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

Percentage Accurate: 85.3% → 91.4%

Time: 23.8s

Alternatives: 15

Speedup: 0.5×

• 50.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.4% accurate, 0.5× speedup

Math

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

FPCore

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

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.6%

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

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

   1. Initial program 0.0%

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

      1. sub-neg 0.0%

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

      2. associate-+l- 0.0%

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

      3. sub-neg 0.0%

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

      4. sub-neg 0.0%

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

      5. distribute-rgt-out-- 19.4%

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

      6. associate-*l* 19.4%

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

      7. distribute-lft-neg-in 19.4%

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

      8. cancel-sign-sub 19.4%

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

      9. associate-*l* 19.4%

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

      10. associate-*l* 19.4%

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

   3. Simplified 19.4%

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

   4. Taylor expanded in t around inf 64.9%

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

4. Final simplification 92.8%

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

Alternative 2: 79.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+70} \lor \neg \left(t \leq 1.45 \cdot 10^{+86}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(\left(j \cdot k\right) \cdot -27 + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\right)\\ \end{array} \end{array} \]

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 (or (<= t -2.4e+70) (not (<= t 1.45e+86)))
   (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))
   (+
    (* b c)
    (+ (* (* j k) -27.0) (* x (+ (* 18.0 (* y (* z t))) (* i -4.0)))))))

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 tmp;
	if ((t <= -2.4e+70) || !(t <= 1.45e+86)) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else {
		tmp = (b * c) + (((j * k) * -27.0) + (x * ((18.0 * (y * (z * t))) + (i * -4.0))));
	}
	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) :: tmp
    if ((t <= (-2.4d+70)) .or. (.not. (t <= 1.45d+86))) then
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    else
        tmp = (b * c) + (((j * k) * (-27.0d0)) + (x * ((18.0d0 * (y * (z * t))) + (i * (-4.0d0)))))
    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 tmp;
	if ((t <= -2.4e+70) || !(t <= 1.45e+86)) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else {
		tmp = (b * c) + (((j * k) * -27.0) + (x * ((18.0 * (y * (z * t))) + (i * -4.0))));
	}
	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):
	tmp = 0
	if (t <= -2.4e+70) or not (t <= 1.45e+86):
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	else:
		tmp = (b * c) + (((j * k) * -27.0) + (x * ((18.0 * (y * (z * t))) + (i * -4.0))))
	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)
	tmp = 0.0
	if ((t <= -2.4e+70) || !(t <= 1.45e+86))
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	else
		tmp = Float64(Float64(b * c) + Float64(Float64(Float64(j * k) * -27.0) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) + Float64(i * -4.0)))));
	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)
	tmp = 0.0;
	if ((t <= -2.4e+70) || ~((t <= 1.45e+86)))
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	else
		tmp = (b * c) + (((j * k) * -27.0) + (x * ((18.0 * (y * (z * t))) + (i * -4.0))));
	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_] := If[Or[LessEqual[t, -2.4e+70], N[Not[LessEqual[t, 1.45e+86]], $MachinePrecision]], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.39999999999999987e70 or 1.44999999999999995e86 < t

   1. Initial program 80.0%

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

      1. sub-neg 80.0%

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

      2. associate-+l- 80.0%

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

      3. sub-neg 80.0%

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

      4. sub-neg 80.0%

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

      5. distribute-rgt-out-- 86.3%

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

      6. associate-*l* 85.2%

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

      7. distribute-lft-neg-in 85.2%

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

      8. cancel-sign-sub 85.2%

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

      9. associate-*l* 85.2%

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

      10. associate-*l* 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in t around inf 82.0%

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

   if -2.39999999999999987e70 < t < 1.44999999999999995e86

   1. Initial program 87.8%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in a around 0 88.5%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+70} \lor \neg \left(t \leq 1.45 \cdot 10^{+86}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(\left(j \cdot k\right) \cdot -27 + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\right)\\ \end{array} \]

Alternative 3: 82.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+68}:\\ \;\;\;\;\left(t_1 + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c + \left(\left(j \cdot k\right) \cdot -27 + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (- (* 18.0 (* y (* x z))) (* a 4.0)))))
   (if (<= t -4.2e+68)
     (- (+ t_1 (* b c)) (* 27.0 (* j k)))
     (if (<= t 1.95e+86)
       (+
        (* b c)
        (+ (* (* j k) -27.0) (* x (+ (* 18.0 (* y (* z t))) (* i -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 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double tmp;
	if (t <= -4.2e+68) {
		tmp = (t_1 + (b * c)) - (27.0 * (j * k));
	} else if (t <= 1.95e+86) {
		tmp = (b * c) + (((j * k) * -27.0) + (x * ((18.0 * (y * (z * t))) + (i * -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 = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    if (t <= (-4.2d+68)) then
        tmp = (t_1 + (b * c)) - (27.0d0 * (j * k))
    else if (t <= 1.95d+86) then
        tmp = (b * c) + (((j * k) * (-27.0d0)) + (x * ((18.0d0 * (y * (z * t))) + (i * (-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 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double tmp;
	if (t <= -4.2e+68) {
		tmp = (t_1 + (b * c)) - (27.0 * (j * k));
	} else if (t <= 1.95e+86) {
		tmp = (b * c) + (((j * k) * -27.0) + (x * ((18.0 * (y * (z * t))) + (i * -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 = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	tmp = 0
	if t <= -4.2e+68:
		tmp = (t_1 + (b * c)) - (27.0 * (j * k))
	elif t <= 1.95e+86:
		tmp = (b * c) + (((j * k) * -27.0) + (x * ((18.0 * (y * (z * t))) + (i * -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(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -4.2e+68)
		tmp = Float64(Float64(t_1 + Float64(b * c)) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 1.95e+86)
		tmp = Float64(Float64(b * c) + Float64(Float64(Float64(j * k) * -27.0) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) + Float64(i * -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 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -4.2e+68)
		tmp = (t_1 + (b * c)) - (27.0 * (j * k));
	elseif (t <= 1.95e+86)
		tmp = (b * c) + (((j * k) * -27.0) + (x * ((18.0 * (y * (z * t))) + (i * -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[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+68], N[(N[(t$95$1 + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+86], N[(N[(b * c), $MachinePrecision] + N[(N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.20000000000000002e68

