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

Percentage Accurate: 85.3% → 91.7%

Time: 20.0s

Alternatives: 17

Speedup: 0.9×

• 50.6% 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: 85.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.7% accurate, 0.5× speedup

Math

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

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

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

Python

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.0%

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

   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-- 16.0%

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

      4. associate-*l* 28.0%

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

      5. associate-*l* 28.0%

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

   3. Simplified 28.0%

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

   4. Taylor expanded in x around inf 80.0%

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

4. Final simplification 93.5%

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

Alternative 2: 56.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := b \cdot c + 18 \cdot \left(t \cdot t_1\right)\\ t_3 := b \cdot c - j \cdot \left(27 \cdot k\right)\\ t_4 := k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ t_5 := t \cdot \left(18 \cdot t_1 - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+125}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+38}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-56}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-177}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-302}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-223}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-184}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-22}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+81}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

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 (+ (* b c) (* 18.0 (* t t_1))))
        (t_3 (- (* b c) (* j (* 27.0 k))))
        (t_4 (+ (* k (* j -27.0)) (* -4.0 (* x i))))
        (t_5 (* t (- (* 18.0 t_1) (* a 4.0)))))
   (if (<= t -1.15e+125)
     t_5
     (if (<= t -1.25e+38)
       t_4
       (if (<= t -5e+14)
         t_2
         (if (<= t -4.5e-56)
           t_4
           (if (<= t -7e-136)
             t_2
             (if (<= t -5.8e-177)
               t_4
               (if (<= t 7.8e-302)
                 t_3
                 (if (<= t 5.5e-223)
                   (- (* b c) (* 4.0 (* x i)))
                   (if (<= t 9.5e-184)
                     t_3
                     (if (<= t 5.6e-22)
                       t_4
                       (if (<= t 6.2e+51)
                         t_2
                         (if (<= t 2.3e+81) t_4 t_5))))))))))))))

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 = (b * c) + (18.0 * (t * t_1));
	double t_3 = (b * c) - (j * (27.0 * k));
	double t_4 = (k * (j * -27.0)) + (-4.0 * (x * i));
	double t_5 = t * ((18.0 * t_1) - (a * 4.0));
	double tmp;
	if (t <= -1.15e+125) {
		tmp = t_5;
	} else if (t <= -1.25e+38) {
		tmp = t_4;
	} else if (t <= -5e+14) {
		tmp = t_2;
	} else if (t <= -4.5e-56) {
		tmp = t_4;
	} else if (t <= -7e-136) {
		tmp = t_2;
	} else if (t <= -5.8e-177) {
		tmp = t_4;
	} else if (t <= 7.8e-302) {
		tmp = t_3;
	} else if (t <= 5.5e-223) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 9.5e-184) {
		tmp = t_3;
	} else if (t <= 5.6e-22) {
		tmp = t_4;
	} else if (t <= 6.2e+51) {
		tmp = t_2;
	} else if (t <= 2.3e+81) {
		tmp = t_4;
	} else {
		tmp = t_5;
	}
	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 = x * (y * z)
    t_2 = (b * c) + (18.0d0 * (t * t_1))
    t_3 = (b * c) - (j * (27.0d0 * k))
    t_4 = (k * (j * (-27.0d0))) + ((-4.0d0) * (x * i))
    t_5 = t * ((18.0d0 * t_1) - (a * 4.0d0))
    if (t <= (-1.15d+125)) then
        tmp = t_5
    else if (t <= (-1.25d+38)) then
        tmp = t_4
    else if (t <= (-5d+14)) then
        tmp = t_2
    else if (t <= (-4.5d-56)) then
        tmp = t_4
    else if (t <= (-7d-136)) then
        tmp = t_2
    else if (t <= (-5.8d-177)) then
        tmp = t_4
    else if (t <= 7.8d-302) then
        tmp = t_3
    else if (t <= 5.5d-223) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t <= 9.5d-184) then
        tmp = t_3
    else if (t <= 5.6d-22) then
        tmp = t_4
    else if (t <= 6.2d+51) then
        tmp = t_2
    else if (t <= 2.3d+81) then
        tmp = t_4
    else
        tmp = t_5
    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 = (b * c) + (18.0 * (t * t_1));
	double t_3 = (b * c) - (j * (27.0 * k));
	double t_4 = (k * (j * -27.0)) + (-4.0 * (x * i));
	double t_5 = t * ((18.0 * t_1) - (a * 4.0));
	double tmp;
	if (t <= -1.15e+125) {
		tmp = t_5;
	} else if (t <= -1.25e+38) {
		tmp = t_4;
	} else if (t <= -5e+14) {
		tmp = t_2;
	} else if (t <= -4.5e-56) {
		tmp = t_4;
	} else if (t <= -7e-136) {
		tmp = t_2;
	} else if (t <= -5.8e-177) {
		tmp = t_4;
	} else if (t <= 7.8e-302) {
		tmp = t_3;
	} else if (t <= 5.5e-223) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 9.5e-184) {
		tmp = t_3;
	} else if (t <= 5.6e-22) {
		tmp = t_4;
	} else if (t <= 6.2e+51) {
		tmp = t_2;
	} else if (t <= 2.3e+81) {
		tmp = t_4;
	} else {
		tmp = t_5;
	}
	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 = (b * c) + (18.0 * (t * t_1))
	t_3 = (b * c) - (j * (27.0 * k))
	t_4 = (k * (j * -27.0)) + (-4.0 * (x * i))
	t_5 = t * ((18.0 * t_1) - (a * 4.0))
	tmp = 0
	if t <= -1.15e+125:
		tmp = t_5
	elif t <= -1.25e+38:
		tmp = t_4
	elif t <= -5e+14:
		tmp = t_2
	elif t <= -4.5e-56:
		tmp = t_4
	elif t <= -7e-136:
		tmp = t_2
	elif t <= -5.8e-177:
		tmp = t_4
	elif t <= 7.8e-302:
		tmp = t_3
	elif t <= 5.5e-223:
		tmp = (b * c) - (4.0 * (x * i))
	elif t <= 9.5e-184:
		tmp = t_3
	elif t <= 5.6e-22:
		tmp = t_4
	elif t <= 6.2e+51:
		tmp = t_2
	elif t <= 2.3e+81:
		tmp = t_4
	else:
		tmp = t_5
	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(Float64(b * c) + Float64(18.0 * Float64(t * t_1)))
	t_3 = Float64(Float64(b * c) - Float64(j * Float64(27.0 * k)))
	t_4 = Float64(Float64(k * Float64(j * -27.0)) + Float64(-4.0 * Float64(x * i)))
	t_5 = Float64(t * Float64(Float64(18.0 * t_1) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -1.15e+125)
		tmp = t_5;
	elseif (t <= -1.25e+38)
		tmp = t_4;
	elseif (t <= -5e+14)
		tmp = t_2;
	elseif (t <= -4.5e-56)
		tmp = t_4;
	elseif (t <= -7e-136)
		tmp = t_2;
	elseif (t <= -5.8e-177)
		tmp = t_4;
	elseif (t <= 7.8e-302)
		tmp = t_3;
	elseif (t <= 5.5e-223)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t <= 9.5e-184)
		tmp = t_3;
	elseif (t <= 5.6e-22)
		tmp = t_4;
	elseif (t <= 6.2e+51)
		tmp = t_2;
	elseif (t <= 2.3e+81)
		tmp = t_4;
	else
		tmp = t_5;
	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 = (b * c) + (18.0 * (t * t_1));
	t_3 = (b * c) - (j * (27.0 * k));
	t_4 = (k * (j * -27.0)) + (-4.0 * (x * i));
	t_5 = t * ((18.0 * t_1) - (a * 4.0));
	tmp = 0.0;
	if (t <= -1.15e+125)
		tmp = t_5;
	elseif (t <= -1.25e+38)
		tmp = t_4;
	elseif (t <= -5e+14)
		tmp = t_2;
	elseif (t <= -4.5e-56)
		tmp = t_4;
	elseif (t <= -7e-136)
		tmp = t_2;
	elseif (t <= -5.8e-177)
		tmp = t_4;
	elseif (t <= 7.8e-302)
		tmp = t_3;
	elseif (t <= 5.5e-223)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t <= 9.5e-184)
		tmp = t_3;
	elseif (t <= 5.6e-22)
		tmp = t_4;
	elseif (t <= 6.2e+51)
		tmp = t_2;
	elseif (t <= 2.3e+81)
		tmp = t_4;
	else
		tmp = t_5;
	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[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t * N[(N[(18.0 * t$95$1), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+125], t$95$5, If[LessEqual[t, -1.25e+38], t$95$4, If[LessEqual[t, -5e+14], t$95$2, If[LessEqual[t, -4.5e-56], t$95$4, If[LessEqual[t, -7e-136], t$95$2, If[LessEqual[t, -5.8e-177], t$95$4, If[LessEqual[t, 7.8e-302], t$95$3, If[LessEqual[t, 5.5e-223], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-184], t$95$3, If[LessEqual[t, 5.6e-22], t$95$4, If[LessEqual[t, 6.2e+51], t$95$2, If[LessEqual[t, 2.3e+81], t$95$4, t$95$5]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.15000000000000006e125 or 2.2999999999999999e81 < t

