-- 78.6%

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

      4. associate-*l* 78.6%

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

      5. associate-*l* 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in i around 0 88.5%

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

   5. Taylor expanded in j around 0 82.5%

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

   6. Taylor expanded in b around 0 77.8%

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

   7. Taylor expanded in x around 0 44.4%

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

      1. *-commutative 44.4%

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

   9. Simplified 44.4%

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

   if -7.5000000000000006e125 < t < 9.60000000000000059e154

   1. Initial program 88.3%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in j around inf 30.2%

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

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+125} \lor \neg \left(t \leq 9.6 \cdot 10^{+154}\right):\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \]

Alternative 24: 23.8% accurate, 6.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ -27 \cdot \left(k \cdot j\right) \end{array} \]

FPCore

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

C

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

Fortran

NOTE: y and z 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 = (-27.0d0) * (k * j)
end function

Java

assert y < z;
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 -27.0 * (k * j);
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	return -27.0 * (k * j)

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(-27.0 * Float64(k * j))
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = -27.0 * (k * j);
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.8%

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

3. Simplified 89.5%

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

4. Taylor expanded in j around inf 26.2%

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

5. Final simplification 26.2%

   \[\leadsto -27 \cdot \left(k \cdot j\right) \]

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 2023318 
(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)))