   1. Initial program 83.6%

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

      1. sub-neg 83.6%

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

      2. associate-+l- 83.6%

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

      3. sub-neg 83.6%

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

      4. sub-neg 83.6%

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

      5. distribute-rgt-out-- 90.1%

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

      6. associate-*l* 88.4%

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

      7. distribute-lft-neg-in 88.4%

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

      8. cancel-sign-sub 88.4%

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

      9. associate-*l* 88.4%

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

      10. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in i around 0 90.9%

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

   if -4.20000000000000002e68 < t < 1.9500000000000001e86

   1. Initial program 87.8%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in a around 0 88.5%

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

   if 1.9500000000000001e86 < t

   1. Initial program 73.5%

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

      1. sub-neg 73.5%

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

      2. associate-+l- 73.5%

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

      3. sub-neg 73.5%

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

      4. sub-neg 73.5%

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

      5. distribute-rgt-out-- 79.4%

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

      6. associate-*l* 79.4%

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

      7. distribute-lft-neg-in 79.4%

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

      8. cancel-sign-sub 79.4%

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

      9. associate-*l* 79.4%

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

      10. associate-*l* 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in t around inf 88.7%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+68}:\\ \;\;\;\;\left(t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) + b \cdot c\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c + \left(\left(j \cdot k\right) \cdot -27 + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 4: 48.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := \left(j \cdot k\right) \cdot -27 + -4 \cdot \left(x \cdot i\right)\\ t_2 := 27 \cdot \left(j \cdot k\right)\\ t_3 := -4 \cdot \left(t \cdot a\right) - t_2\\ t_4 := b \cdot c - t_2\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+180}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{+68}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-72}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+85}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+150}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

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 (+ (* (* j k) -27.0) (* -4.0 (* x i))))
        (t_2 (* 27.0 (* j k)))
        (t_3 (- (* -4.0 (* t a)) t_2))
        (t_4 (- (* b c) t_2)))
   (if (<= t -2.7e+180)
     (* 18.0 (* y (* z (* x t))))
     (if (<= t -2.05e+68)
       t_3
       (if (<= t 1.35e-283)
         t_1
         (if (<= t 2.2e-72)
           t_4
           (if (<= t 3.1e+54)
             t_1
             (if (<= t 4.2e+85)
               t_4
               (if (<= t 1.75e+150) t_3 (* 18.0 (* y (* t (* x z)))))))))))))

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 * k) * -27.0) + (-4.0 * (x * i));
	double t_2 = 27.0 * (j * k);
	double t_3 = (-4.0 * (t * a)) - t_2;
	double t_4 = (b * c) - t_2;
	double tmp;
	if (t <= -2.7e+180) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if (t <= -2.05e+68) {
		tmp = t_3;
	} else if (t <= 1.35e-283) {
		tmp = t_1;
	} else if (t <= 2.2e-72) {
		tmp = t_4;
	} else if (t <= 3.1e+54) {
		tmp = t_1;
	} else if (t <= 4.2e+85) {
		tmp = t_4;
	} else if (t <= 1.75e+150) {
		tmp = t_3;
	} else {
		tmp = 18.0 * (y * (t * (x * z)));
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = ((j * k) * (-27.0d0)) + ((-4.0d0) * (x * i))
    t_2 = 27.0d0 * (j * k)
    t_3 = ((-4.0d0) * (t * a)) - t_2
    t_4 = (b * c) - t_2
    if (t <= (-2.7d+180)) then
        tmp = 18.0d0 * (y * (z * (x * t)))
    else if (t <= (-2.05d+68)) then
        tmp = t_3
    else if (t <= 1.35d-283) then
        tmp = t_1
    else if (t <= 2.2d-72) then
        tmp = t_4
    else if (t <= 3.1d+54) then
        tmp = t_1
    else if (t <= 4.2d+85) then
        tmp = t_4
    else if (t <= 1.75d+150) then
        tmp = t_3
    else
        tmp = 18.0d0 * (y * (t * (x * z)))
    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 * k) * -27.0) + (-4.0 * (x * i));
	double t_2 = 27.0 * (j * k);
	double t_3 = (-4.0 * (t * a)) - t_2;
	double t_4 = (b * c) - t_2;
	double tmp;
	if (t <= -2.7e+180) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if (t <= -2.05e+68) {
		tmp = t_3;
	} else if (t <= 1.35e-283) {
		tmp = t_1;
	} else if (t <= 2.2e-72) {
		tmp = t_4;
	} else if (t <= 3.1e+54) {
		tmp = t_1;
	} else if (t <= 4.2e+85) {
		tmp = t_4;
	} else if (t <= 1.75e+150) {
		tmp = t_3;
	} else {
		tmp = 18.0 * (y * (t * (x * z)));
	}
	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 * k) * -27.0) + (-4.0 * (x * i))
	t_2 = 27.0 * (j * k)
	t_3 = (-4.0 * (t * a)) - t_2
	t_4 = (b * c) - t_2
	tmp = 0
	if t <= -2.7e+180:
		tmp = 18.0 * (y * (z * (x * t)))
	elif t <= -2.05e+68:
		tmp = t_3
	elif t <= 1.35e-283:
		tmp = t_1
	elif t <= 2.2e-72:
		tmp = t_4
	elif t <= 3.1e+54:
		tmp = t_1
	elif t <= 4.2e+85:
		tmp = t_4
	elif t <= 1.75e+150:
		tmp = t_3
	else:
		tmp = 18.0 * (y * (t * (x * z)))
	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(j * k) * -27.0) + Float64(-4.0 * Float64(x * i)))
	t_2 = Float64(27.0 * Float64(j * k))
	t_3 = Float64(Float64(-4.0 * Float64(t * a)) - t_2)
	t_4 = Float64(Float64(b * c) - t_2)
	tmp = 0.0
	if (t <= -2.7e+180)
		tmp = Float64(18.0 * Float64(y * Float64(z * Float64(x * t))));
	elseif (t <= -2.05e+68)
		tmp = t_3;
	elseif (t <= 1.35e-283)
		tmp = t_1;
	elseif (t <= 2.2e-72)
		tmp = t_4;
	elseif (t <= 3.1e+54)
		tmp = t_1;
	elseif (t <= 4.2e+85)
		tmp = t_4;
	elseif (t <= 1.75e+150)
		tmp = t_3;
	else
		tmp = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))));
	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 * k) * -27.0) + (-4.0 * (x * i));
	t_2 = 27.0 * (j * k);
	t_3 = (-4.0 * (t * a)) - t_2;
	t_4 = (b * c) - t_2;
	tmp = 0.0;
	if (t <= -2.7e+180)
		tmp = 18.0 * (y * (z * (x * t)));
	elseif (t <= -2.05e+68)
		tmp = t_3;
	elseif (t <= 1.35e-283)
		tmp = t_1;
	elseif (t <= 2.2e-72)
		tmp = t_4;
	elseif (t <= 3.1e+54)
		tmp = t_1;
	elseif (t <= 4.2e+85)
		tmp = t_4;
	elseif (t <= 1.75e+150)
		tmp = t_3;
	else
		tmp = 18.0 * (y * (t * (x * z)));
	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[(j * k), $MachinePrecision] * -27.0), $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[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * c), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[t, -2.7e+180], N[(18.0 * N[(y * N[(z * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.05e+68], t$95$3, If[LessEqual[t, 1.35e-283], t$95$1, If[LessEqual[t, 2.2e-72], t$95$4, If[LessEqual[t, 3.1e+54], t$95$1, If[LessEqual[t, 4.2e+85], t$95$4, If[LessEqual[t, 1.75e+150], t$95$3, N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.70000000000000016e180