   1. Initial program 84.4%

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

      1. associate-*l* 84.3%

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

      2. associate--l+ 84.3%

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

      3. distribute-rgt-out-- 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* 89.8%

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

      5. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in t around inf 81.8%

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

   5. Taylor expanded in t around inf 76.1%

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

   if -1.15000000000000006e125 < t < -1.24999999999999992e38 or -5e14 < t < -4.5000000000000001e-56 or -7.00000000000000058e-136 < t < -5.79999999999999994e-177 or 9.4999999999999991e-184 < t < 5.5999999999999999e-22 or 6.20000000000000022e51 < t < 2.2999999999999999e81

   1. Initial program 83.1%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in i around inf 70.9%

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

      1. *-commutative 70.9%

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

   6. Simplified 70.9%

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

   if -1.24999999999999992e38 < t < -5e14 or -4.5000000000000001e-56 < t < -7.00000000000000058e-136 or 5.5999999999999999e-22 < t < 6.20000000000000022e51

   1. Initial program 92.2%

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

      1. associate-*l* 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* 89.5%

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

      5. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in i around 0 84.2%

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

   5. Taylor expanded in j around 0 81.8%

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

   6. Taylor expanded in a around 0 76.4%

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

   if -5.79999999999999994e-177 < t < 7.7999999999999998e-302 or 5.5e-223 < t < 9.4999999999999991e-184

   1. Initial program 91.4%

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

      1. associate-*l* 91.4%

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

      2. associate--l+ 91.4%

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

      3. distribute-rgt-out-- 91.4%

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

      4. associate-*l* 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* 91.4%

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

      2. distribute-rgt-out-- 91.4%

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

      3. cancel-sign-sub-inv 91.4%

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

      4. associate-*l* 88.1%

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

      5. fma-def 88.1%

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

      6. associate-*l* 88.1%

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

   5. Applied egg-rr 88.1%

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

   6. Taylor expanded in b around inf 85.7%

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

   if 7.7999999999999998e-302 < t < 5.5e-223

   1. Initial program 78.7%

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

      1. associate-*l* 78.8%

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

      2. associate--l+ 78.8%

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

      3. distribute-rgt-out-- 78.8%

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

      4. associate-*l* 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 t around 0 92.9%

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

   5. Taylor expanded in j around 0 86.2%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+38}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+14}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-56}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-136}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-177}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-302}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-223}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-184}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-22}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+51}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+81}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 3: 57.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := b \cdot c - j \cdot \left(27 \cdot k\right)\\ t_3 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_4 := b \cdot c + 18 \cdot \left(t \cdot t_1\right)\\ t_5 := t \cdot \left(18 \cdot t_1 - a \cdot 4\right)\\ t_6 := k \cdot \left(j \cdot -27\right)\\ t_7 := t_6 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+125}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{+38}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+16}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-57}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-146}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-170}:\\ \;\;\;\;t_6 + z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-222}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-23}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+48}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+81}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

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 (- (* b c) (* j (* 27.0 k))))
        (t_3 (- (* b c) (* 4.0 (* x i))))
        (t_4 (+ (* b c) (* 18.0 (* t t_1))))
        (t_5 (* t (- (* 18.0 t_1) (* a 4.0))))
        (t_6 (* k (* j -27.0)))
        (t_7 (+ t_6 (* -4.0 (* x i)))))
   (if (<= t -1.15e+125)
     t_5
     (if (<= t -3.7e+38)
       t_7
       (if (<= t -4e+16)
         t_4
         (if (<= t -3.8e-57)
           t_7
           (if (<= t -1.9e-146)
             t_3
             (if (<= t -2.4e-170)
               (+ t_6 (* z (* t (* x (* 18.0 y)))))
               (if (<= t 1.45e-307)
                 t_2
                 (if (<= t 2.25e-222)
                   t_3
                   (if (<= t 2.1e-181)
                     t_2
                     (if (<= t 3.3e-23)
                       t_7
                       (if (<= t 2.8e+48)
                         t_4
                         (if (<= t 2.3e+81) t_7 t_5))))))))))))))

