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

Percentage Accurate: 85.4% → 90.3%

Time: 39.3s

Alternatives: 25

Speedup: 1.0×

• 49.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	double tmp;
	if (((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1) <= Double.POSITIVE_INFINITY) {
		tmp = (((b * c) + t_2) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = x * ((18.0 * (z * (y * t))) - (4.0 * i))
	tmp = 0
	if ((((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)) - t_1) <= math.inf:
		tmp = (((b * c) + t_2) - (4.0 * (t * a))) - t_1
	else:
		tmp = t_2
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.8%

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

   2. Taylor expanded in x around 0 95.6%

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

      1. pow1 95.6%

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

   4. Applied egg-rr 95.6%

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

      1. unpow1 95.6%

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

      2. associate-*r* 95.5%

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

   6. Simplified 95.5%

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

   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%

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

   3. Simplified 20.0%

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

   4. Taylor expanded in x around inf 60.2%

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

      1. pow1 26.7%

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

   6. Applied egg-rr 60.2%

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

      1. unpow1 26.7%

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

      2. associate-*r* 26.7%

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

   8. Simplified 60.2%

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

4. Final simplification 91.4%

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

Alternative 2: 88.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_1 \leq 4 \cdot 10^{+307}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 4e+307)
     (-
      (-
       (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))
       (* 4.0 (* t a)))
      t_1)
     (* j (* k -27.0)))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= 4e+307) {
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t_1 <= 4d+307) then
        tmp = (((b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))) - (4.0d0 * (t * a))) - t_1
    else
        tmp = j * (k * (-27.0d0))
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= 4e+307) {
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= 4e+307:
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - t_1
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= 4e+307)
		tmp = Float64(Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))) - Float64(4.0 * Float64(t * a))) - t_1);
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= 4e+307)
		tmp = (((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - (4.0 * (t * a))) - t_1;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+307], N[(N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j 27) k) < 3.99999999999999994e307

   1. Initial program 85.8%

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

   2. Taylor expanded in x around 0 89.0%

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

   if 3.99999999999999994e307 < (*.f64 (*.f64 j 27) k)

   1. Initial program 41.7%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in j around inf 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-*l* 91.7%

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

   6. Simplified 91.7%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq 4 \cdot 10^{+307}:\\ \;\;\;\;\left(\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 3: 87.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{+90}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x 1.55e+90)
   (-
    (+ (* b c) (* t (- (* (* x 18.0) (* y z)) (* a 4.0))))
    (+ (* x (* 4.0 i)) (* j (* 27.0 k))))
   (-
    (+ (* b c) (* x (- (* 18.0 (* y (* z t))) (* 4.0 i))))
    (* 27.0 (* j k)))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= 1.55e+90) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (x <= 1.55d+90) then
        tmp = ((b * c) + (t * (((x * 18.0d0) * (y * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    else
        tmp = ((b * c) + (x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i)))) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= 1.55e+90) {
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	} else {
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= 1.55e+90:
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	else:
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - (27.0 * (j * k))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= 1.55e+90)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(x * 18.0) * Float64(y * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)))) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= 1.55e+90)
		tmp = ((b * c) + (t * (((x * 18.0) * (y * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	else
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, 1.55e+90], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.54999999999999994e90

   1. Initial program 84.8%

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

   3. Simplified 86.7%

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

   if 1.54999999999999994e90 < x

   1. Initial program 78.0%

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

   2. Taylor expanded in x around 0 94.9%

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

   3. Taylor expanded in a around 0 97.4%

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

      1. expm1-log1p-u 79.8%

         \[\leadsto \left(b \cdot c + x \cdot \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)} - 4 \cdot i\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      2. expm1-udef 74.5%

         \[\leadsto \left(b \cdot c + x \cdot \left(\color{blue}{\left(e^{\mathsf{log1p}\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} - 1\right)} - 4 \cdot i\right)\right) - 27 \cdot \left(j \cdot k\right) \]

   5. Applied egg-rr 74.5%

      \[\leadsto \left(b \cdot c + x \cdot \left(\color{blue}{\left(e^{\mathsf{log1p}\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} - 1\right)} - 4 \cdot i\right)\right) - 27 \cdot \left(j \cdot k\right) \]
   6. Step-by-step derivation

      1. expm1-def 79.8%

         \[\leadsto \left(b \cdot c + x \cdot \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)} - 4 \cdot i\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      2. expm1-log1p 97.4%

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

      3. *-commutative 97.4%

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

      4. associate-*r* 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{+90}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 4: 71.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(x \cdot \left(y \cdot z\right)\right) \cdot -18\right) - t_1\\ \mathbf{elif}\;t \leq 520000:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+49}:\\ \;\;\;\;b \cdot c - \left(t \cdot -18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+69} \lor \neg \left(t \leq 2 \cdot 10^{+129}\right):\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t -1.02e-50)
     (- (* t (- (* a (- 4.0)) (* (* x (* y z)) -18.0))) t_1)
     (if (<= t 520000.0)
       (- (- (* b c) (* 4.0 (* x i))) t_1)
       (if (<= t 1.85e+49)
         (- (* b c) (* (* t -18.0) (* z (* x y))))
         (if (or (<= t 7.8e+69) (not (<= t 2e+129)))
           (- (- (* b c) (* 4.0 (* t a))) t_1)
           (-
            (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))
            (* 27.0 (* j k)))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t <= -1.02e-50) {
		tmp = (t * ((a * -4.0) - ((x * (y * z)) * -18.0))) - t_1;
	} else if (t <= 520000.0) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (t <= 1.85e+49) {
		tmp = (b * c) - ((t * -18.0) * (z * (x * y)));
	} else if ((t <= 7.8e+69) || !(t <= 2e+129)) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    if (t <= (-1.02d-50)) then
        tmp = (t * ((a * -4.0d0) - ((x * (y * z)) * (-18.0d0)))) - t_1
    else if (t <= 520000.0d0) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else if (t <= 1.85d+49) then
        tmp = (b * c) - ((t * (-18.0d0)) * (z * (x * y)))
    else if ((t <= 7.8d+69) .or. (.not. (t <= 2d+129))) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else
        tmp = (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t <= -1.02e-50) {
		tmp = (t * ((a * -4.0) - ((x * (y * z)) * -18.0))) - t_1;
	} else if (t <= 520000.0) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (t <= 1.85e+49) {
		tmp = (b * c) - ((t * -18.0) * (z * (x * y)));
	} else if ((t <= 7.8e+69) || !(t <= 2e+129)) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t <= -1.02e-50:
		tmp = (t * ((a * -4.0) - ((x * (y * z)) * -18.0))) - t_1
	elif t <= 520000.0:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	elif t <= 1.85e+49:
		tmp = (b * c) - ((t * -18.0) * (z * (x * y)))
	elif (t <= 7.8e+69) or not (t <= 2e+129):
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	else:
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - (27.0 * (j * k))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t <= -1.02e-50)
		tmp = Float64(Float64(t * Float64(Float64(a * Float64(-4.0)) - Float64(Float64(x * Float64(y * z)) * -18.0))) - t_1);
	elseif (t <= 520000.0)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	elseif (t <= 1.85e+49)
		tmp = Float64(Float64(b * c) - Float64(Float64(t * -18.0) * Float64(z * Float64(x * y))));
	elseif ((t <= 7.8e+69) || !(t <= 2e+129))
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	else
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t <= -1.02e-50)
		tmp = (t * ((a * -4.0) - ((x * (y * z)) * -18.0))) - t_1;
	elseif (t <= 520000.0)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	elseif (t <= 1.85e+49)
		tmp = (b * c) - ((t * -18.0) * (z * (x * y)));
	elseif ((t <= 7.8e+69) || ~((t <= 2e+129)))
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	else
		tmp = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t, -1.02e-50], N[(N[(t * N[(N[(a * (-4.0)), $MachinePrecision] - N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 520000.0], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 1.85e+49], N[(N[(b * c), $MachinePrecision] - N[(N[(t * -18.0), $MachinePrecision] * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 7.8e+69], N[Not[LessEqual[t, 2e+129]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.0199999999999999e-50

   1. Initial program 85.3%

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

   2. Taylor expanded in t around -inf 81.5%

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

      1. associate-*r* 81.5%

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

      2. neg-mul-1 81.5%

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

      3. cancel-sign-sub-inv 81.5%

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

      4. *-commutative 81.5%

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

      5. metadata-eval 81.5%

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

   4. Simplified 81.5%

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

   if -1.0199999999999999e-50 < t < 5.2e5

   1. Initial program 85.7%

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

   2. Taylor expanded in t around 0 78.2%

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

   if 5.2e5 < t < 1.85000000000000009e49

   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 67.3%

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

   4. Taylor expanded in x around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-*r* 67.3%

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

      3. associate-*r* 82.8%

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

      4. associate-*l* 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in x around inf 83.3%

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

      1. associate-*r* 83.3%

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

      2. *-commutative 83.3%

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

   9. Simplified 83.3%

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

   10. Taylor expanded in x around -inf 84.0%

       \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) + b \cdot c} \]
   11. Step-by-step derivation

       1. +-commutative 84.0%

          \[\leadsto \color{blue}{b \cdot c + -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]

       2. mul-1-neg 84.0%

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

       3. unsub-neg 84.0%

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

       4. cancel-sign-sub-inv 84.0%

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

       5. associate-*r* 84.0%

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

       6. metadata-eval 84.0%

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

       7. fma-def 84.0%

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

       8. *-commutative 84.0%

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

   12. Simplified 84.0%

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

   13. Taylor expanded in t around inf 84.0%

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

       1. associate-*r* 83.7%

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

       2. *-commutative 83.7%

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

       3. associate-*r* 100.0%

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

   15. Simplified 100.0%

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

   if 1.85000000000000009e49 < t < 7.7999999999999998e69 or 2e129 < t

   1. Initial program 75.0%

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

   2. Taylor expanded in x around 0 78.7%

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

   if 7.7999999999999998e69 < t < 2e129

   1. Initial program 81.2%

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

   2. Taylor expanded in x around 0 87.4%

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

   3. Taylor expanded in a around 0 93.7%

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

   4. Taylor expanded in b around 0 82.5%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right) - \left(x \cdot \left(y \cdot z\right)\right) \cdot -18\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 520000:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+49}:\\ \;\;\;\;b \cdot c - \left(t \cdot -18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+69} \lor \neg \left(t \leq 2 \cdot 10^{+129}\right):\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 5: 72.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 10^{-157}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-55}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \mathbf{elif}\;x \leq 42000000:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k))
        (t_2 (- (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))) (* 27.0 (* j k)))))
   (if (<= x -6e-89)
     t_2
     (if (<= x 1e-157)
       (- (- (* b c) (* 4.0 (* t a))) t_1)
       (if (<= x 2e-55)
         (- (- (* b c) (* 4.0 (* x i))) t_1)
         (if (<= x 42000000.0)
           (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
           t_2))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - (27.0 * (j * k));
	double tmp;
	if (x <= -6e-89) {
		tmp = t_2;
	} else if (x <= 1e-157) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 2e-55) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (x <= 42000000.0) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))) - (27.0d0 * (j * k))
    if (x <= (-6d-89)) then
        tmp = t_2
    else if (x <= 1d-157) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else if (x <= 2d-55) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else if (x <= 42000000.0d0) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - (27.0 * (j * k));
	double tmp;
	if (x <= -6e-89) {
		tmp = t_2;
	} else if (x <= 1e-157) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else if (x <= 2e-55) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (x <= 42000000.0) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - (27.0 * (j * k))
	tmp = 0
	if x <= -6e-89:
		tmp = t_2
	elif x <= 1e-157:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	elif x <= 2e-55:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	elif x <= 42000000.0:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	else:
		tmp = t_2
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))) - Float64(27.0 * Float64(j * k)))
	tmp = 0.0
	if (x <= -6e-89)
		tmp = t_2;
	elseif (x <= 1e-157)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	elseif (x <= 2e-55)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	elseif (x <= 42000000.0)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - (27.0 * (j * k));
	tmp = 0.0;
	if (x <= -6e-89)
		tmp = t_2;
	elseif (x <= 1e-157)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	elseif (x <= 2e-55)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	elseif (x <= 42000000.0)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e-89], t$95$2, If[LessEqual[x, 1e-157], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 2e-55], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 42000000.0], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.9999999999999999e-89 or 4.2e7 < x