   1. Initial program 79.3%

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

      1. sub-neg 79.3%

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

      2. associate-+l- 79.3%

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

      3. sub-neg 79.3%

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

      4. sub-neg 79.3%

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

      5. distribute-rgt-out-- 89.6%

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

      6. associate-*l* 86.1%

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

      7. distribute-lft-neg-in 86.1%

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

      8. cancel-sign-sub 86.1%

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

      9. associate-*l* 86.1%

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

      10. associate-*l* 86.1%

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

   3. Simplified 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 i around 0 93.0%

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

   5. Taylor expanded in a around 0 66.0%

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

   6. Taylor expanded in y around inf 63.1%

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

      1. *-commutative 63.1%

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

      2. *-commutative 63.1%

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

      3. *-commutative 63.1%

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

      4. associate-*l* 69.7%

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

   8. Simplified 69.7%

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

   if -2.70000000000000016e180 < t < -2.05e68 or 4.2000000000000002e85 < t < 1.74999999999999992e150

   1. Initial program 88.1%

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

      1. sub-neg 88.1%

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

      2. associate-+l- 88.1%

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

      3. sub-neg 88.1%

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

      4. sub-neg 88.1%

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

      5. distribute-rgt-out-- 90.4%

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

      6. associate-*l* 90.4%

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

      7. distribute-lft-neg-in 90.4%

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

      8. cancel-sign-sub 90.4%

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

      9. associate-*l* 90.4%

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

      10. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in x around 0 69.3%

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

   5. Taylor expanded in c around 0 65.8%

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

   if -2.05e68 < t < 1.35e-283 or 2.20000000000000002e-72 < t < 3.0999999999999999e54

   1. Initial program 87.9%

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

      1. sub-neg 87.9%

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

      2. +-commutative 87.9%

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

      3. associate-*l* 88.0%

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

      4. distribute-rgt-neg-in 88.0%

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

      5. fma-def 88.0%

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

      6. *-commutative 88.0%

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

      7. distribute-rgt-neg-in 88.0%

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

      8. metadata-eval 88.0%

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

      9. sub-neg 88.0%

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

      10. +-commutative 88.0%

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

      11. associate-*l* 88.0%

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

      12. distribute-rgt-neg-in 88.0%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in x around inf 67.2%

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

      1. *-commutative 67.2%

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

      2. associate-*r* 65.4%

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

      3. associate-*l* 64.5%

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

      4. *-commutative 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in z around 0 59.5%

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

   if 1.35e-283 < t < 2.20000000000000002e-72 or 3.0999999999999999e54 < t < 4.2000000000000002e85

   1. Initial program 87.5%

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

      1. sub-neg 87.5%

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

      2. associate-+l- 87.5%

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

      3. sub-neg 87.5%

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

      4. sub-neg 87.5%

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

      5. distribute-rgt-out-- 87.5%

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

      6. associate-*l* 84.1%

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

      7. distribute-lft-neg-in 84.1%

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

      8. cancel-sign-sub 84.1%

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

      9. associate-*l* 84.1%

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

      10. associate-*l* 84.2%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in x around 0 69.7%

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

   5. Taylor expanded in a around 0 68.0%

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

   if 1.74999999999999992e150 < t

   1. Initial program 66.7%

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

      1. sub-neg 66.7%

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

      2. associate-+l- 66.7%

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

      3. sub-neg 66.7%

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

      4. sub-neg 66.7%

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

      5. distribute-rgt-out-- 75.0%

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

      6. associate-*l* 75.0%

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

      7. distribute-lft-neg-in 75.0%

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

      8. cancel-sign-sub 75.0%

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

      9. associate-*l* 75.0%

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

      10. associate-*l* 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in x around inf 68.1%

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

   5. Taylor expanded in y around inf 68.1%

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

      1. *-commutative 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in y around 0 71.9%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+180}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{+68}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-283}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-72}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+54}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+85}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+150}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 5: 58.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ t_2 := \left(j \cdot k\right) \cdot -27 + -4 \cdot \left(x \cdot i\right)\\ t_3 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+67}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-283}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

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 (- (* b c) (* 27.0 (* j k))))
        (t_2 (+ (* (* j k) -27.0) (* -4.0 (* x i))))
        (t_3 (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))))
   (if (<= t -1.2e+67)
     t_3
     (if (<= t 2.7e-283)
       t_2
       (if (<= t 2.4e-72)
         t_1
         (if (<= t 6.9e+55) t_2 (if (<= t 4.9e+85) t_1 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 = (b * c) - (27.0 * (j * k));
	double t_2 = ((j * k) * -27.0) + (-4.0 * (x * i));
	double t_3 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.2e+67) {
		tmp = t_3;
	} else if (t <= 2.7e-283) {
		tmp = t_2;
	} else if (t <= 2.4e-72) {
		tmp = t_1;
	} else if (t <= 6.9e+55) {
		tmp = t_2;
	} else if (t <= 4.9e+85) {
		tmp = t_1;
	} 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 = (b * c) - (27.0d0 * (j * k))
    t_2 = ((j * k) * (-27.0d0)) + ((-4.0d0) * (x * i))
    t_3 = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    if (t <= (-1.2d+67)) then
        tmp = t_3
    else if (t <= 2.7d-283) then
        tmp = t_2
    else if (t <= 2.4d-72) then
        tmp = t_1
    else if (t <= 6.9d+55) then
        tmp = t_2
    else if (t <= 4.9d+85) then
        tmp = t_1
    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 = (b * c) - (27.0 * (j * k));
	double t_2 = ((j * k) * -27.0) + (-4.0 * (x * i));
	double t_3 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	double tmp;
	if (t <= -1.2e+67) {
		tmp = t_3;
	} else if (t <= 2.7e-283) {
		tmp = t_2;
	} else if (t <= 2.4e-72) {
		tmp = t_1;
	} else if (t <= 6.9e+55) {
		tmp = t_2;
	} else if (t <= 4.9e+85) {
		tmp = t_1;
	} 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 = (b * c) - (27.0 * (j * k))
	t_2 = ((j * k) * -27.0) + (-4.0 * (x * i))
	t_3 = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	tmp = 0
	if t <= -1.2e+67:
		tmp = t_3
	elif t <= 2.7e-283:
		tmp = t_2
	elif t <= 2.4e-72:
		tmp = t_1
	elif t <= 6.9e+55:
		tmp = t_2
	elif t <= 4.9e+85:
		tmp = t_1
	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(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	t_2 = Float64(Float64(Float64(j * k) * -27.0) + Float64(-4.0 * Float64(x * i)))
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -1.2e+67)
		tmp = t_3;
	elseif (t <= 2.7e-283)
		tmp = t_2;
	elseif (t <= 2.4e-72)
		tmp = t_1;
	elseif (t <= 6.9e+55)
		tmp = t_2;
	elseif (t <= 4.9e+85)
		tmp = t_1;
	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 = (b * c) - (27.0 * (j * k));
	t_2 = ((j * k) * -27.0) + (-4.0 * (x * i));
	t_3 = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -1.2e+67)
		tmp = t_3;
	elseif (t <= 2.7e-283)
		tmp = t_2;
	elseif (t <= 2.4e-72)
		tmp = t_1;
	elseif (t <= 6.9e+55)
		tmp = t_2;
	elseif (t <= 4.9e+85)
		tmp = t_1;
	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[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e+67], t$95$3, If[LessEqual[t, 2.7e-283], t$95$2, If[LessEqual[t, 2.4e-72], t$95$1, If[LessEqual[t, 6.9e+55], t$95$2, If[LessEqual[t, 4.9e+85], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.20000000000000001e67 or 4.8999999999999997e85 < t