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 = (b * c) - (j * (27.0 * k));
	double t_3 = (b * c) - (4.0 * (x * i));
	double t_4 = (b * c) + (18.0 * (t * t_1));
	double t_5 = t * ((18.0 * t_1) - (a * 4.0));
	double t_6 = k * (j * -27.0);
	double t_7 = t_6 + (-4.0 * (x * i));
	double tmp;
	if (t <= -1.15e+125) {
		tmp = t_5;
	} else if (t <= -3.7e+38) {
		tmp = t_7;
	} else if (t <= -4e+16) {
		tmp = t_4;
	} else if (t <= -3.8e-57) {
		tmp = t_7;
	} else if (t <= -1.9e-146) {
		tmp = t_3;
	} else if (t <= -2.4e-170) {
		tmp = t_6 + (z * (t * (x * (18.0 * y))));
	} else if (t <= 1.45e-307) {
		tmp = t_2;
	} else if (t <= 2.25e-222) {
		tmp = t_3;
	} else if (t <= 2.1e-181) {
		tmp = t_2;
	} else if (t <= 3.3e-23) {
		tmp = t_7;
	} else if (t <= 2.8e+48) {
		tmp = t_4;
	} else if (t <= 2.3e+81) {
		tmp = t_7;
	} else {
		tmp = t_5;
	}
	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) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = (b * c) - (j * (27.0d0 * k))
    t_3 = (b * c) - (4.0d0 * (x * i))
    t_4 = (b * c) + (18.0d0 * (t * t_1))
    t_5 = t * ((18.0d0 * t_1) - (a * 4.0d0))
    t_6 = k * (j * (-27.0d0))
    t_7 = t_6 + ((-4.0d0) * (x * i))
    if (t <= (-1.15d+125)) then
        tmp = t_5
    else if (t <= (-3.7d+38)) then
        tmp = t_7
    else if (t <= (-4d+16)) then
        tmp = t_4
    else if (t <= (-3.8d-57)) then
        tmp = t_7
    else if (t <= (-1.9d-146)) then
        tmp = t_3
    else if (t <= (-2.4d-170)) then
        tmp = t_6 + (z * (t * (x * (18.0d0 * y))))
    else if (t <= 1.45d-307) then
        tmp = t_2
    else if (t <= 2.25d-222) then
        tmp = t_3
    else if (t <= 2.1d-181) then
        tmp = t_2
    else if (t <= 3.3d-23) then
        tmp = t_7
    else if (t <= 2.8d+48) then
        tmp = t_4
    else if (t <= 2.3d+81) then
        tmp = t_7
    else
        tmp = t_5
    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 = (b * c) - (j * (27.0 * k));
	double t_3 = (b * c) - (4.0 * (x * i));
	double t_4 = (b * c) + (18.0 * (t * t_1));
	double t_5 = t * ((18.0 * t_1) - (a * 4.0));
	double t_6 = k * (j * -27.0);
	double t_7 = t_6 + (-4.0 * (x * i));
	double tmp;
	if (t <= -1.15e+125) {
		tmp = t_5;
	} else if (t <= -3.7e+38) {
		tmp = t_7;
	} else if (t <= -4e+16) {
		tmp = t_4;
	} else if (t <= -3.8e-57) {
		tmp = t_7;
	} else if (t <= -1.9e-146) {
		tmp = t_3;
	} else if (t <= -2.4e-170) {
		tmp = t_6 + (z * (t * (x * (18.0 * y))));
	} else if (t <= 1.45e-307) {
		tmp = t_2;
	} else if (t <= 2.25e-222) {
		tmp = t_3;
	} else if (t <= 2.1e-181) {
		tmp = t_2;
	} else if (t <= 3.3e-23) {
		tmp = t_7;
	} else if (t <= 2.8e+48) {
		tmp = t_4;
	} else if (t <= 2.3e+81) {
		tmp = t_7;
	} else {
		tmp = t_5;
	}
	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 = (b * c) - (j * (27.0 * k))
	t_3 = (b * c) - (4.0 * (x * i))
	t_4 = (b * c) + (18.0 * (t * t_1))
	t_5 = t * ((18.0 * t_1) - (a * 4.0))
	t_6 = k * (j * -27.0)
	t_7 = t_6 + (-4.0 * (x * i))
	tmp = 0
	if t <= -1.15e+125:
		tmp = t_5
	elif t <= -3.7e+38:
		tmp = t_7
	elif t <= -4e+16:
		tmp = t_4
	elif t <= -3.8e-57:
		tmp = t_7
	elif t <= -1.9e-146:
		tmp = t_3
	elif t <= -2.4e-170:
		tmp = t_6 + (z * (t * (x * (18.0 * y))))
	elif t <= 1.45e-307:
		tmp = t_2
	elif t <= 2.25e-222:
		tmp = t_3
	elif t <= 2.1e-181:
		tmp = t_2
	elif t <= 3.3e-23:
		tmp = t_7
	elif t <= 2.8e+48:
		tmp = t_4
	elif t <= 2.3e+81:
		tmp = t_7
	else:
		tmp = t_5
	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(Float64(b * c) - Float64(j * Float64(27.0 * k)))
	t_3 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	t_4 = Float64(Float64(b * c) + Float64(18.0 * Float64(t * t_1)))
	t_5 = Float64(t * Float64(Float64(18.0 * t_1) - Float64(a * 4.0)))
	t_6 = Float64(k * Float64(j * -27.0))
	t_7 = Float64(t_6 + Float64(-4.0 * Float64(x * i)))
	tmp = 0.0
	if (t <= -1.15e+125)
		tmp = t_5;
	elseif (t <= -3.7e+38)
		tmp = t_7;
	elseif (t <= -4e+16)
		tmp = t_4;
	elseif (t <= -3.8e-57)
		tmp = t_7;
	elseif (t <= -1.9e-146)
		tmp = t_3;
	elseif (t <= -2.4e-170)
		tmp = Float64(t_6 + Float64(z * Float64(t * Float64(x * Float64(18.0 * y)))));
	elseif (t <= 1.45e-307)
		tmp = t_2;
	elseif (t <= 2.25e-222)
		tmp = t_3;
	elseif (t <= 2.1e-181)
		tmp = t_2;
	elseif (t <= 3.3e-23)
		tmp = t_7;
	elseif (t <= 2.8e+48)
		tmp = t_4;
	elseif (t <= 2.3e+81)
		tmp = t_7;
	else
		tmp = t_5;
	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 = (b * c) - (j * (27.0 * k));
	t_3 = (b * c) - (4.0 * (x * i));
	t_4 = (b * c) + (18.0 * (t * t_1));
	t_5 = t * ((18.0 * t_1) - (a * 4.0));
	t_6 = k * (j * -27.0);
	t_7 = t_6 + (-4.0 * (x * i));
	tmp = 0.0;
	if (t <= -1.15e+125)
		tmp = t_5;
	elseif (t <= -3.7e+38)
		tmp = t_7;
	elseif (t <= -4e+16)
		tmp = t_4;
	elseif (t <= -3.8e-57)
		tmp = t_7;
	elseif (t <= -1.9e-146)
		tmp = t_3;
	elseif (t <= -2.4e-170)
		tmp = t_6 + (z * (t * (x * (18.0 * y))));
	elseif (t <= 1.45e-307)
		tmp = t_2;
	elseif (t <= 2.25e-222)
		tmp = t_3;
	elseif (t <= 2.1e-181)
		tmp = t_2;
	elseif (t <= 3.3e-23)
		tmp = t_7;
	elseif (t <= 2.8e+48)
		tmp = t_4;
	elseif (t <= 2.3e+81)
		tmp = t_7;
	else
		tmp = t_5;
	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[(N[(b * c), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t * N[(N[(18.0 * t$95$1), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$6 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+125], t$95$5, If[LessEqual[t, -3.7e+38], t$95$7, If[LessEqual[t, -4e+16], t$95$4, If[LessEqual[t, -3.8e-57], t$95$7, If[LessEqual[t, -1.9e-146], t$95$3, If[LessEqual[t, -2.4e-170], N[(t$95$6 + N[(z * N[(t * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e-307], t$95$2, If[LessEqual[t, 2.25e-222], t$95$3, If[LessEqual[t, 2.1e-181], t$95$2, If[LessEqual[t, 3.3e-23], t$95$7, If[LessEqual[t, 2.8e+48], t$95$4, If[LessEqual[t, 2.3e+81], t$95$7, t$95$5]]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.15000000000000006e125 or 2.2999999999999999e81 < t

   1. Initial program 84.4%

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

      1. associate-*l* 84.3%

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

      2. associate--l+ 84.3%

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

      3. distribute-rgt-out-- 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* 89.8%

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

      5. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in t around inf 81.8%

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

   5. Taylor expanded in t around inf 76.1%

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

   if -1.15000000000000006e125 < t < -3.7000000000000001e38 or -4e16 < t < -3.7999999999999997e-57 or 2.10000000000000003e-181 < t < 3.30000000000000021e-23 or 2.80000000000000012e48 < t < 2.2999999999999999e81

   1. Initial program 84.3%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in i around inf 73.3%

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

      1. *-commutative 73.3%

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

   6. Simplified 73.3%

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

   if -3.7000000000000001e38 < t < -4e16 or 3.30000000000000021e-23 < t < 2.80000000000000012e48

   1. Initial program 80.9%

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

      1. associate-*l* 80.9%

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

      2. associate--l+ 80.9%

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

      3. distribute-rgt-out-- 80.9%

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

      4. associate-*l* 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 80.5%

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

   5. Taylor expanded in j around 0 87.5%

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

   6. Taylor expanded in a around 0 87.5%

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

   if -3.7999999999999997e-57 < t < -1.89999999999999997e-146 or 1.45e-307 < t < 2.25000000000000007e-222