   1. Initial program 76.5%

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

   2. Taylor expanded in x around 0 86.2%

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

   3. Taylor expanded in a around 0 80.7%

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

   4. Taylor expanded in b around 0 72.0%

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

   if -5.9999999999999999e-89 < x < 9.99999999999999943e-158

   1. Initial program 93.8%

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

   2. Taylor expanded in x around 0 85.9%

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

   if 9.99999999999999943e-158 < x < 1.99999999999999999e-55

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 78.8%

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

   if 1.99999999999999999e-55 < x < 4.2e7

   1. Initial program 85.0%

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

   2. Taylor expanded in x around 0 85.0%

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

   3. Taylor expanded in t around inf 85.9%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 10^{-157}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-55}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 42000000:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 6: 71.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 10^{-157}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-53}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right)\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;x \leq 112000000000:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))) (* 27.0 (* j k)))))
   (if (<= x -1.2e-88)
     t_1
     (if (<= x 1e-157)
       (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))
       (if (<= x 2.7e-53)
         (- (+ (* b c) (* t (* (* x y) (* 18.0 z)))) (* x (* 4.0 i)))
         (if (<= x 112000000000.0)
           (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))
           t_1))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - (27.0 * (j * k));
	double tmp;
	if (x <= -1.2e-88) {
		tmp = t_1;
	} else if (x <= 1e-157) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if (x <= 2.7e-53) {
		tmp = ((b * c) + (t * ((x * y) * (18.0 * z)))) - (x * (4.0 * i));
	} else if (x <= 112000000000.0) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))) - (27.0d0 * (j * k))
    if (x <= (-1.2d-88)) then
        tmp = t_1
    else if (x <= 1d-157) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    else if (x <= 2.7d-53) then
        tmp = ((b * c) + (t * ((x * y) * (18.0d0 * z)))) - (x * (4.0d0 * i))
    else if (x <= 112000000000.0d0) then
        tmp = t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - (27.0 * (j * k));
	double tmp;
	if (x <= -1.2e-88) {
		tmp = t_1;
	} else if (x <= 1e-157) {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	} else if (x <= 2.7e-53) {
		tmp = ((b * c) + (t * ((x * y) * (18.0 * z)))) - (x * (4.0 * i));
	} else if (x <= 112000000000.0) {
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - (27.0 * (j * k))
	tmp = 0
	if x <= -1.2e-88:
		tmp = t_1
	elif x <= 1e-157:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	elif x <= 2.7e-53:
		tmp = ((b * c) + (t * ((x * y) * (18.0 * z)))) - (x * (4.0 * i))
	elif x <= 112000000000.0:
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0))
	else:
		tmp = t_1
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i))) - Float64(27.0 * Float64(j * k)))
	tmp = 0.0
	if (x <= -1.2e-88)
		tmp = t_1;
	elseif (x <= 1e-157)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k));
	elseif (x <= 2.7e-53)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(x * y) * Float64(18.0 * z)))) - Float64(x * Float64(4.0 * i)));
	elseif (x <= 112000000000.0)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (x * ((18.0 * (t * (y * z))) - (4.0 * i))) - (27.0 * (j * k));
	tmp = 0.0;
	if (x <= -1.2e-88)
		tmp = t_1;
	elseif (x <= 1e-157)
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	elseif (x <= 2.7e-53)
		tmp = ((b * c) + (t * ((x * y) * (18.0 * z)))) - (x * (4.0 * i));
	elseif (x <= 112000000000.0)
		tmp = t * ((18.0 * (x * (y * z))) - (a * 4.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e-88], t$95$1, If[LessEqual[x, 1e-157], 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, 2.7e-53], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(x * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 112000000000.0], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.2e-88 or 1.12e11 < x

   1. Initial program 76.0%

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

   2. Taylor expanded in x around 0 85.9%

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

   3. Taylor expanded in a around 0 81.0%

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

   4. Taylor expanded in b around 0 72.7%

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

   if -1.2e-88 < x < 9.99999999999999943e-158

   1. Initial program 93.8%

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

   2. Taylor expanded in x around 0 85.9%

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

   if 9.99999999999999943e-158 < x < 2.6999999999999999e-53

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 93.4%

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

      1. *-commutative 93.4%

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

      2. associate-*r* 93.4%

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

      3. associate-*r* 93.4%

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

      4. associate-*l* 93.3%

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

   6. Simplified 93.3%

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

   7. Taylor expanded in x around inf 80.9%

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

      1. associate-*r* 80.9%

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

      2. *-commutative 80.9%

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

   9. Simplified 80.9%

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

   if 2.6999999999999999e-53 < x < 1.12e11

   1. Initial program 89.4%

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

   2. Taylor expanded in x around 0 89.4%

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

   3. Taylor expanded in t around inf 70.7%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;x \leq 10^{-157}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-53}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right)\right)\right) - x \cdot \left(4 \cdot i\right)\\ \mathbf{elif}\;x \leq 112000000000:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 7: 81.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-86} \lor \neg \left(t \leq 260000\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -4.2e-86) (not (<= t 260000.0)))
   (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) (* 27.0 (* j k)))
   (- (- (* b c) (* 4.0 (* x i))) (* (* j 27.0) k))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -4.2e-86) || !(t <= 260000.0)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	} 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.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-4.2d-86)) .or. (.not. (t <= 260000.0d0))) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - (27.0d0 * (j * k))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -4.2e-86) || !(t <= 260000.0)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -4.2e-86) or not (t <= 260000.0):
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k))
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k)
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -4.2e-86) || !(t <= 260000.0))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -4.2e-86) || ~((t <= 260000.0)))
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - (27.0 * (j * k));
	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.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -4.2e-86], N[Not[LessEqual[t, 260000.0]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.2e-86 or 2.6e5 < t

   1. Initial program 83.0%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in i around 0 82.0%

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

   if -4.2e-86 < t < 2.6e5

   1. Initial program 84.7%

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

   2. Taylor expanded in t around 0 79.2%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-86} \lor \neg \left(t \leq 260000\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 8: 79.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{-27}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+129}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 27.0 (* j k))))
   (if (<= t -2.2e-27)
     (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) t_1)
     (if (<= t 1.35e+129)
       (- (+ (* b c) (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))) t_1)
       (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double tmp;
	if (t <= -2.2e-27) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	} else if (t <= 1.35e+129) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1;
	} 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.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (j * k)
    if (t <= (-2.2d-27)) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - t_1
    else if (t <= 1.35d+129) then
        tmp = ((b * c) + (x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i)))) - t_1
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double tmp;
	if (t <= -2.2e-27) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	} else if (t <= 1.35e+129) {
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	tmp = 0
	if t <= -2.2e-27:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1
	elif t <= 1.35e+129:
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	tmp = 0.0
	if (t <= -2.2e-27)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - t_1);
	elseif (t <= 1.35e+129)
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)))) - t_1);
	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])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 27.0 * (j * k);
	tmp = 0.0;
	if (t <= -2.2e-27)
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	elseif (t <= 1.35e+129)
		tmp = ((b * c) + (x * ((18.0 * (t * (y * z))) - (4.0 * i)))) - t_1;
	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.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e-27], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 1.35e+129], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.19999999999999987e-27

   1. Initial program 83.9%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in i around 0 84.4%

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

   if -2.19999999999999987e-27 < t < 1.35e129

   1. Initial program 85.5%

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

   2. Taylor expanded in x around 0 90.1%

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

   3. Taylor expanded in a around 0 86.2%

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

   if 1.35e129 < t

   1. Initial program 75.0%

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

   2. Taylor expanded in x around 0 76.0%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-27}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+129}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 9: 81.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{-28}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - t_1\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{+129}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 27.0 (* j k))))
   (if (<= t -8.5e-28)
     (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) t_1)
     (if (<= t 1.28e+129)
       (- (+ (* b c) (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))) t_1)
       (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double tmp;
	if (t <= -8.5e-28) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	} else if (t <= 1.28e+129) {
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - t_1;
	} 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.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 27.0d0 * (j * k)
    if (t <= (-8.5d-28)) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - t_1
    else if (t <= 1.28d+129) then
        tmp = ((b * c) + (x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i)))) - t_1
    else
        tmp = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double tmp;
	if (t <= -8.5e-28) {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	} else if (t <= 1.28e+129) {
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	tmp = 0
	if t <= -8.5e-28:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1
	elif t <= 1.28e+129:
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - t_1
	else:
		tmp = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	tmp = 0.0
	if (t <= -8.5e-28)
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - t_1);
	elseif (t <= 1.28e+129)
		tmp = Float64(Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)))) - t_1);
	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])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 27.0 * (j * k);
	tmp = 0.0;
	if (t <= -8.5e-28)
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	elseif (t <= 1.28e+129)
		tmp = ((b * c) + (x * ((18.0 * (y * (z * t))) - (4.0 * i)))) - t_1;
	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.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e-28], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 1.28e+129], N[(N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.49999999999999925e-28

   1. Initial program 83.9%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in i around 0 84.4%

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

   if -8.49999999999999925e-28 < t < 1.27999999999999994e129

   1. Initial program 85.5%

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

   2. Taylor expanded in x around 0 90.1%

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

   3. Taylor expanded in a around 0 86.2%

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

      1. expm1-log1p-u 71.8%

         \[\leadsto \left(b \cdot c + x \cdot \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)} - 4 \cdot i\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      2. expm1-udef 70.6%

         \[\leadsto \left(b \cdot c + x \cdot \left(\color{blue}{\left(e^{\mathsf{log1p}\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} - 1\right)} - 4 \cdot i\right)\right) - 27 \cdot \left(j \cdot k\right) \]

   5. Applied egg-rr 70.6%

      \[\leadsto \left(b \cdot c + x \cdot \left(\color{blue}{\left(e^{\mathsf{log1p}\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)} - 1\right)} - 4 \cdot i\right)\right) - 27 \cdot \left(j \cdot k\right) \]
   6. Step-by-step derivation

      1. expm1-def 71.8%

         \[\leadsto \left(b \cdot c + x \cdot \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)} - 4 \cdot i\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      2. expm1-log1p 86.2%