   1. Initial program 80.0%

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

      1. sub-neg 80.0%

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

      2. associate-+l- 80.0%

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

      3. sub-neg 80.0%

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

      4. sub-neg 80.0%

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

      5. distribute-rgt-out-- 86.3%

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

      6. associate-*l* 85.2%

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

      7. distribute-lft-neg-in 85.2%

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

      8. cancel-sign-sub 85.2%

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

      9. associate-*l* 85.2%

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

      10. associate-*l* 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in t around inf 82.0%

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

   if -1.20000000000000001e67 < t < 2.7e-283 or 2.4e-72 < t < 6.9000000000000004e55

   1. Initial program 87.9%

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

      1. sub-neg 87.9%

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

      2. +-commutative 87.9%

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

      3. associate-*l* 88.0%

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

      4. distribute-rgt-neg-in 88.0%

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

      5. fma-def 88.0%

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

      6. *-commutative 88.0%

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

      7. distribute-rgt-neg-in 88.0%

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

      8. metadata-eval 88.0%

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

      9. sub-neg 88.0%

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

      10. +-commutative 88.0%

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

      11. associate-*l* 88.0%

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

      12. distribute-rgt-neg-in 88.0%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in x around inf 67.2%

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

      1. *-commutative 67.2%

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

      2. associate-*r* 65.4%

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

      3. associate-*l* 64.5%

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

      4. *-commutative 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in z around 0 59.5%

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

   if 2.7e-283 < t < 2.4e-72 or 6.9000000000000004e55 < t < 4.8999999999999997e85

   1. Initial program 87.5%

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

      1. sub-neg 87.5%

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

      2. associate-+l- 87.5%

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

      3. sub-neg 87.5%

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

      4. sub-neg 87.5%

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

      5. distribute-rgt-out-- 87.5%

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

      6. associate-*l* 84.1%

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

      7. distribute-lft-neg-in 84.1%

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

      8. cancel-sign-sub 84.1%

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

      9. associate-*l* 84.1%

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

      10. associate-*l* 84.2%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in x around 0 69.7%

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

   5. Taylor expanded in a around 0 68.0%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-283}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-72}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{+55}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+85}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 6: 33.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-262}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-154}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+54}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (* 18.0 (* y (* t (* x z))))))
   (if (<= z -5.6e-56)
     t_1
     (if (<= z 3.7e-262)
       (* (* j k) -27.0)
       (if (<= z 4.7e-172)
         (* x (* i -4.0))
         (if (<= z 3.7e-154)
           (* k (* j -27.0))
           (if (<= z 1.75e+54) (* -4.0 (* t a)) 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 * (y * (t * (x * z)));
	double tmp;
	if (z <= -5.6e-56) {
		tmp = t_1;
	} else if (z <= 3.7e-262) {
		tmp = (j * k) * -27.0;
	} else if (z <= 4.7e-172) {
		tmp = x * (i * -4.0);
	} else if (z <= 3.7e-154) {
		tmp = k * (j * -27.0);
	} else if (z <= 1.75e+54) {
		tmp = -4.0 * (t * a);
	} 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 * (y * (t * (x * z)))
    if (z <= (-5.6d-56)) then
        tmp = t_1
    else if (z <= 3.7d-262) then
        tmp = (j * k) * (-27.0d0)
    else if (z <= 4.7d-172) then
        tmp = x * (i * (-4.0d0))
    else if (z <= 3.7d-154) then
        tmp = k * (j * (-27.0d0))
    else if (z <= 1.75d+54) then
        tmp = (-4.0d0) * (t * a)
    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 * (y * (t * (x * z)));
	double tmp;
	if (z <= -5.6e-56) {
		tmp = t_1;
	} else if (z <= 3.7e-262) {
		tmp = (j * k) * -27.0;
	} else if (z <= 4.7e-172) {
		tmp = x * (i * -4.0);
	} else if (z <= 3.7e-154) {
		tmp = k * (j * -27.0);
	} else if (z <= 1.75e+54) {
		tmp = -4.0 * (t * a);
	} 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 * (y * (t * (x * z)))
	tmp = 0
	if z <= -5.6e-56:
		tmp = t_1
	elif z <= 3.7e-262:
		tmp = (j * k) * -27.0
	elif z <= 4.7e-172:
		tmp = x * (i * -4.0)
	elif z <= 3.7e-154:
		tmp = k * (j * -27.0)
	elif z <= 1.75e+54:
		tmp = -4.0 * (t * a)
	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(y * Float64(t * Float64(x * z))))
	tmp = 0.0
	if (z <= -5.6e-56)
		tmp = t_1;
	elseif (z <= 3.7e-262)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (z <= 4.7e-172)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (z <= 3.7e-154)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (z <= 1.75e+54)
		tmp = Float64(-4.0 * Float64(t * a));
	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 * (y * (t * (x * z)));
	tmp = 0.0;
	if (z <= -5.6e-56)
		tmp = t_1;
	elseif (z <= 3.7e-262)
		tmp = (j * k) * -27.0;
	elseif (z <= 4.7e-172)
		tmp = x * (i * -4.0);
	elseif (z <= 3.7e-154)
		tmp = k * (j * -27.0);
	elseif (z <= 1.75e+54)
		tmp = -4.0 * (t * a);
	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[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e-56], t$95$1, If[LessEqual[z, 3.7e-262], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[z, 4.7e-172], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-154], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+54], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.59999999999999986e-56 or 1.7500000000000001e54 < z

   1. Initial program 80.6%

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

      1. sub-neg 80.6%

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

      2. associate-+l- 80.6%

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

      3. sub-neg 80.6%

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

      4. sub-neg 80.6%

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

      5. distribute-rgt-out-- 84.4%

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

      6. associate-*l* 80.7%

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

      7. distribute-lft-neg-in 80.7%

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

      8. cancel-sign-sub 80.7%

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

      9. associate-*l* 80.7%

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

      10. associate-*l* 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in x around inf 52.4%