   1. Initial program 91.9%

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

      1. associate-*l* 91.9%

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

      2. associate--l+ 91.9%

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

      3. distribute-rgt-out-- 91.9%

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

      4. associate-*l* 89.3%

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

      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 81.8%

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

   5. Taylor expanded in j around 0 74.0%

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

   if -1.89999999999999997e-146 < t < -2.4e-170

   1. Initial program 73.0%

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

   3. Simplified 31.4%

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

      1. fma-udef 31.4%

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

   5. Applied egg-rr 31.4%

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

   6. Taylor expanded in z around inf 26.5%

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

      1. *-commutative 26.5%

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

      2. *-commutative 26.5%

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

      3. associate-*r* 26.5%

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

      4. associate-*r* 26.5%

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

      5. associate-*r* 26.5%

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

      6. *-commutative 26.5%

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

      7. *-commutative 26.5%

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

      8. associate-*r* 54.0%

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

      9. associate-*r* 81.6%

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

      10. *-commutative 81.6%

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

   8. Simplified 81.6%

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

   9. Taylor expanded in x around 0 81.6%

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

       1. *-commutative 81.6%

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

       2. associate-*r* 81.6%

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

       3. *-commutative 81.6%

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

       4. associate-*r* 81.6%

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

       5. *-commutative 81.6%

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

       6. associate-*l* 81.3%

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

       7. associate-*r* 81.3%

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

       8. *-commutative 81.3%

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

   11. Simplified 81.3%

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

   if -2.4e-170 < t < 1.45e-307 or 2.25000000000000007e-222 < t < 2.10000000000000003e-181

   1. Initial program 89.7%

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

      1. associate-*l* 89.7%

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

      2. associate--l+ 89.7%

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

      3. distribute-rgt-out-- 89.7%

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

      4. associate-*l* 86.8%

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

      5. associate-*l* 86.8%

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

   3. Simplified 86.8%

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

      1. associate-*r* 89.7%

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

      2. distribute-rgt-out-- 89.7%

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

      3. cancel-sign-sub-inv 89.7%

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

      4. associate-*l* 86.8%

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

      5. fma-def 86.8%

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

      6. associate-*l* 86.8%

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

   5. Applied egg-rr 86.8%

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

   6. Taylor expanded in b around inf 82.1%

      \[\leadsto \color{blue}{b \cdot c} - j \cdot \left(27 \cdot k\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{+38}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+16}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-57}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-146}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-170}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-307}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-222}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-181}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-23}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+48}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+81}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 4: 52.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ t_3 := t_2 + t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \cdot c \leq -5.5 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -1.25 \cdot 10^{+25}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot c \leq -7.4 \cdot 10^{-179}:\\ \;\;\;\;t_2 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 9.6 \cdot 10^{-57} \lor \neg \left(b \cdot c \leq 2.7 \cdot 10^{+36}\right) \land b \cdot c \leq 5.8 \cdot 10^{+156}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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) (* 4.0 (* x i))))
        (t_2 (* k (* j -27.0)))
        (t_3 (+ t_2 (* t (* a -4.0)))))
   (if (<= (* b c) -5.5e+133)
     t_1
     (if (<= (* b c) -1.25e+25)
       t_3
       (if (<= (* b c) -7.4e-179)
         (+ t_2 (* -4.0 (* x i)))
         (if (or (<= (* b c) 9.6e-57)
                 (and (not (<= (* b c) 2.7e+36)) (<= (* b c) 5.8e+156)))
           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) - (4.0 * (x * i));
	double t_2 = k * (j * -27.0);
	double t_3 = t_2 + (t * (a * -4.0));
	double tmp;
	if ((b * c) <= -5.5e+133) {
		tmp = t_1;
	} else if ((b * c) <= -1.25e+25) {
		tmp = t_3;
	} else if ((b * c) <= -7.4e-179) {
		tmp = t_2 + (-4.0 * (x * i));
	} else if (((b * c) <= 9.6e-57) || (!((b * c) <= 2.7e+36) && ((b * c) <= 5.8e+156))) {
		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) :: tmp
    t_1 = (b * c) - (4.0d0 * (x * i))
    t_2 = k * (j * (-27.0d0))
    t_3 = t_2 + (t * (a * (-4.0d0)))
    if ((b * c) <= (-5.5d+133)) then
        tmp = t_1
    else if ((b * c) <= (-1.25d+25)) then
        tmp = t_3
    else if ((b * c) <= (-7.4d-179)) then
        tmp = t_2 + ((-4.0d0) * (x * i))
    else if (((b * c) <= 9.6d-57) .or. (.not. ((b * c) <= 2.7d+36)) .and. ((b * c) <= 5.8d+156)) 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) - (4.0 * (x * i));
	double t_2 = k * (j * -27.0);
	double t_3 = t_2 + (t * (a * -4.0));
	double tmp;
	if ((b * c) <= -5.5e+133) {
		tmp = t_1;
	} else if ((b * c) <= -1.25e+25) {
		tmp = t_3;
	} else if ((b * c) <= -7.4e-179) {
		tmp = t_2 + (-4.0 * (x * i));
	} else if (((b * c) <= 9.6e-57) || (!((b * c) <= 2.7e+36) && ((b * c) <= 5.8e+156))) {
		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) - (4.0 * (x * i))
	t_2 = k * (j * -27.0)
	t_3 = t_2 + (t * (a * -4.0))
	tmp = 0
	if (b * c) <= -5.5e+133:
		tmp = t_1
	elif (b * c) <= -1.25e+25:
		tmp = t_3
	elif (b * c) <= -7.4e-179:
		tmp = t_2 + (-4.0 * (x * i))
	elif ((b * c) <= 9.6e-57) or (not ((b * c) <= 2.7e+36) and ((b * c) <= 5.8e+156)):
		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(4.0 * Float64(x * i)))
	t_2 = Float64(k * Float64(j * -27.0))
	t_3 = Float64(t_2 + Float64(t * Float64(a * -4.0)))
	tmp = 0.0
	if (Float64(b * c) <= -5.5e+133)
		tmp = t_1;
	elseif (Float64(b * c) <= -1.25e+25)
		tmp = t_3;
	elseif (Float64(b * c) <= -7.4e-179)
		tmp = Float64(t_2 + Float64(-4.0 * Float64(x * i)));
	elseif ((Float64(b * c) <= 9.6e-57) || (!(Float64(b * c) <= 2.7e+36) && (Float64(b * c) <= 5.8e+156)))
		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) - (4.0 * (x * i));
	t_2 = k * (j * -27.0);
	t_3 = t_2 + (t * (a * -4.0));
	tmp = 0.0;
	if ((b * c) <= -5.5e+133)
		tmp = t_1;
	elseif ((b * c) <= -1.25e+25)
		tmp = t_3;
	elseif ((b * c) <= -7.4e-179)
		tmp = t_2 + (-4.0 * (x * i));
	elseif (((b * c) <= 9.6e-57) || (~(((b * c) <= 2.7e+36)) && ((b * c) <= 5.8e+156)))
		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[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5.5e+133], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1.25e+25], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], -7.4e-179], N[(t$95$2 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(b * c), $MachinePrecision], 9.6e-57], And[N[Not[LessEqual[N[(b * c), $MachinePrecision], 2.7e+36]], $MachinePrecision], LessEqual[N[(b * c), $MachinePrecision], 5.8e+156]]], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -5.5e133 or 9.60000000000000025e-57 < (*.f64 b c) < 2.7000000000000001e36 or 5.80000000000000021e156 < (*.f64 b c)

   1. Initial program 82.3%

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

      1. associate-*l* 82.3%

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

      2. associate--l+ 82.3%

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

      3. distribute-rgt-out-- 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* 84.5%