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

      3. *-commutative 86.2%

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

      4. associate-*r* 90.0%

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

   7. Simplified 90.0%

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

   if 1.27999999999999994e129 < t

   1. Initial program 75.0%

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

   2. Taylor expanded in x around 0 76.0%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-28}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{+129}:\\ \;\;\;\;\left(b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 10: 45.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_2 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;z \leq -9200000000:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+139}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* j k)))) (t_2 (- (* b c) (* 4.0 (* x i)))))
   (if (<= z -9200000000.0)
     (* 18.0 (* x (* t (* y z))))
     (if (<= z -1.12e-52)
       t_1
       (if (<= z -3.45e-155)
         (* t (* a -4.0))
         (if (<= z 2e-246)
           t_2
           (if (<= z 1e-190)
             t_1
             (if (<= z 4.4e-15)
               t_2
               (if (<= z 6e+89)
                 t_1
                 (if (<= z 1.08e+139)
                   t_2
                   (* x (* 18.0 (* y (* z t))))))))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double t_2 = (b * c) - (4.0 * (x * i));
	double tmp;
	if (z <= -9200000000.0) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (z <= -1.12e-52) {
		tmp = t_1;
	} else if (z <= -3.45e-155) {
		tmp = t * (a * -4.0);
	} else if (z <= 2e-246) {
		tmp = t_2;
	} else if (z <= 1e-190) {
		tmp = t_1;
	} else if (z <= 4.4e-15) {
		tmp = t_2;
	} else if (z <= 6e+89) {
		tmp = t_1;
	} else if (z <= 1.08e+139) {
		tmp = t_2;
	} else {
		tmp = x * (18.0 * (y * (z * t)));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) - (27.0d0 * (j * k))
    t_2 = (b * c) - (4.0d0 * (x * i))
    if (z <= (-9200000000.0d0)) then
        tmp = 18.0d0 * (x * (t * (y * z)))
    else if (z <= (-1.12d-52)) then
        tmp = t_1
    else if (z <= (-3.45d-155)) then
        tmp = t * (a * (-4.0d0))
    else if (z <= 2d-246) then
        tmp = t_2
    else if (z <= 1d-190) then
        tmp = t_1
    else if (z <= 4.4d-15) then
        tmp = t_2
    else if (z <= 6d+89) then
        tmp = t_1
    else if (z <= 1.08d+139) then
        tmp = t_2
    else
        tmp = x * (18.0d0 * (y * (z * t)))
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double t_2 = (b * c) - (4.0 * (x * i));
	double tmp;
	if (z <= -9200000000.0) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (z <= -1.12e-52) {
		tmp = t_1;
	} else if (z <= -3.45e-155) {
		tmp = t * (a * -4.0);
	} else if (z <= 2e-246) {
		tmp = t_2;
	} else if (z <= 1e-190) {
		tmp = t_1;
	} else if (z <= 4.4e-15) {
		tmp = t_2;
	} else if (z <= 6e+89) {
		tmp = t_1;
	} else if (z <= 1.08e+139) {
		tmp = t_2;
	} else {
		tmp = x * (18.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (27.0 * (j * k))
	t_2 = (b * c) - (4.0 * (x * i))
	tmp = 0
	if z <= -9200000000.0:
		tmp = 18.0 * (x * (t * (y * z)))
	elif z <= -1.12e-52:
		tmp = t_1
	elif z <= -3.45e-155:
		tmp = t * (a * -4.0)
	elif z <= 2e-246:
		tmp = t_2
	elif z <= 1e-190:
		tmp = t_1
	elif z <= 4.4e-15:
		tmp = t_2
	elif z <= 6e+89:
		tmp = t_1
	elif z <= 1.08e+139:
		tmp = t_2
	else:
		tmp = x * (18.0 * (y * (z * t)))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_2 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	tmp = 0.0
	if (z <= -9200000000.0)
		tmp = Float64(18.0 * Float64(x * Float64(t * Float64(y * z))));
	elseif (z <= -1.12e-52)
		tmp = t_1;
	elseif (z <= -3.45e-155)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (z <= 2e-246)
		tmp = t_2;
	elseif (z <= 1e-190)
		tmp = t_1;
	elseif (z <= 4.4e-15)
		tmp = t_2;
	elseif (z <= 6e+89)
		tmp = t_1;
	elseif (z <= 1.08e+139)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (27.0 * (j * k));
	t_2 = (b * c) - (4.0 * (x * i));
	tmp = 0.0;
	if (z <= -9200000000.0)
		tmp = 18.0 * (x * (t * (y * z)));
	elseif (z <= -1.12e-52)
		tmp = t_1;
	elseif (z <= -3.45e-155)
		tmp = t * (a * -4.0);
	elseif (z <= 2e-246)
		tmp = t_2;
	elseif (z <= 1e-190)
		tmp = t_1;
	elseif (z <= 4.4e-15)
		tmp = t_2;
	elseif (z <= 6e+89)
		tmp = t_1;
	elseif (z <= 1.08e+139)
		tmp = t_2;
	else
		tmp = x * (18.0 * (y * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9200000000.0], N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.12e-52], t$95$1, If[LessEqual[z, -3.45e-155], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-246], t$95$2, If[LessEqual[z, 1e-190], t$95$1, If[LessEqual[z, 4.4e-15], t$95$2, If[LessEqual[z, 6e+89], t$95$1, If[LessEqual[z, 1.08e+139], t$95$2, N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -9.2e9

   1. Initial program 86.6%

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

   2. Taylor expanded in x around 0 84.9%

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

   3. Taylor expanded in a around 0 80.3%

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

   4. Taylor expanded in t around inf 48.7%

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

      1. *-commutative 48.7%

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

      2. associate-*l* 48.7%

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

      3. *-commutative 48.7%

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

   6. Simplified 48.7%

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

   if -9.2e9 < z < -1.11999999999999994e-52 or 1.99999999999999991e-246 < z < 1e-190 or 4.39999999999999971e-15 < z < 6.00000000000000025e89

   1. Initial program 86.0%

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

   2. Taylor expanded in t around 0 70.5%

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

   3. Taylor expanded in i around 0 66.0%

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

   if -1.11999999999999994e-52 < z < -3.44999999999999987e-155

   1. Initial program 81.4%

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

   2. Taylor expanded in x around 0 95.2%

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

   3. Taylor expanded in a around inf 25.4%

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

      1. associate-*r* 25.4%

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

      2. *-commutative 25.4%

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

   5. Simplified 25.4%

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

   if -3.44999999999999987e-155 < z < 1.99999999999999991e-246 or 1e-190 < z < 4.39999999999999971e-15 or 6.00000000000000025e89 < z < 1.08000000000000004e139

   1. Initial program 86.9%

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

   2. Taylor expanded in t around 0 66.9%

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

   3. Taylor expanded in j around 0 49.2%

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

   if 1.08000000000000004e139 < z

   1. Initial program 71.6%

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

   2. Taylor expanded in x around 0 73.9%

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

   3. Taylor expanded in a around 0 72.0%

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

   4. Taylor expanded in t around inf 58.4%

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

      1. metadata-eval 58.4%

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

      2. distribute-lft-neg-in 58.4%

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

      3. *-commutative 58.4%

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

      4. associate-*r* 60.2%

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

      5. associate-*l* 60.3%

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

      6. *-commutative 60.3%

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

      7. distribute-rgt-neg-in 60.3%

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

      8. distribute-lft-neg-in 60.3%

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

      9. metadata-eval 60.3%

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

      10. *-commutative 60.3%

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

      11. associate-*r* 64.5%

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

   6. Simplified 64.5%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9200000000:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-52}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-246}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;z \leq 10^{-190}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-15}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+89}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+139}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 11: 45.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_2 := 27 \cdot \left(j \cdot k\right)\\ t_3 := b \cdot c - t_2\\ \mathbf{if}\;z \leq -38000000000:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-192}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - t_2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+89}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* x i))))
        (t_2 (* 27.0 (* j k)))
        (t_3 (- (* b c) t_2)))
   (if (<= z -38000000000.0)
     (* 18.0 (* x (* t (* y z))))
     (if (<= z -6.4e-56)
       t_3
       (if (<= z -3.5e-155)
         (* t (* a -4.0))
         (if (<= z 2.9e-246)
           t_1
           (if (<= z 2.7e-192)
             t_3
             (if (<= z 2.15e-30)
               (- (* x (* i -4.0)) t_2)
               (if (<= z 1.1e+89)
                 t_3
                 (if (<= z 5.9e+138) t_1 (* x (* 18.0 (* y (* z t))))))))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double t_2 = 27.0 * (j * k);
	double t_3 = (b * c) - t_2;
	double tmp;
	if (z <= -38000000000.0) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (z <= -6.4e-56) {
		tmp = t_3;
	} else if (z <= -3.5e-155) {
		tmp = t * (a * -4.0);
	} else if (z <= 2.9e-246) {
		tmp = t_1;
	} else if (z <= 2.7e-192) {
		tmp = t_3;
	} else if (z <= 2.15e-30) {
		tmp = (x * (i * -4.0)) - t_2;
	} else if (z <= 1.1e+89) {
		tmp = t_3;
	} else if (z <= 5.9e+138) {
		tmp = t_1;
	} else {
		tmp = x * (18.0 * (y * (z * t)));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * (x * i))
    t_2 = 27.0d0 * (j * k)
    t_3 = (b * c) - t_2
    if (z <= (-38000000000.0d0)) then
        tmp = 18.0d0 * (x * (t * (y * z)))
    else if (z <= (-6.4d-56)) then
        tmp = t_3
    else if (z <= (-3.5d-155)) then
        tmp = t * (a * (-4.0d0))
    else if (z <= 2.9d-246) then
        tmp = t_1
    else if (z <= 2.7d-192) then
        tmp = t_3
    else if (z <= 2.15d-30) then
        tmp = (x * (i * (-4.0d0))) - t_2
    else if (z <= 1.1d+89) then
        tmp = t_3
    else if (z <= 5.9d+138) then
        tmp = t_1
    else
        tmp = x * (18.0d0 * (y * (z * t)))
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double t_2 = 27.0 * (j * k);
	double t_3 = (b * c) - t_2;
	double tmp;
	if (z <= -38000000000.0) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (z <= -6.4e-56) {
		tmp = t_3;
	} else if (z <= -3.5e-155) {
		tmp = t * (a * -4.0);
	} else if (z <= 2.9e-246) {
		tmp = t_1;
	} else if (z <= 2.7e-192) {
		tmp = t_3;
	} else if (z <= 2.15e-30) {
		tmp = (x * (i * -4.0)) - t_2;
	} else if (z <= 1.1e+89) {
		tmp = t_3;
	} else if (z <= 5.9e+138) {
		tmp = t_1;
	} else {
		tmp = x * (18.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (x * i))
	t_2 = 27.0 * (j * k)
	t_3 = (b * c) - t_2
	tmp = 0
	if z <= -38000000000.0:
		tmp = 18.0 * (x * (t * (y * z)))
	elif z <= -6.4e-56:
		tmp = t_3
	elif z <= -3.5e-155:
		tmp = t * (a * -4.0)
	elif z <= 2.9e-246:
		tmp = t_1
	elif z <= 2.7e-192:
		tmp = t_3
	elif z <= 2.15e-30:
		tmp = (x * (i * -4.0)) - t_2
	elif z <= 1.1e+89:
		tmp = t_3
	elif z <= 5.9e+138:
		tmp = t_1
	else:
		tmp = x * (18.0 * (y * (z * t)))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	t_2 = Float64(27.0 * Float64(j * k))
	t_3 = Float64(Float64(b * c) - t_2)
	tmp = 0.0
	if (z <= -38000000000.0)
		tmp = Float64(18.0 * Float64(x * Float64(t * Float64(y * z))));
	elseif (z <= -6.4e-56)
		tmp = t_3;
	elseif (z <= -3.5e-155)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (z <= 2.9e-246)
		tmp = t_1;
	elseif (z <= 2.7e-192)
		tmp = t_3;
	elseif (z <= 2.15e-30)
		tmp = Float64(Float64(x * Float64(i * -4.0)) - t_2);
	elseif (z <= 1.1e+89)
		tmp = t_3;
	elseif (z <= 5.9e+138)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (x * i));
	t_2 = 27.0 * (j * k);
	t_3 = (b * c) - t_2;
	tmp = 0.0;
	if (z <= -38000000000.0)
		tmp = 18.0 * (x * (t * (y * z)));
	elseif (z <= -6.4e-56)
		tmp = t_3;
	elseif (z <= -3.5e-155)
		tmp = t * (a * -4.0);
	elseif (z <= 2.9e-246)
		tmp = t_1;
	elseif (z <= 2.7e-192)
		tmp = t_3;
	elseif (z <= 2.15e-30)
		tmp = (x * (i * -4.0)) - t_2;
	elseif (z <= 1.1e+89)
		tmp = t_3;
	elseif (z <= 5.9e+138)
		tmp = t_1;
	else
		tmp = x * (18.0 * (y * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[z, -38000000000.0], N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.4e-56], t$95$3, If[LessEqual[z, -3.5e-155], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-246], t$95$1, If[LessEqual[z, 2.7e-192], t$95$3, If[LessEqual[z, 2.15e-30], N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[z, 1.1e+89], t$95$3, If[LessEqual[z, 5.9e+138], t$95$1, N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.8e10

   1. Initial program 86.6%

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

   2. Taylor expanded in x around 0 84.9%

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

   3. Taylor expanded in a around 0 80.3%

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

   4. Taylor expanded in t around inf 48.7%

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

      1. *-commutative 48.7%

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

      2. associate-*l* 48.7%

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

      3. *-commutative 48.7%

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

   6. Simplified 48.7%

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

   if -3.8e10 < z < -6.39999999999999971e-56 or 2.9e-246 < z < 2.69999999999999991e-192 or 2.14999999999999983e-30 < z < 1.1e89

   1. Initial program 87.9%

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

   2. Taylor expanded in t around 0 68.7%

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

   3. Taylor expanded in i around 0 64.8%

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

   if -6.39999999999999971e-56 < z < -3.50000000000000015e-155

   1. Initial program 81.4%

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

   2. Taylor expanded in x around 0 95.2%

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

   3. Taylor expanded in a around inf 25.4%

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

      1. associate-*r* 25.4%

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

      2. *-commutative 25.4%

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

   5. Simplified 25.4%

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

   if -3.50000000000000015e-155 < z < 2.9e-246 or 1.1e89 < z < 5.8999999999999999e138