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

   5. Taylor expanded in y around inf 40.7%

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

      1. *-commutative 40.7%

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

   7. Simplified 40.7%

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

   8. Taylor expanded in y around 0 45.1%

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

   if -5.59999999999999986e-56 < z < 3.7e-262

   1. Initial program 90.4%

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

      1. sub-neg 90.4%

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

      2. +-commutative 90.4%

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

      3. associate-*l* 90.5%

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

      4. distribute-rgt-neg-in 90.5%

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

      5. fma-def 90.5%

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

      6. *-commutative 90.5%

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

      7. distribute-rgt-neg-in 90.5%

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

      8. metadata-eval 90.5%

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

      9. sub-neg 90.5%

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

      10. +-commutative 90.5%

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

      11. associate-*l* 90.5%

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

      12. distribute-rgt-neg-in 90.5%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in j around inf 35.7%

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

   if 3.7e-262 < z < 4.69999999999999976e-172

   1. Initial program 95.6%

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

      1. sub-neg 95.6%

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

      2. associate-+l- 95.6%

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

      3. sub-neg 95.6%

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

      4. sub-neg 95.6%

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

      5. distribute-rgt-out-- 95.6%

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

      6. associate-*l* 95.6%

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

      7. distribute-lft-neg-in 95.6%

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

      8. cancel-sign-sub 95.6%

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

      9. associate-*l* 95.6%

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

      10. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in x around inf 31.0%

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

   5. Taylor expanded in y around 0 31.0%

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

   if 4.69999999999999976e-172 < z < 3.69999999999999987e-154

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-*l* 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. fma-def 100.0%

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

      6. *-commutative 100.0%

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

      7. distribute-rgt-neg-in 100.0%

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

      8. metadata-eval 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate-*l* 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in j around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. associate-*r* 50.9%

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

      3. *-commutative 50.9%

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

   6. Simplified 50.9%

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

   if 3.69999999999999987e-154 < z < 1.7500000000000001e54

   1. Initial program 83.2%

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

      1. sub-neg 83.2%

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

      2. associate-+l- 83.2%

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

      3. sub-neg 83.2%

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

      4. sub-neg 83.2%

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

      5. distribute-rgt-out-- 86.1%

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

      6. associate-*l* 88.7%

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

      7. distribute-lft-neg-in 88.7%

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

      8. cancel-sign-sub 88.7%

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

      9. associate-*l* 88.7%

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

      10. associate-*l* 88.7%

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

   3. Simplified 88.7%

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

      1. associate--l+ 88.7%

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

      2. associate-*r* 86.1%

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

      3. associate-*r* 88.7%

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

      4. associate-*l* 88.7%

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

      5. fma-def 88.7%

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

      6. *-commutative 88.7%

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

      7. associate-*r* 88.7%

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

   5. Applied egg-rr 88.7%

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

   6. Taylor expanded in x around 0 81.9%

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

      1. associate-*r* 81.9%

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

      2. *-commutative 81.9%

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

   8. Simplified 81.9%

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

   9. Taylor expanded in a around inf 27.4%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-56}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-262}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-154}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+54}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 7: 33.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-53}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-261}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-171}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-154}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+54}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

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 -3.9e-53)
   (* 18.0 (* y (* z (* x t))))
   (if (<= z 1.8e-261)
     (* (* j k) -27.0)
     (if (<= z 1.35e-171)
       (* x (* i -4.0))
       (if (<= z 5.3e-154)
         (* k (* j -27.0))
         (if (<= z 2.05e+54)
           (* -4.0 (* t a))
           (* 18.0 (* y (* t (* x z))))))))))

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 <= -3.9e-53) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if (z <= 1.8e-261) {
		tmp = (j * k) * -27.0;
	} else if (z <= 1.35e-171) {
		tmp = x * (i * -4.0);
	} else if (z <= 5.3e-154) {
		tmp = k * (j * -27.0);
	} else if (z <= 2.05e+54) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = 18.0 * (y * (t * (x * z)));
	}
	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 <= (-3.9d-53)) then
        tmp = 18.0d0 * (y * (z * (x * t)))
    else if (z <= 1.8d-261) then
        tmp = (j * k) * (-27.0d0)
    else if (z <= 1.35d-171) then
        tmp = x * (i * (-4.0d0))
    else if (z <= 5.3d-154) then
        tmp = k * (j * (-27.0d0))
    else if (z <= 2.05d+54) then
        tmp = (-4.0d0) * (t * a)
    else
        tmp = 18.0d0 * (y * (t * (x * z)))
    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 <= -3.9e-53) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if (z <= 1.8e-261) {
		tmp = (j * k) * -27.0;
	} else if (z <= 1.35e-171) {
		tmp = x * (i * -4.0);
	} else if (z <= 5.3e-154) {
		tmp = k * (j * -27.0);
	} else if (z <= 2.05e+54) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = 18.0 * (y * (t * (x * z)));
	}
	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 <= -3.9e-53:
		tmp = 18.0 * (y * (z * (x * t)))
	elif z <= 1.8e-261:
		tmp = (j * k) * -27.0
	elif z <= 1.35e-171:
		tmp = x * (i * -4.0)
	elif z <= 5.3e-154:
		tmp = k * (j * -27.0)
	elif z <= 2.05e+54:
		tmp = -4.0 * (t * a)
	else:
		tmp = 18.0 * (y * (t * (x * z)))
	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 <= -3.9e-53)
		tmp = Float64(18.0 * Float64(y * Float64(z * Float64(x * t))));
	elseif (z <= 1.8e-261)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (z <= 1.35e-171)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (z <= 5.3e-154)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (z <= 2.05e+54)
		tmp = Float64(-4.0 * Float64(t * a));
	else
		tmp = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))));
	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 <= -3.9e-53)
		tmp = 18.0 * (y * (z * (x * t)));
	elseif (z <= 1.8e-261)
		tmp = (j * k) * -27.0;
	elseif (z <= 1.35e-171)
		tmp = x * (i * -4.0);
	elseif (z <= 5.3e-154)
		tmp = k * (j * -27.0);
	elseif (z <= 2.05e+54)
		tmp = -4.0 * (t * a);
	else
		tmp = 18.0 * (y * (t * (x * z)));
	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, -3.9e-53], N[(18.0 * N[(y * N[(z * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-261], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[z, 1.35e-171], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e-154], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+54], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.9000000000000002e-53

   1. Initial program 82.3%

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

      1. sub-neg 82.3%

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

      2. associate-+l- 82.3%

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

      3. sub-neg 82.3%

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

      4. sub-neg 82.3%

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

      5. distribute-rgt-out-- 83.4%

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

      6. associate-*l* 79.3%

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

      7. distribute-lft-neg-in 79.3%

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

      8. cancel-sign-sub 79.3%

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

      9. associate-*l* 79.3%

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

      10. associate-*l* 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in i around 0 77.5%