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

      5. associate-*l* 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in t around 0 74.8%

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

   5. Taylor expanded in j around 0 72.3%

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

   if -5.5e133 < (*.f64 b c) < -1.25000000000000006e25 or -7.39999999999999981e-179 < (*.f64 b c) < 9.60000000000000025e-57 or 2.7000000000000001e36 < (*.f64 b c) < 5.80000000000000021e156

   1. Initial program 90.4%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in a around inf 60.8%

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

      1. *-commutative 60.8%

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

      2. *-commutative 60.8%

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

      3. associate-*r* 60.8%

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

      4. *-commutative 60.8%

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

   6. Simplified 60.8%

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

   if -1.25000000000000006e25 < (*.f64 b c) < -7.39999999999999981e-179

   1. Initial program 76.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in i around inf 64.7%

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

      1. *-commutative 64.7%

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

   6. Simplified 64.7%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.5 \cdot 10^{+133}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1.25 \cdot 10^{+25}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -7.4 \cdot 10^{-179}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 9.6 \cdot 10^{-57} \lor \neg \left(b \cdot c \leq 2.7 \cdot 10^{+36}\right) \land b \cdot c \leq 5.8 \cdot 10^{+156}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 5: 88.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;t \leq -4 \cdot 10^{-156} \lor \neg \left(t \leq 5.4 \cdot 10^{-170}\right):\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \end{array} \end{array} \]

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 (* 27.0 k))))
   (if (or (<= t -4e-156) (not (<= t 5.4e-170)))
     (-
      (+
       (* t (- (* (* x 18.0) (* y z)) (* a 4.0)))
       (- (* b c) (* x (* 4.0 i))))
      t_1)
     (- (- (+ (* b c) (* -4.0 (* t a))) (* 4.0 (* 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 * (27.0 * k);
	double tmp;
	if ((t <= -4e-156) || !(t <= 5.4e-170)) {
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + ((b * c) - (x * (4.0 * i)))) - t_1;
	} else {
		tmp = (((b * c) + (-4.0 * (t * a))) - (4.0 * (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 * (27.0d0 * k)
    if ((t <= (-4d-156)) .or. (.not. (t <= 5.4d-170))) then
        tmp = ((t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0))) + ((b * c) - (x * (4.0d0 * i)))) - t_1
    else
        tmp = (((b * c) + ((-4.0d0) * (t * a))) - (4.0d0 * (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 * (27.0 * k);
	double tmp;
	if ((t <= -4e-156) || !(t <= 5.4e-170)) {
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + ((b * c) - (x * (4.0 * i)))) - t_1;
	} else {
		tmp = (((b * c) + (-4.0 * (t * a))) - (4.0 * (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 * (27.0 * k)
	tmp = 0
	if (t <= -4e-156) or not (t <= 5.4e-170):
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + ((b * c) - (x * (4.0 * i)))) - t_1
	else:
		tmp = (((b * c) + (-4.0 * (t * a))) - (4.0 * (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(27.0 * k))
	tmp = 0.0
	if ((t <= -4e-156) || !(t <= 5.4e-170))
		tmp = Float64(Float64(Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0))) + Float64(Float64(b * c) - Float64(x * Float64(4.0 * i)))) - t_1);
	else
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(4.0 * 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 * (27.0 * k);
	tmp = 0.0;
	if ((t <= -4e-156) || ~((t <= 5.4e-170)))
		tmp = ((t * (((x * 18.0) * (y * z)) - (a * 4.0))) + ((b * c) - (x * (4.0 * i)))) - t_1;
	else
		tmp = (((b * c) + (-4.0 * (t * a))) - (4.0 * (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[(27.0 * k), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -4e-156], N[Not[LessEqual[t, 5.4e-170]], $MachinePrecision]], N[(N[(N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.00000000000000016e-156 or 5.3999999999999997e-170 < t

   1. Initial program 86.4%

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

      1. associate-*l* 86.4%

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

      2. associate--l+ 86.4%

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

      3. distribute-rgt-out-- 88.4%

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

      4. associate-*l* 90.4%

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

      5. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

   if -4.00000000000000016e-156 < t < 5.3999999999999997e-170

   1. Initial program 83.5%

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

      1. 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* 78.2%

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

      5. associate-*l* 78.2%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in y around 0 94.7%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-156} \lor \neg \left(t \leq 5.4 \cdot 10^{-170}\right):\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + \left(b \cdot c - x \cdot \left(4 \cdot i\right)\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\\ \end{array} \]

Alternative 6: 58.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := b \cdot c - j \cdot \left(27 \cdot k\right)\\ t_2 := k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ t_3 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+125}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-223}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

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) (* j (* 27.0 k))))
        (t_2 (+ (* k (* j -27.0)) (* -4.0 (* x i))))
        (t_3 (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))))
   (if (<= t -1.15e+125)
     t_3
     (if (<= t -2.6e-47)
       t_2
       (if (<= t 3.4e-307)
         t_1
         (if (<= t 3.1e-223)
           (- (* b c) (* 4.0 (* x i)))
           (if (<= t 5.6e-183) t_1 (if (<= t 7e-14) 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) - (j * (27.0 * k));
	double t_2 = (k * (j * -27.0)) + (-4.0 * (x * i));
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.15e+125) {
		tmp = t_3;
	} else if (t <= -2.6e-47) {
		tmp = t_2;
	} else if (t <= 3.4e-307) {
		tmp = t_1;
	} else if (t <= 3.1e-223) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 5.6e-183) {
		tmp = t_1;
	} else if (t <= 7e-14) {
		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) :: tmp
    t_1 = (b * c) - (j * (27.0d0 * k))
    t_2 = (k * (j * (-27.0d0))) + ((-4.0d0) * (x * i))
    t_3 = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    if (t <= (-1.15d+125)) then
        tmp = t_3
    else if (t <= (-2.6d-47)) then
        tmp = t_2
    else if (t <= 3.4d-307) then
        tmp = t_1
    else if (t <= 3.1d-223) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (t <= 5.6d-183) then
        tmp = t_1
    else if (t <= 7d-14) 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) - (j * (27.0 * k));
	double t_2 = (k * (j * -27.0)) + (-4.0 * (x * i));
	double t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.15e+125) {
		tmp = t_3;
	} else if (t <= -2.6e-47) {
		tmp = t_2;
	} else if (t <= 3.4e-307) {
		tmp = t_1;
	} else if (t <= 3.1e-223) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (t <= 5.6e-183) {
		tmp = t_1;
	} else if (t <= 7e-14) {
		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) - (j * (27.0 * k))
	t_2 = (k * (j * -27.0)) + (-4.0 * (x * i))
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	tmp = 0
	if t <= -1.15e+125:
		tmp = t_3
	elif t <= -2.6e-47:
		tmp = t_2
	elif t <= 3.4e-307:
		tmp = t_1
	elif t <= 3.1e-223:
		tmp = (b * c) - (4.0 * (x * i))
	elif t <= 5.6e-183:
		tmp = t_1
	elif t <= 7e-14:
		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(j * Float64(27.0 * k)))
	t_2 = Float64(Float64(k * Float64(j * -27.0)) + Float64(-4.0 * Float64(x * i)))
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -1.15e+125)
		tmp = t_3;
	elseif (t <= -2.6e-47)
		tmp = t_2;
	elseif (t <= 3.4e-307)
		tmp = t_1;
	elseif (t <= 3.1e-223)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (t <= 5.6e-183)
		tmp = t_1;
	elseif (t <= 7e-14)
		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) - (j * (27.0 * k));
	t_2 = (k * (j * -27.0)) + (-4.0 * (x * i));
	t_3 = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -1.15e+125)
		tmp = t_3;
	elseif (t <= -2.6e-47)
		tmp = t_2;
	elseif (t <= 3.4e-307)
		tmp = t_1;
	elseif (t <= 3.1e-223)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (t <= 5.6e-183)
		tmp = t_1;
	elseif (t <= 7e-14)
		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[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+125], t$95$3, If[LessEqual[t, -2.6e-47], t$95$2, If[LessEqual[t, 3.4e-307], t$95$1, If[LessEqual[t, 3.1e-223], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e-183], t$95$1, If[LessEqual[t, 7e-14], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.15000000000000006e125 or 7.0000000000000005e-14 < t