   1. Initial program 83.8%

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

   2. Taylor expanded in t around 0 66.3%

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

   3. Taylor expanded in j around 0 47.3%

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

   if 2.69999999999999991e-192 < z < 2.14999999999999983e-30

   1. Initial program 88.7%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in a around 0 77.7%

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

   4. Taylor expanded in i around inf 61.2%

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

      1. *-commutative 61.2%

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

      2. *-commutative 61.2%

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

      3. associate-*r* 61.2%

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

   6. Simplified 61.2%

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

   if 5.8999999999999999e138 < z

   1. Initial program 71.6%

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

   2. Taylor expanded in x around 0 73.9%

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

   3. Taylor expanded in a around 0 72.0%

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

   4. Taylor expanded in t around inf 58.4%

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

      1. metadata-eval 58.4%

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

      2. distribute-lft-neg-in 58.4%

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

      3. *-commutative 58.4%

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

      4. associate-*r* 60.2%

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

      5. associate-*l* 60.3%

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

      6. *-commutative 60.3%

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

      7. distribute-rgt-neg-in 60.3%

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

      8. distribute-lft-neg-in 60.3%

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

      9. metadata-eval 60.3%

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

      10. *-commutative 60.3%

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

      11. associate-*r* 64.5%

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

   6. Simplified 64.5%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -38000000000:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-56}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-246}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-192}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+89}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+138}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 12: 47.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := b \cdot c - t_1\\ t_3 := t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{-207}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - t_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+135}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+179}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 27.0 (* j k)))
        (t_2 (- (* b c) t_1))
        (t_3 (* t (+ (* 18.0 (* z (* x y))) (* a -4.0)))))
   (if (<= z -4e-207)
     t_3
     (if (<= z 2.1e-195)
       t_2
       (if (<= z 9.8e-31)
         (- (* x (* i -4.0)) t_1)
         (if (<= z 3.9e+90)
           t_2
           (if (<= z 4.5e+135)
             (- (* b c) (* 4.0 (* x i)))
             (if (<= z 2.45e+179) (* 18.0 (* x (* t (* y z)))) t_3))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double t_2 = (b * c) - t_1;
	double t_3 = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	double tmp;
	if (z <= -4e-207) {
		tmp = t_3;
	} else if (z <= 2.1e-195) {
		tmp = t_2;
	} else if (z <= 9.8e-31) {
		tmp = (x * (i * -4.0)) - t_1;
	} else if (z <= 3.9e+90) {
		tmp = t_2;
	} else if (z <= 4.5e+135) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (z <= 2.45e+179) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 27.0d0 * (j * k)
    t_2 = (b * c) - t_1
    t_3 = t * ((18.0d0 * (z * (x * y))) + (a * (-4.0d0)))
    if (z <= (-4d-207)) then
        tmp = t_3
    else if (z <= 2.1d-195) then
        tmp = t_2
    else if (z <= 9.8d-31) then
        tmp = (x * (i * (-4.0d0))) - t_1
    else if (z <= 3.9d+90) then
        tmp = t_2
    else if (z <= 4.5d+135) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (z <= 2.45d+179) then
        tmp = 18.0d0 * (x * (t * (y * z)))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double t_2 = (b * c) - t_1;
	double t_3 = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	double tmp;
	if (z <= -4e-207) {
		tmp = t_3;
	} else if (z <= 2.1e-195) {
		tmp = t_2;
	} else if (z <= 9.8e-31) {
		tmp = (x * (i * -4.0)) - t_1;
	} else if (z <= 3.9e+90) {
		tmp = t_2;
	} else if (z <= 4.5e+135) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (z <= 2.45e+179) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	t_2 = (b * c) - t_1
	t_3 = t * ((18.0 * (z * (x * y))) + (a * -4.0))
	tmp = 0
	if z <= -4e-207:
		tmp = t_3
	elif z <= 2.1e-195:
		tmp = t_2
	elif z <= 9.8e-31:
		tmp = (x * (i * -4.0)) - t_1
	elif z <= 3.9e+90:
		tmp = t_2
	elif z <= 4.5e+135:
		tmp = (b * c) - (4.0 * (x * i))
	elif z <= 2.45e+179:
		tmp = 18.0 * (x * (t * (y * z)))
	else:
		tmp = t_3
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	t_2 = Float64(Float64(b * c) - t_1)
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(z * Float64(x * y))) + Float64(a * -4.0)))
	tmp = 0.0
	if (z <= -4e-207)
		tmp = t_3;
	elseif (z <= 2.1e-195)
		tmp = t_2;
	elseif (z <= 9.8e-31)
		tmp = Float64(Float64(x * Float64(i * -4.0)) - t_1);
	elseif (z <= 3.9e+90)
		tmp = t_2;
	elseif (z <= 4.5e+135)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (z <= 2.45e+179)
		tmp = Float64(18.0 * Float64(x * Float64(t * Float64(y * z))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 27.0 * (j * k);
	t_2 = (b * c) - t_1;
	t_3 = t * ((18.0 * (z * (x * y))) + (a * -4.0));
	tmp = 0.0;
	if (z <= -4e-207)
		tmp = t_3;
	elseif (z <= 2.1e-195)
		tmp = t_2;
	elseif (z <= 9.8e-31)
		tmp = (x * (i * -4.0)) - t_1;
	elseif (z <= 3.9e+90)
		tmp = t_2;
	elseif (z <= 4.5e+135)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (z <= 2.45e+179)
		tmp = 18.0 * (x * (t * (y * z)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e-207], t$95$3, If[LessEqual[z, 2.1e-195], t$95$2, If[LessEqual[z, 9.8e-31], N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[z, 3.9e+90], t$95$2, If[LessEqual[z, 4.5e+135], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e+179], N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.9999999999999997e-207 or 2.4499999999999999e179 < z

   1. Initial program 83.0%

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

   2. Taylor expanded in x around 0 83.7%

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

   3. Taylor expanded in t around inf 57.2%

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

      1. cancel-sign-sub-inv 57.2%

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

      2. metadata-eval 57.2%

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

      3. associate-*r* 58.0%

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

   5. Simplified 58.0%

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

   if -3.9999999999999997e-207 < z < 2.1e-195 or 9.80000000000000047e-31 < z < 3.9000000000000002e90

   1. Initial program 88.3%

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

   2. Taylor expanded in t around 0 69.8%

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

   3. Taylor expanded in i around 0 61.3%

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

   if 2.1e-195 < z < 9.80000000000000047e-31

   1. Initial program 88.7%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in a around 0 77.7%

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

   4. Taylor expanded in i around inf 61.2%

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

      1. *-commutative 61.2%

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

      2. *-commutative 61.2%

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

      3. associate-*r* 61.2%

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

   6. Simplified 61.2%

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

   if 3.9000000000000002e90 < z < 4.50000000000000007e135

   1. Initial program 75.3%

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

   2. Taylor expanded in t around 0 60.1%

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

   3. Taylor expanded in j around 0 47.0%

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

   if 4.50000000000000007e135 < z < 2.4499999999999999e179

   1. Initial program 36.0%

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

   2. Taylor expanded in x around 0 67.1%

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

   3. Taylor expanded in a around 0 67.1%

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

   4. Taylor expanded in t around inf 36.0%

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

      1. *-commutative 36.0%

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

      2. associate-*l* 63.8%

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

      3. *-commutative 63.8%

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

   6. Simplified 63.8%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-207}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-195}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+90}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+135}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+179}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 13: 46.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := b \cdot c - t_1\\ t_3 := t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right) - a \cdot 4\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-206}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+137}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+179}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 27.0 (* j k)))
        (t_2 (- (* b c) t_1))
        (t_3 (* t (- (* (* x y) (* 18.0 z)) (* a 4.0)))))
   (if (<= z -2.5e-206)
     t_3
     (if (<= z 9.5e-194)
       t_2
       (if (<= z 1.15e-30)
         (- (* x (* i -4.0)) t_1)
         (if (<= z 5.8e+89)
           t_2
           (if (<= z 1.1e+137)
             (- (* b c) (* 4.0 (* x i)))
             (if (<= z 2.45e+179) (* 18.0 (* x (* t (* y z)))) t_3))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double t_2 = (b * c) - t_1;
	double t_3 = t * (((x * y) * (18.0 * z)) - (a * 4.0));
	double tmp;
	if (z <= -2.5e-206) {
		tmp = t_3;
	} else if (z <= 9.5e-194) {
		tmp = t_2;
	} else if (z <= 1.15e-30) {
		tmp = (x * (i * -4.0)) - t_1;
	} else if (z <= 5.8e+89) {
		tmp = t_2;
	} else if (z <= 1.1e+137) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (z <= 2.45e+179) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 27.0d0 * (j * k)
    t_2 = (b * c) - t_1
    t_3 = t * (((x * y) * (18.0d0 * z)) - (a * 4.0d0))
    if (z <= (-2.5d-206)) then
        tmp = t_3
    else if (z <= 9.5d-194) then
        tmp = t_2
    else if (z <= 1.15d-30) then
        tmp = (x * (i * (-4.0d0))) - t_1
    else if (z <= 5.8d+89) then
        tmp = t_2
    else if (z <= 1.1d+137) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (z <= 2.45d+179) then
        tmp = 18.0d0 * (x * (t * (y * z)))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double t_2 = (b * c) - t_1;
	double t_3 = t * (((x * y) * (18.0 * z)) - (a * 4.0));
	double tmp;
	if (z <= -2.5e-206) {
		tmp = t_3;
	} else if (z <= 9.5e-194) {
		tmp = t_2;
	} else if (z <= 1.15e-30) {
		tmp = (x * (i * -4.0)) - t_1;
	} else if (z <= 5.8e+89) {
		tmp = t_2;
	} else if (z <= 1.1e+137) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (z <= 2.45e+179) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	t_2 = (b * c) - t_1
	t_3 = t * (((x * y) * (18.0 * z)) - (a * 4.0))
	tmp = 0
	if z <= -2.5e-206:
		tmp = t_3
	elif z <= 9.5e-194:
		tmp = t_2
	elif z <= 1.15e-30:
		tmp = (x * (i * -4.0)) - t_1
	elif z <= 5.8e+89:
		tmp = t_2
	elif z <= 1.1e+137:
		tmp = (b * c) - (4.0 * (x * i))
	elif z <= 2.45e+179:
		tmp = 18.0 * (x * (t * (y * z)))
	else:
		tmp = t_3
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	t_2 = Float64(Float64(b * c) - t_1)
	t_3 = Float64(t * Float64(Float64(Float64(x * y) * Float64(18.0 * z)) - Float64(a * 4.0)))
	tmp = 0.0
	if (z <= -2.5e-206)
		tmp = t_3;
	elseif (z <= 9.5e-194)
		tmp = t_2;
	elseif (z <= 1.15e-30)
		tmp = Float64(Float64(x * Float64(i * -4.0)) - t_1);
	elseif (z <= 5.8e+89)
		tmp = t_2;
	elseif (z <= 1.1e+137)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (z <= 2.45e+179)
		tmp = Float64(18.0 * Float64(x * Float64(t * Float64(y * z))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 27.0 * (j * k);
	t_2 = (b * c) - t_1;
	t_3 = t * (((x * y) * (18.0 * z)) - (a * 4.0));
	tmp = 0.0;
	if (z <= -2.5e-206)
		tmp = t_3;
	elseif (z <= 9.5e-194)
		tmp = t_2;
	elseif (z <= 1.15e-30)
		tmp = (x * (i * -4.0)) - t_1;
	elseif (z <= 5.8e+89)
		tmp = t_2;
	elseif (z <= 1.1e+137)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (z <= 2.45e+179)
		tmp = 18.0 * (x * (t * (y * z)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(N[(x * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e-206], t$95$3, If[LessEqual[z, 9.5e-194], t$95$2, If[LessEqual[z, 1.15e-30], N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[z, 5.8e+89], t$95$2, If[LessEqual[z, 1.1e+137], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e+179], N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.5e-206 or 2.4499999999999999e179 < z

   1. Initial program 83.0%

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

   2. Taylor expanded in x around 0 83.7%

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

   3. Taylor expanded in t around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. associate-*r* 58.0%

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

      3. associate-*r* 58.0%

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

      4. pow1 58.0%

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

      5. associate-*l* 57.2%

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

   5. Applied egg-rr 57.2%

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

      1. unpow1 57.2%

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

      2. associate-*r* 58.0%

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

   7. Simplified 58.0%

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

   if -2.5e-206 < z < 9.50000000000000009e-194 or 1.14999999999999992e-30 < z < 5.80000000000000051e89