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

   5. Taylor expanded in a around 0 67.7%

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

   6. Taylor expanded in y around inf 38.5%

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

      1. *-commutative 38.5%

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

      2. *-commutative 38.5%

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

      3. *-commutative 38.5%

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

      4. associate-*l* 37.5%

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

   8. Simplified 37.5%

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

   if -3.9000000000000002e-53 < z < 1.79999999999999999e-261

   1. Initial program 90.4%

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

      1. sub-neg 90.4%

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

      2. +-commutative 90.4%

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

      3. associate-*l* 90.5%

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

      4. distribute-rgt-neg-in 90.5%

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

      5. fma-def 90.5%

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

      6. *-commutative 90.5%

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

      7. distribute-rgt-neg-in 90.5%

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

      8. metadata-eval 90.5%

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

      9. sub-neg 90.5%

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

      10. +-commutative 90.5%

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

      11. associate-*l* 90.5%

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

      12. distribute-rgt-neg-in 90.5%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in j around inf 35.7%

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

   if 1.79999999999999999e-261 < z < 1.35000000000000007e-171

   1. Initial program 95.6%

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

      1. sub-neg 95.6%

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

      2. associate-+l- 95.6%

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

      3. sub-neg 95.6%

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

      4. sub-neg 95.6%

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

      5. distribute-rgt-out-- 95.6%

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

      6. associate-*l* 95.6%

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

      7. distribute-lft-neg-in 95.6%

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

      8. cancel-sign-sub 95.6%

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

      9. associate-*l* 95.6%

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

      10. associate-*l* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in x around inf 31.0%

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

   5. Taylor expanded in y around 0 31.0%

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

   if 1.35000000000000007e-171 < z < 5.3000000000000002e-154

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-*l* 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. fma-def 100.0%

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

      6. *-commutative 100.0%

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

      7. distribute-rgt-neg-in 100.0%

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

      8. metadata-eval 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate-*l* 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in j around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. associate-*r* 50.9%

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

      3. *-commutative 50.9%

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

   6. Simplified 50.9%

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

   if 5.3000000000000002e-154 < z < 2.04999999999999984e54

   1. Initial program 83.2%

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

      1. sub-neg 83.2%

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

      2. associate-+l- 83.2%

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

      3. sub-neg 83.2%

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

      4. sub-neg 83.2%

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

      5. distribute-rgt-out-- 86.1%

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

      6. associate-*l* 88.7%

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

      7. distribute-lft-neg-in 88.7%

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

      8. cancel-sign-sub 88.7%

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

      9. associate-*l* 88.7%

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

      10. associate-*l* 88.7%

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

   3. Simplified 88.7%

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

      1. associate--l+ 88.7%

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

      2. associate-*r* 86.1%

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

      3. associate-*r* 88.7%

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

      4. associate-*l* 88.7%

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

      5. fma-def 88.7%

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

      6. *-commutative 88.7%

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

      7. associate-*r* 88.7%

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

   5. Applied egg-rr 88.7%

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

   6. Taylor expanded in x around 0 81.9%

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

      1. associate-*r* 81.9%

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

      2. *-commutative 81.9%

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

   8. Simplified 81.9%

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

   9. Taylor expanded in a around inf 27.4%

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

   if 2.04999999999999984e54 < z

   1. Initial program 76.4%

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

      1. sub-neg 76.4%

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

      2. associate-+l- 76.4%

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

      3. sub-neg 76.4%

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

      4. sub-neg 76.4%

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

      5. distribute-rgt-out-- 87.0%

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

      6. associate-*l* 84.3%

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

      7. distribute-lft-neg-in 84.3%

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

      8. cancel-sign-sub 84.3%

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

      9. associate-*l* 84.3%

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

      10. associate-*l* 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in x around inf 69.4%

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

   5. Taylor expanded in y around inf 59.0%

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

      1. *-commutative 59.0%

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

   7. Simplified 59.0%

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

   8. Taylor expanded in y around 0 61.5%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-53}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-261}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-171}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-154}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+54}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 8: 47.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+157}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+57}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+150}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

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)))))
   (if (<= t -6.2e+157)
     (* 18.0 (* y (* z (* x t))))
     (if (<= t 2.8e-72)
       t_1
       (if (<= t 5.6e+57)
         (+ (* (* j k) -27.0) (* -4.0 (* x i)))
         (if (<= t 9.5e+87)
           t_1
           (if (<= t 4.6e+150)
             (* -4.0 (* t a))
             (* 18.0 (* y (* t (* x z)))))))))))

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 tmp;
	if (t <= -6.2e+157) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if (t <= 2.8e-72) {
		tmp = t_1;
	} else if (t <= 5.6e+57) {
		tmp = ((j * k) * -27.0) + (-4.0 * (x * i));
	} else if (t <= 9.5e+87) {
		tmp = t_1;
	} else if (t <= 4.6e+150) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = 18.0 * (y * (t * (x * z)));
	}
	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) - (27.0d0 * (j * k))
    if (t <= (-6.2d+157)) then
        tmp = 18.0d0 * (y * (z * (x * t)))
    else if (t <= 2.8d-72) then
        tmp = t_1
    else if (t <= 5.6d+57) then
        tmp = ((j * k) * (-27.0d0)) + ((-4.0d0) * (x * i))
    else if (t <= 9.5d+87) then
        tmp = t_1
    else if (t <= 4.6d+150) then
        tmp = (-4.0d0) * (t * a)
    else
        tmp = 18.0d0 * (y * (t * (x * z)))
    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 tmp;
	if (t <= -6.2e+157) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if (t <= 2.8e-72) {
		tmp = t_1;
	} else if (t <= 5.6e+57) {
		tmp = ((j * k) * -27.0) + (-4.0 * (x * i));
	} else if (t <= 9.5e+87) {
		tmp = t_1;
	} else if (t <= 4.6e+150) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = 18.0 * (y * (t * (x * z)));
	}
	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))
	tmp = 0
	if t <= -6.2e+157:
		tmp = 18.0 * (y * (z * (x * t)))
	elif t <= 2.8e-72:
		tmp = t_1
	elif t <= 5.6e+57:
		tmp = ((j * k) * -27.0) + (-4.0 * (x * i))
	elif t <= 9.5e+87:
		tmp = t_1
	elif t <= 4.6e+150:
		tmp = -4.0 * (t * a)
	else:
		tmp = 18.0 * (y * (t * (x * z)))
	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)))
	tmp = 0.0
	if (t <= -6.2e+157)
		tmp = Float64(18.0 * Float64(y * Float64(z * Float64(x * t))));
	elseif (t <= 2.8e-72)
		tmp = t_1;
	elseif (t <= 5.6e+57)
		tmp = Float64(Float64(Float64(j * k) * -27.0) + Float64(-4.0 * Float64(x * i)));
	elseif (t <= 9.5e+87)
		tmp = t_1;
	elseif (t <= 4.6e+150)
		tmp = Float64(-4.0 * Float64(t * a));
	else
		tmp = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))));
	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));
	tmp = 0.0;
	if (t <= -6.2e+157)
		tmp = 18.0 * (y * (z * (x * t)));
	elseif (t <= 2.8e-72)
		tmp = t_1;
	elseif (t <= 5.6e+57)
		tmp = ((j * k) * -27.0) + (-4.0 * (x * i));
	elseif (t <= 9.5e+87)
		tmp = t_1;
	elseif (t <= 4.6e+150)
		tmp = -4.0 * (t * a);
	else
		tmp = 18.0 * (y * (t * (x * z)));
	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]}, If[LessEqual[t, -6.2e+157], N[(18.0 * N[(y * N[(z * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-72], t$95$1, If[LessEqual[t, 5.6e+57], N[(N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision] + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+87], t$95$1, If[LessEqual[t, 4.6e+150], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.1999999999999994e157