   1. Initial program 85.4%

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

      1. associate-*l* 85.4%

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

      2. associate--l+ 85.4%

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

      3. distribute-rgt-out-- 89.3%

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

      4. associate-*l* 91.0%

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

      5. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in t around inf 79.2%

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

   5. Taylor expanded in t around inf 72.2%

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

   if -1.15000000000000006e125 < t < -2.6e-47 or 5.5999999999999997e-183 < t < 7.0000000000000005e-14

   1. Initial program 81.9%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in i around inf 67.2%

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

      1. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   if -2.6e-47 < t < 3.39999999999999989e-307 or 3.10000000000000018e-223 < t < 5.5999999999999997e-183

   1. Initial program 91.6%

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

      1. associate-*l* 91.6%

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

      2. associate--l+ 91.6%

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

      3. distribute-rgt-out-- 91.6%

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

      4. associate-*l* 84.4%

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

      5. associate-*l* 84.4%

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

   3. Simplified 84.4%

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

      1. associate-*r* 91.6%

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

      2. distribute-rgt-out-- 91.6%

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

      3. cancel-sign-sub-inv 91.6%

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

      4. associate-*l* 92.6%

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

      5. fma-def 92.6%

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

      6. associate-*l* 92.7%

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

   5. Applied egg-rr 92.7%

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

   6. Taylor expanded in b around inf 68.5%

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

   if 3.39999999999999989e-307 < t < 3.10000000000000018e-223

   1. Initial program 78.7%

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

      1. associate-*l* 78.8%

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

      2. associate--l+ 78.8%

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

      3. distribute-rgt-out-- 78.8%

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

      4. associate-*l* 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 t around 0 92.9%

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

   5. Taylor expanded in j around 0 86.2%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-47}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-307}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-223}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-183}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-14}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 7: 81.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;x \leq -1.66 \cdot 10^{+158} \lor \neg \left(x \leq 1.1 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \end{array} \end{array} \]

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 (* 27.0 k))))
   (if (or (<= x -1.66e+158) (not (<= x 1.1e+43)))
     (- (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))) t_1)
     (- (- (+ (* b c) (* -4.0 (* t a))) (* 4.0 (* 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 * (27.0 * k);
	double tmp;
	if ((x <= -1.66e+158) || !(x <= 1.1e+43)) {
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_1;
	} else {
		tmp = (((b * c) + (-4.0 * (t * a))) - (4.0 * (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 * (27.0d0 * k)
    if ((x <= (-1.66d+158)) .or. (.not. (x <= 1.1d+43))) then
        tmp = (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))) - t_1
    else
        tmp = (((b * c) + ((-4.0d0) * (t * a))) - (4.0d0 * (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 * (27.0 * k);
	double tmp;
	if ((x <= -1.66e+158) || !(x <= 1.1e+43)) {
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_1;
	} else {
		tmp = (((b * c) + (-4.0 * (t * a))) - (4.0 * (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 * (27.0 * k)
	tmp = 0
	if (x <= -1.66e+158) or not (x <= 1.1e+43):
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_1
	else:
		tmp = (((b * c) + (-4.0 * (t * a))) - (4.0 * (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(27.0 * k))
	tmp = 0.0
	if ((x <= -1.66e+158) || !(x <= 1.1e+43))
		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(-4.0 * Float64(t * a))) - Float64(4.0 * 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 * (27.0 * k);
	tmp = 0.0;
	if ((x <= -1.66e+158) || ~((x <= 1.1e+43)))
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - t_1;
	else
		tmp = (((b * c) + (-4.0 * (t * a))) - (4.0 * (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[(27.0 * k), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -1.66e+158], N[Not[LessEqual[x, 1.1e+43]], $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[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.66000000000000011e158 or 1.1e43 < x

   1. Initial program 74.6%

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

      1. associate-*l* 74.6%

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

      2. associate--l+ 74.6%

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

      3. distribute-rgt-out-- 76.9%

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

      4. associate-*l* 83.3%

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

      5. associate-*l* 83.3%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in x around inf 88.0%

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

   if -1.66000000000000011e158 < x < 1.1e43

   1. Initial program 91.7%

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

      1. associate-*l* 91.7%

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

      2. associate--l+ 91.7%

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

      3. distribute-rgt-out-- 92.9%

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

      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 y around 0 90.5%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.66 \cdot 10^{+158} \lor \neg \left(x \leq 1.1 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 4 \cdot \left(x \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\\ \end{array} \]

Alternative 8: 76.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+60} \lor \neg \left(x \leq 3.5 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

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 -7.5e+60) (not (<= x 3.5e+42)))
   (- (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))) (* j (* 27.0 k)))
   (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))))

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 <= -7.5e+60) || !(x <= 3.5e+42)) {
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - (j * (27.0 * k));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	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 <= (-7.5d+60)) .or. (.not. (x <= 3.5d+42))) then
        tmp = (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))) - (j * (27.0d0 * k))
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    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 <= -7.5e+60) || !(x <= 3.5e+42)) {
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - (j * (27.0 * k));
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -7.5e+60) or not (x <= 3.5e+42):
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - (j * (27.0 * k))
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	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 <= -7.5e+60) || !(x <= 3.5e+42))
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))) - Float64(j * Float64(27.0 * k)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	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 <= -7.5e+60) || ~((x <= 3.5e+42)))
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - (j * (27.0 * k));
	else
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	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, -7.5e+60], N[Not[LessEqual[x, 3.5e+42]], $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[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5e60 or 3.50000000000000023e42 < x

   1. Initial program 73.8%

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

      1. associate-*l* 73.8%

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

      2. associate--l+ 73.9%

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

      3. distribute-rgt-out-- 76.5%

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

      4. associate-*l* 85.8%

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

      5. associate-*l* 85.8%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in x around inf 83.7%

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

   if -7.5e60 < x < 3.50000000000000023e42

   1. Initial program 95.1%

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

   2. Taylor expanded in x around 0 87.1%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+60} \lor \neg \left(x \leq 3.5 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 9: 75.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+125} \lor \neg \left(t \leq 9 \cdot 10^{-19}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\\ \end{array} \end{array} \]

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 -1.32e+125) (not (<= t 9e-19)))
   (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))
   (- (- (* b c) (* 4.0 (* x i))) (* j (* 27.0 k)))))

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 <= -1.32e+125) || !(t <= 9e-19)) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (27.0 * k));
	}
	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 <= (-1.32d+125)) .or. (.not. (t <= 9d-19))) then
        tmp = (b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - (j * (27.0d0 * k))
    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 <= -1.32e+125) || !(t <= 9e-19)) {
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (27.0 * k));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.32e+125) or not (t <= 9e-19):
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (27.0 * k))
	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 <= -1.32e+125) || !(t <= 9e-19))
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(j * Float64(27.0 * k)));
	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 <= -1.32e+125) || ~((t <= 9e-19)))
		tmp = (b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)));
	else
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (27.0 * k));
	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, -1.32e+125], N[Not[LessEqual[t, 9e-19]], $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[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.32000000000000006e125 or 9.00000000000000026e-19 < t