   1. Initial program 88.3%

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

   2. Taylor expanded in t around 0 69.8%

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

   3. Taylor expanded in i around 0 61.3%

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

   if 9.50000000000000009e-194 < z < 1.14999999999999992e-30

   1. Initial program 88.7%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in a around 0 77.7%

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

   4. Taylor expanded in i around inf 61.2%

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

      1. *-commutative 61.2%

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

      2. *-commutative 61.2%

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

      3. associate-*r* 61.2%

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

   6. Simplified 61.2%

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

   if 5.80000000000000051e89 < z < 1.10000000000000008e137

   1. Initial program 75.3%

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

   2. Taylor expanded in t around 0 60.1%

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

   3. Taylor expanded in j around 0 47.0%

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

   if 1.10000000000000008e137 < z < 2.4499999999999999e179

   1. Initial program 36.0%

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

   2. Taylor expanded in x around 0 67.1%

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

   3. Taylor expanded in a around 0 67.1%

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

   4. Taylor expanded in t around inf 36.0%

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

      1. *-commutative 36.0%

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

      2. associate-*l* 63.8%

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

      3. *-commutative 63.8%

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

   6. Simplified 63.8%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-206}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right) - a \cdot 4\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-194}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+89}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+137}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+179}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 14: 49.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := 27 \cdot \left(j \cdot k\right)\\ t_3 := b \cdot c - t_2\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{-47}:\\ \;\;\;\;b \cdot c - \left(t \cdot -18\right) \cdot t_1\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-206}:\\ \;\;\;\;t \cdot \left(18 \cdot t_1 + a \cdot -4\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-191}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - t_2\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+101}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* 27.0 (* j k))) (t_3 (- (* b c) t_2)))
   (if (<= z -1.65e-47)
     (- (* b c) (* (* t -18.0) t_1))
     (if (<= z -3.1e-206)
       (* t (+ (* 18.0 t_1) (* a -4.0)))
       (if (<= z 7.5e-191)
         t_3
         (if (<= z 1.22e-30)
           (- (* x (* i -4.0)) t_2)
           (if (<= z 1.26e+101)
             t_3
             (* x (- (* 18.0 (* z (* y t))) (* 4.0 i))))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = z * (x * y);
	double t_2 = 27.0 * (j * k);
	double t_3 = (b * c) - t_2;
	double tmp;
	if (z <= -1.65e-47) {
		tmp = (b * c) - ((t * -18.0) * t_1);
	} else if (z <= -3.1e-206) {
		tmp = t * ((18.0 * t_1) + (a * -4.0));
	} else if (z <= 7.5e-191) {
		tmp = t_3;
	} else if (z <= 1.22e-30) {
		tmp = (x * (i * -4.0)) - t_2;
	} else if (z <= 1.26e+101) {
		tmp = t_3;
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (x * y)
    t_2 = 27.0d0 * (j * k)
    t_3 = (b * c) - t_2
    if (z <= (-1.65d-47)) then
        tmp = (b * c) - ((t * (-18.0d0)) * t_1)
    else if (z <= (-3.1d-206)) then
        tmp = t * ((18.0d0 * t_1) + (a * (-4.0d0)))
    else if (z <= 7.5d-191) then
        tmp = t_3
    else if (z <= 1.22d-30) then
        tmp = (x * (i * (-4.0d0))) - t_2
    else if (z <= 1.26d+101) then
        tmp = t_3
    else
        tmp = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = z * (x * y);
	double t_2 = 27.0 * (j * k);
	double t_3 = (b * c) - t_2;
	double tmp;
	if (z <= -1.65e-47) {
		tmp = (b * c) - ((t * -18.0) * t_1);
	} else if (z <= -3.1e-206) {
		tmp = t * ((18.0 * t_1) + (a * -4.0));
	} else if (z <= 7.5e-191) {
		tmp = t_3;
	} else if (z <= 1.22e-30) {
		tmp = (x * (i * -4.0)) - t_2;
	} else if (z <= 1.26e+101) {
		tmp = t_3;
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = z * (x * y)
	t_2 = 27.0 * (j * k)
	t_3 = (b * c) - t_2
	tmp = 0
	if z <= -1.65e-47:
		tmp = (b * c) - ((t * -18.0) * t_1)
	elif z <= -3.1e-206:
		tmp = t * ((18.0 * t_1) + (a * -4.0))
	elif z <= 7.5e-191:
		tmp = t_3
	elif z <= 1.22e-30:
		tmp = (x * (i * -4.0)) - t_2
	elif z <= 1.26e+101:
		tmp = t_3
	else:
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(27.0 * Float64(j * k))
	t_3 = Float64(Float64(b * c) - t_2)
	tmp = 0.0
	if (z <= -1.65e-47)
		tmp = Float64(Float64(b * c) - Float64(Float64(t * -18.0) * t_1));
	elseif (z <= -3.1e-206)
		tmp = Float64(t * Float64(Float64(18.0 * t_1) + Float64(a * -4.0)));
	elseif (z <= 7.5e-191)
		tmp = t_3;
	elseif (z <= 1.22e-30)
		tmp = Float64(Float64(x * Float64(i * -4.0)) - t_2);
	elseif (z <= 1.26e+101)
		tmp = t_3;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = z * (x * y);
	t_2 = 27.0 * (j * k);
	t_3 = (b * c) - t_2;
	tmp = 0.0;
	if (z <= -1.65e-47)
		tmp = (b * c) - ((t * -18.0) * t_1);
	elseif (z <= -3.1e-206)
		tmp = t * ((18.0 * t_1) + (a * -4.0));
	elseif (z <= 7.5e-191)
		tmp = t_3;
	elseif (z <= 1.22e-30)
		tmp = (x * (i * -4.0)) - t_2;
	elseif (z <= 1.26e+101)
		tmp = t_3;
	else
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[z, -1.65e-47], N[(N[(b * c), $MachinePrecision] - N[(N[(t * -18.0), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e-206], N[(t * N[(N[(18.0 * t$95$1), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-191], t$95$3, If[LessEqual[z, 1.22e-30], N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[z, 1.26e+101], t$95$3, N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.65000000000000002e-47

   1. Initial program 86.8%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in x around inf 81.5%

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

      1. *-commutative 81.5%

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

      2. associate-*r* 81.5%

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

      3. associate-*r* 81.5%

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

      4. associate-*l* 81.5%

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

   6. Simplified 81.5%

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

   7. Taylor expanded in x around inf 72.9%

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

      1. associate-*r* 72.9%

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

      2. *-commutative 72.9%

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

   9. Simplified 72.9%

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

   10. Taylor expanded in x around -inf 75.7%

       \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) + b \cdot c} \]
   11. Step-by-step derivation

       1. +-commutative 75.7%

          \[\leadsto \color{blue}{b \cdot c + -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]

       2. mul-1-neg 75.7%

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

       3. unsub-neg 75.7%

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

       4. cancel-sign-sub-inv 75.7%

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

       5. associate-*r* 75.8%

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

       6. metadata-eval 75.8%

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

       7. fma-def 75.8%

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

       8. *-commutative 75.8%

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

   12. Simplified 75.8%

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

   13. Taylor expanded in t around inf 64.4%

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

       1. associate-*r* 64.3%

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

       2. *-commutative 64.3%

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

       3. associate-*r* 63.0%

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

   15. Simplified 63.0%

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

   if -1.65000000000000002e-47 < z < -3.1000000000000003e-206

   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. Taylor expanded in x around 0 90.2%

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

   3. Taylor expanded in t around inf 46.4%

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

      1. cancel-sign-sub-inv 46.4%

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

      2. metadata-eval 46.4%

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

      3. associate-*r* 43.4%

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

   5. Simplified 43.4%

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

   if -3.1000000000000003e-206 < z < 7.4999999999999995e-191 or 1.22e-30 < z < 1.2600000000000001e101

   1. Initial program 87.3%

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

   2. Taylor expanded in t around 0 69.4%

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

   3. Taylor expanded in i around 0 61.0%

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

   if 7.4999999999999995e-191 < z < 1.22e-30

   1. Initial program 88.7%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in a around 0 77.7%

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

   4. Taylor expanded in i around inf 61.2%

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

      1. *-commutative 61.2%

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

      2. *-commutative 61.2%

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

      3. associate-*r* 61.2%

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

   6. Simplified 61.2%

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

   if 1.2600000000000001e101 < z

   1. Initial program 73.2%

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

   3. Simplified 73.4%

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

   4. Taylor expanded in x around inf 64.2%

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

      1. pow1 75.1%

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

   6. Applied egg-rr 64.2%

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

      1. unpow1 75.1%

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

      2. associate-*r* 80.7%

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

   8. Simplified 66.0%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-47}:\\ \;\;\;\;b \cdot c - \left(t \cdot -18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-206}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(x \cdot y\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-191}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+101}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 15: 60.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;z \leq -2.65 \cdot 10^{-27}:\\ \;\;\;\;b \cdot c - \left(t \cdot -18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k))))
   (if (<= z -2.65e-27)
     (- (* b c) (* (* t -18.0) (* z (* x y))))
     (if (<= z 3.9e-191)
       t_1
       (if (<= z 1.32e-80)
         (- (* x (* i -4.0)) (* 27.0 (* j k)))
         (if (<= z 9.5e+123)
           t_1
           (* x (- (* 18.0 (* z (* y t))) (* 4.0 i)))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	double tmp;
	if (z <= -2.65e-27) {
		tmp = (b * c) - ((t * -18.0) * (z * (x * y)));
	} else if (z <= 3.9e-191) {
		tmp = t_1;
	} else if (z <= 1.32e-80) {
		tmp = (x * (i * -4.0)) - (27.0 * (j * k));
	} else if (z <= 9.5e+123) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    if (z <= (-2.65d-27)) then
        tmp = (b * c) - ((t * (-18.0d0)) * (z * (x * y)))
    else if (z <= 3.9d-191) then
        tmp = t_1
    else if (z <= 1.32d-80) then
        tmp = (x * (i * (-4.0d0))) - (27.0d0 * (j * k))
    else if (z <= 9.5d+123) then
        tmp = t_1
    else
        tmp = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	double tmp;
	if (z <= -2.65e-27) {
		tmp = (b * c) - ((t * -18.0) * (z * (x * y)));
	} else if (z <= 3.9e-191) {
		tmp = t_1;
	} else if (z <= 1.32e-80) {
		tmp = (x * (i * -4.0)) - (27.0 * (j * k));
	} else if (z <= 9.5e+123) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	tmp = 0
	if z <= -2.65e-27:
		tmp = (b * c) - ((t * -18.0) * (z * (x * y)))
	elif z <= 3.9e-191:
		tmp = t_1
	elif z <= 1.32e-80:
		tmp = (x * (i * -4.0)) - (27.0 * (j * k))
	elif z <= 9.5e+123:
		tmp = t_1
	else:
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k))
	tmp = 0.0
	if (z <= -2.65e-27)
		tmp = Float64(Float64(b * c) - Float64(Float64(t * -18.0) * Float64(z * Float64(x * y))));
	elseif (z <= 3.9e-191)
		tmp = t_1;
	elseif (z <= 1.32e-80)
		tmp = Float64(Float64(x * Float64(i * -4.0)) - Float64(27.0 * Float64(j * k)));
	elseif (z <= 9.5e+123)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	tmp = 0.0;
	if (z <= -2.65e-27)
		tmp = (b * c) - ((t * -18.0) * (z * (x * y)));
	elseif (z <= 3.9e-191)
		tmp = t_1;
	elseif (z <= 1.32e-80)
		tmp = (x * (i * -4.0)) - (27.0 * (j * k));
	elseif (z <= 9.5e+123)
		tmp = t_1;
	else
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.65e-27], N[(N[(b * c), $MachinePrecision] - N[(N[(t * -18.0), $MachinePrecision] * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e-191], t$95$1, If[LessEqual[z, 1.32e-80], N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+123], t$95$1, N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.65000000000000003e-27

   1. Initial program 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in x around inf 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-*r* 80.3%

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

      3. associate-*r* 80.4%

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

      4. associate-*l* 80.4%

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

   6. Simplified 80.4%

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

   7. Taylor expanded in x around inf 72.7%

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

      1. associate-*r* 72.7%

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

      2. *-commutative 72.7%

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

   9. Simplified 72.7%

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

   10. Taylor expanded in x around -inf 75.7%

       \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) + b \cdot c} \]
   11. Step-by-step derivation