   1. Initial program 82.8%

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

      1. sub-neg 82.8%

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

      2. associate-+l- 82.8%

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

      3. sub-neg 82.8%

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

      4. sub-neg 82.8%

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

      5. distribute-rgt-out-- 91.4%

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

      6. associate-*l* 88.5%

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

      7. distribute-lft-neg-in 88.5%

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

      8. cancel-sign-sub 88.5%

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

      9. associate-*l* 88.5%

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

      10. associate-*l* 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in i around 0 91.5%

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

   5. Taylor expanded in a around 0 60.7%

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

   6. Taylor expanded in y around inf 58.3%

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

      1. *-commutative 58.3%

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

      2. *-commutative 58.3%

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

      3. *-commutative 58.3%

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

      4. associate-*l* 66.6%

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

   8. Simplified 66.6%

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

   if -6.1999999999999994e157 < t < 2.7999999999999998e-72 or 5.59999999999999999e57 < t < 9.4999999999999992e87

   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. Step-by-step derivation

      1. sub-neg 87.3%

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

      2. associate-+l- 87.3%

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

      3. sub-neg 87.3%

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

      4. sub-neg 87.3%

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

      5. distribute-rgt-out-- 87.9%

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

      6. associate-*l* 87.3%

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

      7. distribute-lft-neg-in 87.3%

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

      8. cancel-sign-sub 87.3%

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

      9. associate-*l* 87.3%

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

      10. associate-*l* 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in x around 0 64.7%

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

   5. Taylor expanded in a around 0 55.2%

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

   if 2.7999999999999998e-72 < t < 5.59999999999999999e57

   1. Initial program 87.9%

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

      1. sub-neg 87.9%

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

      2. +-commutative 87.9%

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

      3. associate-*l* 87.9%

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

      4. distribute-rgt-neg-in 87.9%

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

      5. fma-def 87.9%

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

      6. *-commutative 87.9%

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

      7. distribute-rgt-neg-in 87.9%

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

      8. metadata-eval 87.9%

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

      9. sub-neg 87.9%

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

      10. +-commutative 87.9%

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

      11. associate-*l* 87.9%

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

      12. distribute-rgt-neg-in 87.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in x around inf 76.2%

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

      1. *-commutative 76.2%

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

      2. associate-*r* 76.2%

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

      3. associate-*l* 76.2%

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

      4. *-commutative 76.2%

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

   6. Simplified 76.2%

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

   7. Taylor expanded in z around 0 63.2%

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

   if 9.4999999999999992e87 < t < 4.60000000000000002e150

   1. Initial program 90.0%

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

      1. sub-neg 90.0%

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

      2. associate-+l- 90.0%

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

      3. sub-neg 90.0%

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

      4. sub-neg 90.0%

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

      5. distribute-rgt-out-- 90.0%

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

      6. associate-*l* 90.0%

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

      7. distribute-lft-neg-in 90.0%

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

      8. cancel-sign-sub 90.0%

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

      9. associate-*l* 90.0%

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

      10. associate-*l* 90.0%

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

   3. Simplified 90.0%

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

      1. associate--l+ 90.0%

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

      2. associate-*r* 90.0%

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

      3. associate-*r* 90.0%

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

      4. associate-*l* 90.0%

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

      5. fma-def 90.0%

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

      6. *-commutative 90.0%

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

      7. associate-*r* 90.0%

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

   5. Applied egg-rr 90.0%

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

   6. Taylor expanded in x around 0 80.5%

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

      1. associate-*r* 80.5%

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

      2. *-commutative 80.5%

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

   8. Simplified 80.5%

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

   9. Taylor expanded in a around inf 70.5%

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

   if 4.60000000000000002e150 < t

   1. Initial program 66.7%

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

      1. sub-neg 66.7%

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

      2. associate-+l- 66.7%

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

      3. sub-neg 66.7%

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

      4. sub-neg 66.7%

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

      5. distribute-rgt-out-- 75.0%

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

      6. associate-*l* 75.0%

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

      7. distribute-lft-neg-in 75.0%

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

      8. cancel-sign-sub 75.0%

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

      9. associate-*l* 75.0%

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

      10. associate-*l* 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in x around inf 68.1%

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

   5. Taylor expanded in y around inf 68.1%

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

      1. *-commutative 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in y around 0 71.9%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+157}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-72}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+57}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27 + -4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+87}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+150}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 9: 72.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+73} \lor \neg \left(x \leq 6.6 \cdot 10^{+66}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

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 (or (<= x -4.9e+73) (not (<= x 6.6e+66)))
   (* x (- (* 18.0 (* y (* z t))) (* 4.0 i)))
   (- (+ (* b c) (* -4.0 (* t a))) (* 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 <= -4.9e+73) || !(x <= 6.6e+66)) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - (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 <= (-4.9d+73)) .or. (.not. (x <= 6.6d+66))) then
        tmp = x * ((18.0d0 * (y * (z * t))) - (4.0d0 * i))
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (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 <= -4.9e+73) || !(x <= 6.6e+66)) {
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - (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 <= -4.9e+73) or not (x <= 6.6e+66):
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i))
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - (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 <= -4.9e+73) || !(x <= 6.6e+66))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) - Float64(4.0 * i)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - 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 <= -4.9e+73) || ~((x <= 6.6e+66)))
		tmp = x * ((18.0 * (y * (z * t))) - (4.0 * i));
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - (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[Or[LessEqual[x, -4.9e+73], N[Not[LessEqual[x, 6.6e+66]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8999999999999999e73 or 6.6000000000000003e66 < x