   1. Initial program 85.4%

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

      1. associate-*l* 85.4%

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

      2. associate--l+ 85.4%

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

      3. distribute-rgt-out-- 89.3%

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

      4. associate-*l* 91.0%

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

      5. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in i around 0 90.7%

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

   5. Taylor expanded in j around 0 84.8%

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

   if -1.32000000000000006e125 < t < 9.00000000000000026e-19

   1. Initial program 85.9%

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

      1. associate-*l* 85.9%

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

      2. associate--l+ 85.9%

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

      3. distribute-rgt-out-- 86.0%

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

      4. associate-*l* 85.3%

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

      5. associate-*l* 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in t around 0 80.1%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+125} \lor \neg \left(t \leq 9 \cdot 10^{-19}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\\ \end{array} \]

Alternative 10: 64.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+140}:\\ \;\;\;\;z \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot t\right)\right) + t_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+43}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+238}:\\ \;\;\;\;t_1 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* k (* j -27.0))))
   (if (<= x -2.7e+140)
     (+ (* z (* (* x 18.0) (* y t))) t_1)
     (if (<= x 1.6e+43)
       (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))
       (if (<= x 3.2e+238)
         (+ t_1 (* -4.0 (* x i)))
         (+ (* b c) (* 18.0 (* t (* x (* y 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 t_1 = k * (j * -27.0);
	double tmp;
	if (x <= -2.7e+140) {
		tmp = (z * ((x * 18.0) * (y * t))) + t_1;
	} else if (x <= 1.6e+43) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if (x <= 3.2e+238) {
		tmp = t_1 + (-4.0 * (x * i));
	} else {
		tmp = (b * c) + (18.0 * (t * (x * (y * 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) :: t_1
    real(8) :: tmp
    t_1 = k * (j * (-27.0d0))
    if (x <= (-2.7d+140)) then
        tmp = (z * ((x * 18.0d0) * (y * t))) + t_1
    else if (x <= 1.6d+43) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    else if (x <= 3.2d+238) then
        tmp = t_1 + ((-4.0d0) * (x * i))
    else
        tmp = (b * c) + (18.0d0 * (t * (x * (y * 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 t_1 = k * (j * -27.0);
	double tmp;
	if (x <= -2.7e+140) {
		tmp = (z * ((x * 18.0) * (y * t))) + t_1;
	} else if (x <= 1.6e+43) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if (x <= 3.2e+238) {
		tmp = t_1 + (-4.0 * (x * i));
	} else {
		tmp = (b * c) + (18.0 * (t * (x * (y * z))));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = k * (j * -27.0)
	tmp = 0
	if x <= -2.7e+140:
		tmp = (z * ((x * 18.0) * (y * t))) + t_1
	elif x <= 1.6e+43:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	elif x <= 3.2e+238:
		tmp = t_1 + (-4.0 * (x * i))
	else:
		tmp = (b * c) + (18.0 * (t * (x * (y * z))))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * -27.0))
	tmp = 0.0
	if (x <= -2.7e+140)
		tmp = Float64(Float64(z * Float64(Float64(x * 18.0) * Float64(y * t))) + t_1);
	elseif (x <= 1.6e+43)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	elseif (x <= 3.2e+238)
		tmp = Float64(t_1 + Float64(-4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(b * c) + Float64(18.0 * Float64(t * Float64(x * Float64(y * 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)
	t_1 = k * (j * -27.0);
	tmp = 0.0;
	if (x <= -2.7e+140)
		tmp = (z * ((x * 18.0) * (y * t))) + t_1;
	elseif (x <= 1.6e+43)
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	elseif (x <= 3.2e+238)
		tmp = t_1 + (-4.0 * (x * i));
	else
		tmp = (b * c) + (18.0 * (t * (x * (y * 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_] := Block[{t$95$1 = N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e+140], N[(N[(z * N[(N[(x * 18.0), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 1.6e+43], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+238], N[(t$95$1 + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.70000000000000018e140

   1. Initial program 75.6%

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

   3. Simplified 81.0%

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

      1. fma-udef 81.0%

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

   5. Applied egg-rr 81.0%

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

   6. Taylor expanded in z around inf 60.8%

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

      1. *-commutative 60.8%

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

      2. *-commutative 60.8%

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

      3. associate-*r* 60.8%

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

      4. associate-*r* 60.8%

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

      5. associate-*r* 60.9%

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

      6. *-commutative 60.9%

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

      7. *-commutative 60.9%

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

      8. associate-*r* 60.9%

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

      9. associate-*r* 63.3%

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

      10. *-commutative 63.3%

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

   8. Simplified 63.3%

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

   if -2.70000000000000018e140 < x < 1.60000000000000007e43

   1. Initial program 92.2%

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

   2. Taylor expanded in x around 0 83.3%

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

   if 1.60000000000000007e43 < x < 3.19999999999999981e238

   1. Initial program 76.1%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in i around inf 63.3%

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

      1. *-commutative 63.3%

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

   6. Simplified 63.3%

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

   if 3.19999999999999981e238 < x

   1. Initial program 68.4%

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

      1. associate-*l* 68.4%

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

      2. associate--l+ 68.4%

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

      3. distribute-rgt-out-- 73.7%

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

      4. associate-*l* 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 74.1%

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

   5. Taylor expanded in j around 0 73.9%

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

   6. Taylor expanded in a around 0 68.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+140}:\\ \;\;\;\;z \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot t\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+43}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+238}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 11: 53.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -49 \lor \neg \left(b \cdot c \leq 1.7 \cdot 10^{-63}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

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) -49.0) (not (<= (* b c) 1.7e-63)))
   (- (* b c) (* 4.0 (* x i)))
   (+ (* k (* j -27.0)) (* -4.0 (* x i)))))

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) <= -49.0) || !((b * c) <= 1.7e-63)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (k * (j * -27.0)) + (-4.0 * (x * i));
	}
	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) <= (-49.0d0)) .or. (.not. ((b * c) <= 1.7d-63))) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = (k * (j * (-27.0d0))) + ((-4.0d0) * (x * i))
    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) <= -49.0) || !((b * c) <= 1.7e-63)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (k * (j * -27.0)) + (-4.0 * (x * i));
	}
	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) <= -49.0) or not ((b * c) <= 1.7e-63):
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = (k * (j * -27.0)) + (-4.0 * (x * i))
	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) <= -49.0) || !(Float64(b * c) <= 1.7e-63))
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(k * Float64(j * -27.0)) + Float64(-4.0 * Float64(x * i)));
	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) <= -49.0) || ~(((b * c) <= 1.7e-63)))
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = (k * (j * -27.0)) + (-4.0 * (x * i));
	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], -49.0], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.7e-63]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -49 or 1.69999999999999999e-63 < (*.f64 b c)

   1. Initial program 87.0%

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

      1. associate-*l* 87.0%

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

      2. associate--l+ 87.0%

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

      3. distribute-rgt-out-- 89.2%

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

      4. associate-*l* 87.8%

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

      5. associate-*l* 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in t around 0 66.6%

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

   5. Taylor expanded in j around 0 59.5%

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

   if -49 < (*.f64 b c) < 1.69999999999999999e-63

   1. Initial program 84.2%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in i around inf 56.8%

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

      1. *-commutative 56.8%

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

   6. Simplified 56.8%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -49 \lor \neg \left(b \cdot c \leq 1.7 \cdot 10^{-63}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + -4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 12: 70.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+97}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+96}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \end{array} \]

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 (<= t -1.6e+97)
   (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))
   (if (<= t 3.4e+96)
     (- (- (* b c) (* 4.0 (* x i))) (* j (* 27.0 k)))
     (* t (- (* 18.0 (* x (* y z))) (* a 4.0))))))