       1. +-commutative 75.7%

          \[\leadsto \color{blue}{b \cdot c + -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]

       2. mul-1-neg 75.7%

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

       3. unsub-neg 75.7%

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

       4. cancel-sign-sub-inv 75.7%

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

       5. associate-*r* 75.7%

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

       6. metadata-eval 75.7%

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

       7. fma-def 75.7%

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

       8. *-commutative 75.7%

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

   12. Simplified 75.7%

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

   13. Taylor expanded in t around inf 66.7%

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

       1. associate-*r* 66.6%

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

       2. *-commutative 66.6%

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

       3. associate-*r* 65.2%

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

   15. Simplified 65.2%

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

   if -2.65000000000000003e-27 < z < 3.8999999999999999e-191 or 1.31999999999999995e-80 < z < 9.4999999999999996e123

   1. Initial program 84.8%

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

   2. Taylor expanded in x around 0 71.1%

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

   if 3.8999999999999999e-191 < z < 1.31999999999999995e-80

   1. Initial program 87.7%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in a around 0 87.6%

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

   4. Taylor expanded in i around inf 75.8%

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

      1. *-commutative 75.8%

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

      2. *-commutative 75.8%

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

      3. associate-*r* 75.8%

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

   6. Simplified 75.8%

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

   if 9.4999999999999996e123 < z

   1. Initial program 72.9%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in x around inf 69.1%

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

      1. pow1 75.1%

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

   6. Applied egg-rr 69.1%

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

      1. unpow1 75.1%

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

      2. associate-*r* 79.5%

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

   8. Simplified 71.3%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-27}:\\ \;\;\;\;b \cdot c - \left(t \cdot -18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-191}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+123}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 16: 62.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := \left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{-25}:\\ \;\;\;\;b \cdot c - \left(t \cdot -18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-284}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-79}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)) (t_2 (- (- (* b c) (* 4.0 (* t a))) t_1)))
   (if (<= z -1.02e-25)
     (- (* b c) (* (* t -18.0) (* z (* x y))))
     (if (<= z -1.15e-284)
       t_2
       (if (<= z 1.22e-79)
         (- (- (* b c) (* 4.0 (* x i))) t_1)
         (if (<= z 1.25e+118)
           t_2
           (* x (- (* 18.0 (* z (* y t))) (* 4.0 i)))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = ((b * c) - (4.0 * (t * a))) - t_1;
	double tmp;
	if (z <= -1.02e-25) {
		tmp = (b * c) - ((t * -18.0) * (z * (x * y)));
	} else if (z <= -1.15e-284) {
		tmp = t_2;
	} else if (z <= 1.22e-79) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (z <= 1.25e+118) {
		tmp = t_2;
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * 27.0d0) * k
    t_2 = ((b * c) - (4.0d0 * (t * a))) - t_1
    if (z <= (-1.02d-25)) then
        tmp = (b * c) - ((t * (-18.0d0)) * (z * (x * y)))
    else if (z <= (-1.15d-284)) then
        tmp = t_2
    else if (z <= 1.22d-79) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else if (z <= 1.25d+118) then
        tmp = t_2
    else
        tmp = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double t_2 = ((b * c) - (4.0 * (t * a))) - t_1;
	double tmp;
	if (z <= -1.02e-25) {
		tmp = (b * c) - ((t * -18.0) * (z * (x * y)));
	} else if (z <= -1.15e-284) {
		tmp = t_2;
	} else if (z <= 1.22e-79) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (z <= 1.25e+118) {
		tmp = t_2;
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	t_2 = ((b * c) - (4.0 * (t * a))) - t_1
	tmp = 0
	if z <= -1.02e-25:
		tmp = (b * c) - ((t * -18.0) * (z * (x * y)))
	elif z <= -1.15e-284:
		tmp = t_2
	elif z <= 1.22e-79:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	elif z <= 1.25e+118:
		tmp = t_2
	else:
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	t_2 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1)
	tmp = 0.0
	if (z <= -1.02e-25)
		tmp = Float64(Float64(b * c) - Float64(Float64(t * -18.0) * Float64(z * Float64(x * y))));
	elseif (z <= -1.15e-284)
		tmp = t_2;
	elseif (z <= 1.22e-79)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	elseif (z <= 1.25e+118)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	t_2 = ((b * c) - (4.0 * (t * a))) - t_1;
	tmp = 0.0;
	if (z <= -1.02e-25)
		tmp = (b * c) - ((t * -18.0) * (z * (x * y)));
	elseif (z <= -1.15e-284)
		tmp = t_2;
	elseif (z <= 1.22e-79)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	elseif (z <= 1.25e+118)
		tmp = t_2;
	else
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[z, -1.02e-25], N[(N[(b * c), $MachinePrecision] - N[(N[(t * -18.0), $MachinePrecision] * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e-284], t$95$2, If[LessEqual[z, 1.22e-79], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[z, 1.25e+118], t$95$2, N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.01999999999999998e-25

   1. Initial program 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in x around inf 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-*r* 80.3%

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

      3. associate-*r* 80.4%

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

      4. associate-*l* 80.4%

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

   6. Simplified 80.4%

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

   7. Taylor expanded in x around inf 72.7%

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

      1. associate-*r* 72.7%

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

      2. *-commutative 72.7%

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

   9. Simplified 72.7%

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

   10. Taylor expanded in x around -inf 75.7%

       \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right) + b \cdot c} \]
   11. Step-by-step derivation

       1. +-commutative 75.7%

          \[\leadsto \color{blue}{b \cdot c + -1 \cdot \left(x \cdot \left(-18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - -4 \cdot i\right)\right)} \]

       2. mul-1-neg 75.7%

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

       3. unsub-neg 75.7%

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

       4. cancel-sign-sub-inv 75.7%

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

       5. associate-*r* 75.7%

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

       6. metadata-eval 75.7%

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

       7. fma-def 75.7%

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

       8. *-commutative 75.7%

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

   12. Simplified 75.7%

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

   13. Taylor expanded in t around inf 66.7%

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

       1. associate-*r* 66.6%

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

       2. *-commutative 66.6%

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

       3. associate-*r* 65.2%

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

   15. Simplified 65.2%

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

   if -1.01999999999999998e-25 < z < -1.15e-284 or 1.22e-79 < z < 1.24999999999999993e118

   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. Taylor expanded in x around 0 70.4%

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

   if -1.15e-284 < z < 1.22e-79

   1. Initial program 84.6%

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

   2. Taylor expanded in t around 0 74.4%

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

   if 1.24999999999999993e118 < z

   1. Initial program 73.5%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in x around inf 69.2%

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

      1. pow1 75.6%

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

   6. Applied egg-rr 69.2%

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

      1. unpow1 75.6%

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

      2. associate-*r* 79.9%

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

   8. Simplified 71.3%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-25}:\\ \;\;\;\;b \cdot c - \left(t \cdot -18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-284}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-79}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+118}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 17: 48.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := b \cdot c - t_1\\ \mathbf{if}\;z \leq -6 \cdot 10^{-207}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right) - a \cdot 4\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.92 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 27.0 (* j k))) (t_2 (- (* b c) t_1)))
   (if (<= z -6e-207)
     (* t (- (* (* x y) (* 18.0 z)) (* a 4.0)))
     (if (<= z 3.5e-192)
       t_2
       (if (<= z 1.92e-31)
         (- (* x (* i -4.0)) t_1)
         (if (<= z 4e+115) t_2 (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double t_2 = (b * c) - t_1;
	double tmp;
	if (z <= -6e-207) {
		tmp = t * (((x * y) * (18.0 * z)) - (a * 4.0));
	} else if (z <= 3.5e-192) {
		tmp = t_2;
	} else if (z <= 1.92e-31) {
		tmp = (x * (i * -4.0)) - t_1;
	} else if (z <= 4e+115) {
		tmp = t_2;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 27.0d0 * (j * k)
    t_2 = (b * c) - t_1
    if (z <= (-6d-207)) then
        tmp = t * (((x * y) * (18.0d0 * z)) - (a * 4.0d0))
    else if (z <= 3.5d-192) then
        tmp = t_2
    else if (z <= 1.92d-31) then
        tmp = (x * (i * (-4.0d0))) - t_1
    else if (z <= 4d+115) then
        tmp = t_2
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double t_2 = (b * c) - t_1;
	double tmp;
	if (z <= -6e-207) {
		tmp = t * (((x * y) * (18.0 * z)) - (a * 4.0));
	} else if (z <= 3.5e-192) {
		tmp = t_2;
	} else if (z <= 1.92e-31) {
		tmp = (x * (i * -4.0)) - t_1;
	} else if (z <= 4e+115) {
		tmp = t_2;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	t_2 = (b * c) - t_1
	tmp = 0
	if z <= -6e-207:
		tmp = t * (((x * y) * (18.0 * z)) - (a * 4.0))
	elif z <= 3.5e-192:
		tmp = t_2
	elif z <= 1.92e-31:
		tmp = (x * (i * -4.0)) - t_1
	elif z <= 4e+115:
		tmp = t_2
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	t_2 = Float64(Float64(b * c) - t_1)
	tmp = 0.0
	if (z <= -6e-207)
		tmp = Float64(t * Float64(Float64(Float64(x * y) * Float64(18.0 * z)) - Float64(a * 4.0)));
	elseif (z <= 3.5e-192)
		tmp = t_2;
	elseif (z <= 1.92e-31)
		tmp = Float64(Float64(x * Float64(i * -4.0)) - t_1);
	elseif (z <= 4e+115)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 27.0 * (j * k);
	t_2 = (b * c) - t_1;
	tmp = 0.0;
	if (z <= -6e-207)
		tmp = t * (((x * y) * (18.0 * z)) - (a * 4.0));
	elseif (z <= 3.5e-192)
		tmp = t_2;
	elseif (z <= 1.92e-31)
		tmp = (x * (i * -4.0)) - t_1;
	elseif (z <= 4e+115)
		tmp = t_2;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[z, -6e-207], N[(t * N[(N[(N[(x * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-192], t$95$2, If[LessEqual[z, 1.92e-31], N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[z, 4e+115], t$95$2, N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.9999999999999999e-207

   1. Initial program 85.0%

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

   2. Taylor expanded in x around 0 86.9%

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

   3. Taylor expanded in t around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-*r* 51.7%

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

      3. associate-*r* 51.7%

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

      4. pow1 51.7%

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

      5. associate-*l* 51.6%

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

   5. Applied egg-rr 51.6%

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

      1. unpow1 51.6%

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

      2. associate-*r* 51.7%

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

   7. Simplified 51.7%

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

   if -5.9999999999999999e-207 < z < 3.50000000000000014e-192 or 1.9200000000000001e-31 < z < 4.0000000000000001e115

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0 69.5%

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

   3. Taylor expanded in i around 0 58.0%

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

   if 3.50000000000000014e-192 < z < 1.9200000000000001e-31

   1. Initial program 88.7%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in a around 0 77.7%

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

   4. Taylor expanded in i around inf 61.2%

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

      1. *-commutative 61.2%

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

      2. *-commutative 61.2%

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

      3. associate-*r* 61.2%

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

   6. Simplified 61.2%

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

   if 4.0000000000000001e115 < z

   1. Initial program 74.1%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in x around inf 67.7%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-207}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right) - a \cdot 4\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-192}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 1.92 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+115}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 18: 49.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot k\right)\\ t_2 := b \cdot c - t_1\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{-206}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right) - a \cdot 4\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+101}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 27.0 (* j k))) (t_2 (- (* b c) t_1)))
   (if (<= z -2.15e-206)
     (* t (- (* (* x y) (* 18.0 z)) (* a 4.0)))
     (if (<= z 4.2e-194)
       t_2
       (if (<= z 2.15e-30)
         (- (* x (* i -4.0)) t_1)
         (if (<= z 1.15e+101)
           t_2
           (* x (- (* 18.0 (* z (* y t))) (* 4.0 i)))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double t_2 = (b * c) - t_1;
	double tmp;
	if (z <= -2.15e-206) {
		tmp = t * (((x * y) * (18.0 * z)) - (a * 4.0));
	} else if (z <= 4.2e-194) {
		tmp = t_2;
	} else if (z <= 2.15e-30) {
		tmp = (x * (i * -4.0)) - t_1;
	} else if (z <= 1.15e+101) {
		tmp = t_2;
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 27.0d0 * (j * k)
    t_2 = (b * c) - t_1
    if (z <= (-2.15d-206)) then
        tmp = t * (((x * y) * (18.0d0 * z)) - (a * 4.0d0))
    else if (z <= 4.2d-194) then
        tmp = t_2
    else if (z <= 2.15d-30) then
        tmp = (x * (i * (-4.0d0))) - t_1
    else if (z <= 1.15d+101) then
        tmp = t_2
    else
        tmp = x * ((18.0d0 * (z * (y * t))) - (4.0d0 * i))
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 27.0 * (j * k);
	double t_2 = (b * c) - t_1;
	double tmp;
	if (z <= -2.15e-206) {
		tmp = t * (((x * y) * (18.0 * z)) - (a * 4.0));
	} else if (z <= 4.2e-194) {
		tmp = t_2;
	} else if (z <= 2.15e-30) {
		tmp = (x * (i * -4.0)) - t_1;
	} else if (z <= 1.15e+101) {
		tmp = t_2;
	} else {
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 27.0 * (j * k)
	t_2 = (b * c) - t_1
	tmp = 0
	if z <= -2.15e-206:
		tmp = t * (((x * y) * (18.0 * z)) - (a * 4.0))
	elif z <= 4.2e-194:
		tmp = t_2
	elif z <= 2.15e-30:
		tmp = (x * (i * -4.0)) - t_1
	elif z <= 1.15e+101:
		tmp = t_2
	else:
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(27.0 * Float64(j * k))
	t_2 = Float64(Float64(b * c) - t_1)
	tmp = 0.0
	if (z <= -2.15e-206)
		tmp = Float64(t * Float64(Float64(Float64(x * y) * Float64(18.0 * z)) - Float64(a * 4.0)));
	elseif (z <= 4.2e-194)
		tmp = t_2;
	elseif (z <= 2.15e-30)
		tmp = Float64(Float64(x * Float64(i * -4.0)) - t_1);
	elseif (z <= 1.15e+101)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 27.0 * (j * k);
	t_2 = (b * c) - t_1;
	tmp = 0.0;
	if (z <= -2.15e-206)
		tmp = t * (((x * y) * (18.0 * z)) - (a * 4.0));
	elseif (z <= 4.2e-194)
		tmp = t_2;
	elseif (z <= 2.15e-30)
		tmp = (x * (i * -4.0)) - t_1;
	elseif (z <= 1.15e+101)
		tmp = t_2;
	else
		tmp = x * ((18.0 * (z * (y * t))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[z, -2.15e-206], N[(t * N[(N[(N[(x * y), $MachinePrecision] * N[(18.0 * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-194], t$95$2, If[LessEqual[z, 2.15e-30], N[(N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[z, 1.15e+101], t$95$2, N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.15000000000000012e-206

   1. Initial program 85.0%

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

   2. Taylor expanded in x around 0 86.9%

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

   3. Taylor expanded in t around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-*r* 51.7%

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

      3. associate-*r* 51.7%

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

      4. pow1 51.7%

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

      5. associate-*l* 51.6%

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

   5. Applied egg-rr 51.6%

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

      1. unpow1 51.6%

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

      2. associate-*r* 51.7%

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

   7. Simplified 51.7%

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

   if -2.15000000000000012e-206 < z < 4.2e-194 or 2.14999999999999983e-30 < z < 1.1500000000000001e101

   1. Initial program 87.3%

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

   2. Taylor expanded in t around 0 69.4%

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

   3. Taylor expanded in i around 0 61.0%

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

   if 4.2e-194 < z < 2.14999999999999983e-30

   1. Initial program 88.7%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in a around 0 77.7%

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

   4. Taylor expanded in i around inf 61.2%

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

      1. *-commutative 61.2%

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

      2. *-commutative 61.2%

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

      3. associate-*r* 61.2%

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

   6. Simplified 61.2%

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

   if 1.1500000000000001e101 < z

   1. Initial program 73.2%

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

   3. Simplified 73.4%

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

   4. Taylor expanded in x around inf 64.2%

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

      1. pow1 75.1%

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

   6. Applied egg-rr 64.2%

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

      1. unpow1 75.1%

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

      2. associate-*r* 80.7%

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

   8. Simplified 66.0%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-206}:\\ \;\;\;\;t \cdot \left(\left(x \cdot y\right) \cdot \left(18 \cdot z\right) - a \cdot 4\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-194}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+101}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 19: 32.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-190}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+118}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* t (* z (* x y))))))
   (if (<= z -3.6e-78)
     t_1
     (if (<= z -1.4e-231)
       (* t (* a -4.0))
       (if (<= z 4.5e-190)
         (* b c)
         (if (<= z 2.9e-28)
           (* x (* i -4.0))
           (if (<= z 1.95e+118) (* b c) t_1)))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (z * (x * y)));
	double tmp;
	if (z <= -3.6e-78) {
		tmp = t_1;
	} else if (z <= -1.4e-231) {
		tmp = t * (a * -4.0);
	} else if (z <= 4.5e-190) {
		tmp = b * c;
	} else if (z <= 2.9e-28) {
		tmp = x * (i * -4.0);
	} else if (z <= 1.95e+118) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 18.0d0 * (t * (z * (x * y)))
    if (z <= (-3.6d-78)) then
        tmp = t_1
    else if (z <= (-1.4d-231)) then
        tmp = t * (a * (-4.0d0))
    else if (z <= 4.5d-190) then
        tmp = b * c
    else if (z <= 2.9d-28) then
        tmp = x * (i * (-4.0d0))
    else if (z <= 1.95d+118) then
        tmp = b * c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (z * (x * y)));
	double tmp;
	if (z <= -3.6e-78) {
		tmp = t_1;
	} else if (z <= -1.4e-231) {
		tmp = t * (a * -4.0);
	} else if (z <= 4.5e-190) {
		tmp = b * c;
	} else if (z <= 2.9e-28) {
		tmp = x * (i * -4.0);
	} else if (z <= 1.95e+118) {
		tmp = b * c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (z * (x * y)))
	tmp = 0
	if z <= -3.6e-78:
		tmp = t_1
	elif z <= -1.4e-231:
		tmp = t * (a * -4.0)
	elif z <= 4.5e-190:
		tmp = b * c
	elif z <= 2.9e-28:
		tmp = x * (i * -4.0)
	elif z <= 1.95e+118:
		tmp = b * c
	else:
		tmp = t_1
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(z * Float64(x * y))))
	tmp = 0.0
	if (z <= -3.6e-78)
		tmp = t_1;
	elseif (z <= -1.4e-231)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (z <= 4.5e-190)
		tmp = Float64(b * c);
	elseif (z <= 2.9e-28)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (z <= 1.95e+118)
		tmp = Float64(b * c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (t * (z * (x * y)));
	tmp = 0.0;
	if (z <= -3.6e-78)
		tmp = t_1;
	elseif (z <= -1.4e-231)
		tmp = t * (a * -4.0);
	elseif (z <= 4.5e-190)
		tmp = b * c;
	elseif (z <= 2.9e-28)
		tmp = x * (i * -4.0);
	elseif (z <= 1.95e+118)
		tmp = b * c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e-78], t$95$1, If[LessEqual[z, -1.4e-231], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-190], N[(b * c), $MachinePrecision], If[LessEqual[z, 2.9e-28], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+118], N[(b * c), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6000000000000002e-78 or 1.95e118 < z

   1. Initial program 82.1%

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

   2. Taylor expanded in x around 0 82.0%

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

   3. Taylor expanded in a around 0 79.2%

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

   4. Taylor expanded in t around inf 48.6%

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

      1. associate-*r* 48.6%

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

   6. Simplified 48.6%

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

   if -3.6000000000000002e-78 < z < -1.3999999999999999e-231

   1. Initial program 80.3%

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

   2. Taylor expanded in x around 0 91.9%

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

   3. Taylor expanded in a around inf 33.8%

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

      1. associate-*r* 33.8%

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

      2. *-commutative 33.8%

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

   5. Simplified 33.8%

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

   if -1.3999999999999999e-231 < z < 4.50000000000000021e-190 or 2.90000000000000013e-28 < z < 1.95e118

   1. Initial program 85.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in b around inf 32.2%

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

   if 4.50000000000000021e-190 < z < 2.90000000000000013e-28

   1. Initial program 89.0%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in i around inf 43.2%

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

      1. associate-*r* 43.2%

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

      2. *-commutative 43.2%

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

   6. Simplified 43.2%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-78}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-190}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+118}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 20: 32.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-69}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-227}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-195}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+117}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z -1.8e-69)
   (* 18.0 (* x (* t (* y z))))
   (if (<= z -5.4e-227)
     (* t (* a -4.0))
     (if (<= z 1.8e-195)
       (* b c)
       (if (<= z 5.8e-27)
         (* x (* i -4.0))
         (if (<= z 9e+117) (* b c) (* 18.0 (* t (* z (* x y))))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= -1.8e-69) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (z <= -5.4e-227) {
		tmp = t * (a * -4.0);
	} else if (z <= 1.8e-195) {
		tmp = b * c;
	} else if (z <= 5.8e-27) {
		tmp = x * (i * -4.0);
	} else if (z <= 9e+117) {
		tmp = b * c;
	} else {
		tmp = 18.0 * (t * (z * (x * y)));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (z <= (-1.8d-69)) then
        tmp = 18.0d0 * (x * (t * (y * z)))
    else if (z <= (-5.4d-227)) then
        tmp = t * (a * (-4.0d0))
    else if (z <= 1.8d-195) then
        tmp = b * c
    else if (z <= 5.8d-27) then
        tmp = x * (i * (-4.0d0))
    else if (z <= 9d+117) then
        tmp = b * c
    else
        tmp = 18.0d0 * (t * (z * (x * y)))
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= -1.8e-69) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (z <= -5.4e-227) {
		tmp = t * (a * -4.0);
	} else if (z <= 1.8e-195) {
		tmp = b * c;
	} else if (z <= 5.8e-27) {
		tmp = x * (i * -4.0);
	} else if (z <= 9e+117) {
		tmp = b * c;
	} else {
		tmp = 18.0 * (t * (z * (x * y)));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if z <= -1.8e-69:
		tmp = 18.0 * (x * (t * (y * z)))
	elif z <= -5.4e-227:
		tmp = t * (a * -4.0)
	elif z <= 1.8e-195:
		tmp = b * c
	elif z <= 5.8e-27:
		tmp = x * (i * -4.0)
	elif z <= 9e+117:
		tmp = b * c
	else:
		tmp = 18.0 * (t * (z * (x * y)))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= -1.8e-69)
		tmp = Float64(18.0 * Float64(x * Float64(t * Float64(y * z))));
	elseif (z <= -5.4e-227)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (z <= 1.8e-195)
		tmp = Float64(b * c);
	elseif (z <= 5.8e-27)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (z <= 9e+117)
		tmp = Float64(b * c);
	else
		tmp = Float64(18.0 * Float64(t * Float64(z * Float64(x * y))));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (z <= -1.8e-69)
		tmp = 18.0 * (x * (t * (y * z)));
	elseif (z <= -5.4e-227)
		tmp = t * (a * -4.0);
	elseif (z <= 1.8e-195)
		tmp = b * c;
	elseif (z <= 5.8e-27)
		tmp = x * (i * -4.0);
	elseif (z <= 9e+117)
		tmp = b * c;
	else
		tmp = 18.0 * (t * (z * (x * y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, -1.8e-69], N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.4e-227], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-195], N[(b * c), $MachinePrecision], If[LessEqual[z, 5.8e-27], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+117], N[(b * c), $MachinePrecision], N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.80000000000000009e-69

   1. Initial program 86.6%

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

   2. Taylor expanded in x around 0 85.2%

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

   3. Taylor expanded in a around 0 81.7%

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

   4. Taylor expanded in t around inf 45.9%

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

      1. *-commutative 45.9%

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

      2. associate-*l* 45.9%

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

      3. *-commutative 45.9%

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

   6. Simplified 45.9%

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

   if -1.80000000000000009e-69 < z < -5.3999999999999999e-227

   1. Initial program 82.4%

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

   2. Taylor expanded in x around 0 92.7%

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

   3. Taylor expanded in a around inf 30.3%

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

      1. associate-*r* 30.3%

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

      2. *-commutative 30.3%

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

   5. Simplified 30.3%

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

   if -5.3999999999999999e-227 < z < 1.8e-195 or 5.80000000000000008e-27 < z < 9e117