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 tmp;
	if (t <= -1.6e+97) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if (t <= 3.4e+96) {
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (27.0 * k));
	} else {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	}
	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 <= (-1.6d+97)) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    else if (t <= 3.4d+96) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - (j * (27.0d0 * k))
    else
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    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 <= -1.6e+97) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if (t <= 3.4e+96) {
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (27.0 * k));
	} else {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if t <= -1.6e+97:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	elif t <= 3.4e+96:
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (27.0 * k))
	else:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	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 <= -1.6e+97)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	elseif (t <= 3.4e+96)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(j * Float64(27.0 * k)));
	else
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	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)
	tmp = 0.0;
	if (t <= -1.6e+97)
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	elseif (t <= 3.4e+96)
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (27.0 * k));
	else
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	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_] := If[LessEqual[t, -1.6e+97], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+96], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.60000000000000008e97

   1. Initial program 89.8%

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

   2. Taylor expanded in x around 0 80.0%

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

   if -1.60000000000000008e97 < t < 3.4000000000000001e96

   1. Initial program 86.4%

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

      1. associate-*l* 86.4%

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

      2. associate--l+ 86.4%

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

      3. distribute-rgt-out-- 86.4%

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

      4. associate-*l* 86.3%

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

      5. associate-*l* 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in t around 0 78.6%

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

   if 3.4000000000000001e96 < t

   1. Initial program 78.1%

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

      1. 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-- 85.4%

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

      4. associate-*l* 85.3%

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

      5. associate-*l* 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in t around inf 86.5%

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

   5. Taylor expanded in t around inf 83.7%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+97}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+96}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - j \cdot \left(27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 13: 52.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+68} \lor \neg \left(x \leq 1.3 \cdot 10^{-40}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -9e+68) (not (<= x 1.3e-40)))
   (- (* b c) (* 4.0 (* x i)))
   (+ (* b c) (* k (* j -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 tmp;
	if ((x <= -9e+68) || !(x <= 1.3e-40)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) + (k * (j * -27.0));
	}
	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 <= (-9d+68)) .or. (.not. (x <= 1.3d-40))) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = (b * c) + (k * (j * (-27.0d0)))
    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 <= -9e+68) || !(x <= 1.3e-40)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) + (k * (j * -27.0));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -9e+68) or not (x <= 1.3e-40):
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = (b * c) + (k * (j * -27.0))
	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 <= -9e+68) || !(x <= 1.3e-40))
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(b * c) + Float64(k * Float64(j * -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)
	tmp = 0.0;
	if ((x <= -9e+68) || ~((x <= 1.3e-40)))
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = (b * c) + (k * (j * -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_] := If[Or[LessEqual[x, -9e+68], N[Not[LessEqual[x, 1.3e-40]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.0000000000000007e68 or 1.3000000000000001e-40 < x

   1. Initial program 78.7%

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

      1. associate-*l* 78.7%

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

      2. associate--l+ 78.7%

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

      3. distribute-rgt-out-- 80.2%

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

      4. associate-*l* 87.3%

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

      5. associate-*l* 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in t around 0 64.2%

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

   5. Taylor expanded in j around 0 54.9%

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

   if -9.0000000000000007e68 < x < 1.3000000000000001e-40

   1. Initial program 93.5%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in b around inf 59.0%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+68} \lor \neg \left(x \leq 1.3 \cdot 10^{-40}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 14: 52.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{+69} \lor \neg \left(x \leq 2.6 \cdot 10^{-41}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \end{array} \end{array} \]

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 -3.05e+69) (not (<= x 2.6e-41)))
   (- (* b c) (* 4.0 (* x i)))
   (- (* b c) (* j (* 27.0 k)))))

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 <= -3.05e+69) || !(x <= 2.6e-41)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) - (j * (27.0 * k));
	}
	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 <= (-3.05d+69)) .or. (.not. (x <= 2.6d-41))) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = (b * c) - (j * (27.0d0 * k))
    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 <= -3.05e+69) || !(x <= 2.6e-41)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) - (j * (27.0 * k));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -3.05e+69) or not (x <= 2.6e-41):
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = (b * c) - (j * (27.0 * k))
	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 <= -3.05e+69) || !(x <= 2.6e-41))
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(b * c) - Float64(j * Float64(27.0 * k)));
	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 <= -3.05e+69) || ~((x <= 2.6e-41)))
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = (b * c) - (j * (27.0 * k));
	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, -3.05e+69], N[Not[LessEqual[x, 2.6e-41]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.05e69 or 2.5999999999999999e-41 < x

   1. Initial program 78.7%

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

      1. associate-*l* 78.7%

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

      2. associate--l+ 78.7%

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

      3. distribute-rgt-out-- 80.2%

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

      4. associate-*l* 87.3%

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

      5. associate-*l* 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in t around 0 64.2%

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

   5. Taylor expanded in j around 0 54.9%

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

   if -3.05e69 < x < 2.5999999999999999e-41

   1. Initial program 93.5%

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

      1. associate-*l* 93.5%

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

      2. associate--l+ 93.5%

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

      3. distribute-rgt-out-- 95.1%

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

      4. associate-*l* 87.9%

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

      5. associate-*l* 87.9%

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

   3. Simplified 87.9%

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

      1. associate-*r* 95.1%

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

      2. distribute-rgt-out-- 93.5%

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

      3. cancel-sign-sub-inv 93.5%

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

      4. associate-*l* 90.1%

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

      5. fma-def 90.1%

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

      6. associate-*l* 90.1%

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

   5. Applied egg-rr 90.1%

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

   6. Taylor expanded in b around inf 59.0%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{+69} \lor \neg \left(x \leq 2.6 \cdot 10^{-41}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - j \cdot \left(27 \cdot k\right)\\ \end{array} \]

Alternative 15: 44.8% accurate, 3.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ b \cdot c + k \cdot \left(j \cdot -27\right) \end{array} \]

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
 (+ (* b c) (* k (* j -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) {
	return (b * c) + (k * (j * -27.0));
}

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 = (b * c) + (k * (j * (-27.0d0)))
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 (b * c) + (k * (j * -27.0));
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	return (b * c) + (k * (j * -27.0))

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(b * c) + Float64(k * Float64(j * -27.0)))
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = (b * c) + (k * (j * -27.0));
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[(N[(b * c), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.7%

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

3. Simplified 88.4%

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

4. Taylor expanded in b around inf 44.0%

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

5. Final simplification 44.0%

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

Alternative 16: 24.3% accurate, 6.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ -27 \cdot \left(j \cdot k\right) \end{array} \]

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 (* j k)))

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 * (j * k);
}

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) * (j * k)
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 * (j * k);
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	return -27.0 * (j * k)

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(-27.0 * Float64(j * k))
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = -27.0 * (j * k);
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[(j * k), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.7%

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

3. Simplified 88.4%

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

4. Taylor expanded in k around inf 21.6%

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

5. Final simplification 21.6%

   \[\leadsto -27 \cdot \left(j \cdot k\right) \]

Alternative 17: 24.3% accurate, 6.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ j \cdot \left(k \cdot -27\right) \end{array} \]

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 (* 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) {
	return j * (k * -27.0);
}

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 = j * (k * (-27.0d0))
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 j * (k * -27.0);
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	return j * (k * -27.0)

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(j * Float64(k * -27.0))
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = j * (k * -27.0);
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[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.7%

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

3. Simplified 88.4%

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

4. Taylor expanded in k around inf 21.6%

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

   1. associate-*r* 21.6%

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

   2. *-commutative 21.6%

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

   3. associate-*l* 21.6%

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

6. Simplified 21.6%

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

7. Final simplification 21.6%

   \[\leadsto j \cdot \left(k \cdot -27\right) \]

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 2023305 
(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)))