   1. Initial program 85.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in b around inf 32.2%

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

   if 1.8e-195 < z < 5.80000000000000008e-27

   1. Initial program 89.0%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in i around inf 43.2%

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

      1. associate-*r* 43.2%

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

      2. *-commutative 43.2%

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

   6. Simplified 43.2%

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

   if 9e117 < z

   1. Initial program 73.5%

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

   2. Taylor expanded in x around 0 75.6%

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

   3. Taylor expanded in a around 0 73.8%

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

   4. Taylor expanded in t around inf 56.2%

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

      1. associate-*r* 58.2%

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

   6. Simplified 58.2%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-69}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-227}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-195}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+117}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 21: 32.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-75}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-227}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-195}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+119}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z -2.3e-75)
   (* 18.0 (* x (* t (* y z))))
   (if (<= z -2.1e-227)
     (* t (* a -4.0))
     (if (<= z 2.1e-195)
       (* b c)
       (if (<= z 3.7e-28)
         (* x (* i -4.0))
         (if (<= z 4.4e+119) (* b c) (* x (* 18.0 (* y (* z t))))))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= -2.3e-75) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (z <= -2.1e-227) {
		tmp = t * (a * -4.0);
	} else if (z <= 2.1e-195) {
		tmp = b * c;
	} else if (z <= 3.7e-28) {
		tmp = x * (i * -4.0);
	} else if (z <= 4.4e+119) {
		tmp = b * c;
	} else {
		tmp = x * (18.0 * (y * (z * t)));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (z <= (-2.3d-75)) then
        tmp = 18.0d0 * (x * (t * (y * z)))
    else if (z <= (-2.1d-227)) then
        tmp = t * (a * (-4.0d0))
    else if (z <= 2.1d-195) then
        tmp = b * c
    else if (z <= 3.7d-28) then
        tmp = x * (i * (-4.0d0))
    else if (z <= 4.4d+119) then
        tmp = b * c
    else
        tmp = x * (18.0d0 * (y * (z * t)))
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= -2.3e-75) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (z <= -2.1e-227) {
		tmp = t * (a * -4.0);
	} else if (z <= 2.1e-195) {
		tmp = b * c;
	} else if (z <= 3.7e-28) {
		tmp = x * (i * -4.0);
	} else if (z <= 4.4e+119) {
		tmp = b * c;
	} else {
		tmp = x * (18.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if z <= -2.3e-75:
		tmp = 18.0 * (x * (t * (y * z)))
	elif z <= -2.1e-227:
		tmp = t * (a * -4.0)
	elif z <= 2.1e-195:
		tmp = b * c
	elif z <= 3.7e-28:
		tmp = x * (i * -4.0)
	elif z <= 4.4e+119:
		tmp = b * c
	else:
		tmp = x * (18.0 * (y * (z * t)))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= -2.3e-75)
		tmp = Float64(18.0 * Float64(x * Float64(t * Float64(y * z))));
	elseif (z <= -2.1e-227)
		tmp = Float64(t * Float64(a * -4.0));
	elseif (z <= 2.1e-195)
		tmp = Float64(b * c);
	elseif (z <= 3.7e-28)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (z <= 4.4e+119)
		tmp = Float64(b * c);
	else
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (z <= -2.3e-75)
		tmp = 18.0 * (x * (t * (y * z)));
	elseif (z <= -2.1e-227)
		tmp = t * (a * -4.0);
	elseif (z <= 2.1e-195)
		tmp = b * c;
	elseif (z <= 3.7e-28)
		tmp = x * (i * -4.0);
	elseif (z <= 4.4e+119)
		tmp = b * c;
	else
		tmp = x * (18.0 * (y * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, -2.3e-75], N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e-227], N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-195], N[(b * c), $MachinePrecision], If[LessEqual[z, 3.7e-28], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+119], N[(b * c), $MachinePrecision], N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.3e-75

   1. Initial program 86.7%

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

   2. Taylor expanded in x around 0 85.4%

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

   3. Taylor expanded in a around 0 81.9%

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

   4. Taylor expanded in t around inf 45.3%

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

      1. *-commutative 45.3%

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

      2. associate-*l* 45.3%

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

      3. *-commutative 45.3%

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

   6. Simplified 45.3%

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

   if -2.3e-75 < z < -2.1e-227

   1. Initial program 81.8%

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

   2. Taylor expanded in x around 0 92.5%

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

   3. Taylor expanded in a around inf 31.4%

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

      1. associate-*r* 31.4%

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

      2. *-commutative 31.4%

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

   5. Simplified 31.4%

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

   if -2.1e-227 < z < 2.1e-195 or 3.7000000000000002e-28 < z < 4.4000000000000003e119

   1. Initial program 85.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in b around inf 32.2%

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

   if 2.1e-195 < z < 3.7000000000000002e-28

   1. Initial program 89.0%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in i around inf 43.2%

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

      1. associate-*r* 43.2%

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

      2. *-commutative 43.2%

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

   6. Simplified 43.2%

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

   if 4.4000000000000003e119 < z

   1. Initial program 73.5%

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

   2. Taylor expanded in x around 0 75.6%

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

   3. Taylor expanded in a around 0 73.8%

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

   4. Taylor expanded in t around inf 56.2%

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

      1. metadata-eval 56.2%

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

      2. distribute-lft-neg-in 56.2%

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

      3. *-commutative 56.2%

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

      4. associate-*r* 57.9%

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

      5. associate-*l* 57.9%

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

      6. *-commutative 57.9%

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

      7. distribute-rgt-neg-in 57.9%

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

      8. distribute-lft-neg-in 57.9%

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

      9. metadata-eval 57.9%

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

      10. *-commutative 57.9%

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

      11. associate-*r* 61.9%

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

   6. Simplified 61.9%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-75}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-227}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-195}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+119}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 22: 46.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+19}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+134}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z -7.4e+19)
   (* 18.0 (* x (* t (* y z))))
   (if (<= z 8.2e+134)
     (- (* b c) (* 4.0 (* x i)))
     (* x (* 18.0 (* y (* z t)))))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= -7.4e+19) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (z <= 8.2e+134) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = x * (18.0 * (y * (z * t)));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (z <= (-7.4d+19)) then
        tmp = 18.0d0 * (x * (t * (y * z)))
    else if (z <= 8.2d+134) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = x * (18.0d0 * (y * (z * t)))
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= -7.4e+19) {
		tmp = 18.0 * (x * (t * (y * z)));
	} else if (z <= 8.2e+134) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = x * (18.0 * (y * (z * t)));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if z <= -7.4e+19:
		tmp = 18.0 * (x * (t * (y * z)))
	elif z <= 8.2e+134:
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = x * (18.0 * (y * (z * t)))
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= -7.4e+19)
		tmp = Float64(18.0 * Float64(x * Float64(t * Float64(y * z))));
	elseif (z <= 8.2e+134)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(x * Float64(18.0 * Float64(y * Float64(z * t))));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (z <= -7.4e+19)
		tmp = 18.0 * (x * (t * (y * z)));
	elseif (z <= 8.2e+134)
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = x * (18.0 * (y * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, -7.4e+19], N[(18.0 * N[(x * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+134], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.4e19

   1. Initial program 86.6%

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

   2. Taylor expanded in x around 0 84.9%

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

   3. Taylor expanded in a around 0 80.3%

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

   4. Taylor expanded in t around inf 48.7%

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

      1. *-commutative 48.7%

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

      2. associate-*l* 48.7%

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

      3. *-commutative 48.7%

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

   6. Simplified 48.7%

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

   if -7.4e19 < z < 8.2000000000000007e134

   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. Taylor expanded in t around 0 65.4%

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

   3. Taylor expanded in j around 0 47.5%

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

   if 8.2000000000000007e134 < z

   1. Initial program 71.6%

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

   2. Taylor expanded in x around 0 73.9%

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

   3. Taylor expanded in a around 0 72.0%

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

   4. Taylor expanded in t around inf 58.4%

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

      1. metadata-eval 58.4%

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

      2. distribute-lft-neg-in 58.4%

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

      3. *-commutative 58.4%

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

      4. associate-*r* 60.2%

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

      5. associate-*l* 60.3%

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

      6. *-commutative 60.3%

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

      7. distribute-rgt-neg-in 60.3%

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

      8. distribute-lft-neg-in 60.3%

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

      9. metadata-eval 60.3%

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

      10. *-commutative 60.3%

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

      11. associate-*r* 64.5%

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

   6. Simplified 64.5%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+19}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+134}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 23: 32.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-260}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+141}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= a -5.6e+83)
     t_1
     (if (<= a 2.45e-260)
       (* b c)
       (if (<= a 1.55e+141) (* j (* k -27.0)) t_1)))))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (a <= -5.6e+83) {
		tmp = t_1;
	} else if (a <= 2.45e-260) {
		tmp = b * c;
	} else if (a <= 1.55e+141) {
		tmp = j * (k * -27.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (a <= (-5.6d+83)) then
        tmp = t_1
    else if (a <= 2.45d-260) then
        tmp = b * c
    else if (a <= 1.55d+141) then
        tmp = j * (k * (-27.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (a <= -5.6e+83) {
		tmp = t_1;
	} else if (a <= 2.45e-260) {
		tmp = b * c;
	} else if (a <= 1.55e+141) {
		tmp = j * (k * -27.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if a <= -5.6e+83:
		tmp = t_1
	elif a <= 2.45e-260:
		tmp = b * c
	elif a <= 1.55e+141:
		tmp = j * (k * -27.0)
	else:
		tmp = t_1
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (a <= -5.6e+83)
		tmp = t_1;
	elseif (a <= 2.45e-260)
		tmp = Float64(b * c);
	elseif (a <= 1.55e+141)
		tmp = Float64(j * Float64(k * -27.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (a <= -5.6e+83)
		tmp = t_1;
	elseif (a <= 2.45e-260)
		tmp = b * c;
	elseif (a <= 1.55e+141)
		tmp = j * (k * -27.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e+83], t$95$1, If[LessEqual[a, 2.45e-260], N[(b * c), $MachinePrecision], If[LessEqual[a, 1.55e+141], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.6000000000000001e83 or 1.55000000000000002e141 < a

   1. Initial program 76.9%

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

   2. Taylor expanded in x around 0 78.2%

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

   3. Taylor expanded in a around inf 58.1%

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

      1. associate-*r* 58.1%

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

      2. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   if -5.6000000000000001e83 < a < 2.4500000000000001e-260

   1. Initial program 88.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in b around inf 30.6%

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

   if 2.4500000000000001e-260 < a < 1.55000000000000002e141

   1. Initial program 83.6%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in j around inf 31.0%

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

      1. *-commutative 31.0%

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

      2. associate-*l* 31.1%

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

   6. Simplified 31.1%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+83}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{-260}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+141}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot -4\right)\\ \end{array} \]

Alternative 24: 31.1% accurate, 4.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;j \leq -2.1 \cdot 10^{+67}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= j -2.1e+67) (* j (* k -27.0)) (* b c)))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -2.1e+67) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (j <= (-2.1d+67)) then
        tmp = j * (k * (-27.0d0))
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -2.1e+67) {
		tmp = j * (k * -27.0);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if j <= -2.1e+67:
		tmp = j * (k * -27.0)
	else:
		tmp = b * c
	return tmp

Julia

y, z = sort([y, z])
j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (j <= -2.1e+67)
		tmp = Float64(j * Float64(k * -27.0));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (j <= -2.1e+67)
		tmp = j * (k * -27.0);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[j, -2.1e+67], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -2.1000000000000001e67

   1. Initial program 75.9%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in j around inf 41.7%

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

      1. *-commutative 41.7%

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

      2. associate-*l* 41.8%

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

   6. Simplified 41.8%

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

   if -2.1000000000000001e67 < j

   1. Initial program 85.6%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in b around inf 25.6%

      \[\leadsto \color{blue}{b \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.1 \cdot 10^{+67}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 25: 23.6% accurate, 10.3× speedup

Math

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

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* b c))

C

assert(y < z);
assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = b * c
end function

Java

assert y < z;
assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(b * c), $MachinePrecision]

Derivation

1. Initial program 83.7%

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

3. Simplified 86.1%

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

4. Taylor expanded in b around inf 23.3%

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

5. Final simplification 23.3%

   \[\leadsto b \cdot c \]

Developer target: 89.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023287 
(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)))