   1. Initial program 76.2%

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

      1. sub-neg 76.2%

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

      2. associate-+l- 76.2%

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

      3. sub-neg 76.2%

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

      4. sub-neg 76.2%

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

      5. distribute-rgt-out-- 78.2%

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

      6. associate-*l* 81.1%

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

      7. distribute-lft-neg-in 81.1%

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

      8. cancel-sign-sub 81.1%

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

      9. associate-*l* 81.1%

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

      10. associate-*l* 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in x around inf 71.3%

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

   if -4.8999999999999999e73 < x < 6.6000000000000003e66

   1. Initial program 90.4%

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

      1. sub-neg 90.4%

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

      2. associate-+l- 90.4%

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

      3. sub-neg 90.4%

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

      4. sub-neg 90.4%

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

      5. distribute-rgt-out-- 92.9%

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

      6. associate-*l* 89.8%

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

      7. distribute-lft-neg-in 89.8%

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

      8. cancel-sign-sub 89.8%

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

      9. associate-*l* 89.8%

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

      10. associate-*l* 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in x around 0 73.9%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+73} \lor \neg \left(x \leq 6.6 \cdot 10^{+66}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) - 4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 10: 72.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+67} \lor \neg \left(t \leq 2.2 \cdot 10^{+85}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

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 -4.6e+67) (not (<= t 2.2e+85)))
   (* t (- (* 18.0 (* y (* x z))) (* a 4.0)))
   (- (- (* 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 <= -4.6e+67) || !(t <= 2.2e+85)) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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 <= (-4.6d+67)) .or. (.not. (t <= 2.2d+85))) then
        tmp = t * ((18.0d0 * (y * (x * z))) - (a * 4.0d0))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - ((j * 27.0d0) * k)
    end if
    code = tmp
end function

Java

assert y < z;
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 <= -4.6e+67) || !(t <= 2.2e+85)) {
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	} 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 <= -4.6e+67) or not (t <= 2.2e+85):
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0))
	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 <= -4.6e+67) || !(t <= 2.2e+85))
		tmp = Float64(t * Float64(Float64(18.0 * Float64(y * Float64(x * z))) - Float64(a * 4.0)));
	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 <= -4.6e+67) || ~((t <= 2.2e+85)))
		tmp = t * ((18.0 * (y * (x * z))) - (a * 4.0));
	else
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
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, -4.6e+67], N[Not[LessEqual[t, 2.2e+85]], $MachinePrecision]], N[(t * N[(N[(18.0 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $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 < -4.5999999999999997e67 or 2.2000000000000002e85 < t

   1. Initial program 80.0%

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

      1. sub-neg 80.0%

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

      2. associate-+l- 80.0%

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

      3. sub-neg 80.0%

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

      4. sub-neg 80.0%

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

      5. distribute-rgt-out-- 86.3%

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

      6. associate-*l* 85.2%

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

      7. distribute-lft-neg-in 85.2%

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

      8. cancel-sign-sub 85.2%

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

      9. associate-*l* 85.2%

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

      10. associate-*l* 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in t around inf 82.0%

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

   if -4.5999999999999997e67 < t < 2.2000000000000002e85

   1. Initial program 87.8%

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

   2. Taylor expanded in t around 0 82.7%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+67} \lor \neg \left(t \leq 2.2 \cdot 10^{+85}\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 11: 31.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(i \cdot -4\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.7 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-72}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (* x (* i -4.0))) (t_2 (* -4.0 (* t a))))
   (if (<= t -1.65e+69)
     t_2
     (if (<= t 7.7e-283)
       t_1
       (if (<= t 2.05e-72)
         (* b c)
         (if (<= t 1.7e+59) t_1 (if (<= t 4.4e+86) (* b c) 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 = x * (i * -4.0);
	double t_2 = -4.0 * (t * a);
	double tmp;
	if (t <= -1.65e+69) {
		tmp = t_2;
	} else if (t <= 7.7e-283) {
		tmp = t_1;
	} else if (t <= 2.05e-72) {
		tmp = b * c;
	} else if (t <= 1.7e+59) {
		tmp = t_1;
	} else if (t <= 4.4e+86) {
		tmp = b * c;
	} 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 = x * (i * (-4.0d0))
    t_2 = (-4.0d0) * (t * a)
    if (t <= (-1.65d+69)) then
        tmp = t_2
    else if (t <= 7.7d-283) then
        tmp = t_1
    else if (t <= 2.05d-72) then
        tmp = b * c
    else if (t <= 1.7d+59) then
        tmp = t_1
    else if (t <= 4.4d+86) then
        tmp = b * c
    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 = x * (i * -4.0);
	double t_2 = -4.0 * (t * a);
	double tmp;
	if (t <= -1.65e+69) {
		tmp = t_2;
	} else if (t <= 7.7e-283) {
		tmp = t_1;
	} else if (t <= 2.05e-72) {
		tmp = b * c;
	} else if (t <= 1.7e+59) {
		tmp = t_1;
	} else if (t <= 4.4e+86) {
		tmp = b * c;
	} 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 = x * (i * -4.0)
	t_2 = -4.0 * (t * a)
	tmp = 0
	if t <= -1.65e+69:
		tmp = t_2
	elif t <= 7.7e-283:
		tmp = t_1
	elif t <= 2.05e-72:
		tmp = b * c
	elif t <= 1.7e+59:
		tmp = t_1
	elif t <= 4.4e+86:
		tmp = b * c
	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(x * Float64(i * -4.0))
	t_2 = Float64(-4.0 * Float64(t * a))
	tmp = 0.0
	if (t <= -1.65e+69)
		tmp = t_2;
	elseif (t <= 7.7e-283)
		tmp = t_1;
	elseif (t <= 2.05e-72)
		tmp = Float64(b * c);
	elseif (t <= 1.7e+59)
		tmp = t_1;
	elseif (t <= 4.4e+86)
		tmp = Float64(b * c);
	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 = x * (i * -4.0);
	t_2 = -4.0 * (t * a);
	tmp = 0.0;
	if (t <= -1.65e+69)
		tmp = t_2;
	elseif (t <= 7.7e-283)
		tmp = t_1;
	elseif (t <= 2.05e-72)
		tmp = b * c;
	elseif (t <= 1.7e+59)
		tmp = t_1;
	elseif (t <= 4.4e+86)
		tmp = b * c;
	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[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.65e+69], t$95$2, If[LessEqual[t, 7.7e-283], t$95$1, If[LessEqual[t, 2.05e-72], N[(b * c), $MachinePrecision], If[LessEqual[t, 1.7e+59], t$95$1, If[LessEqual[t, 4.4e+86], N[(b * c), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6499999999999999e69 or 4.40000000000000006e86 < t

   1. Initial program 80.0%

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

      1. sub-neg 80.0%

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

      2. associate-+l- 80.0%

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

      3. sub-neg 80.0%

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

      4. sub-neg 80.0%

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

      5. distribute-rgt-out-- 86.3%

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

      6. associate-*l* 85.2%

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

      7. distribute-lft-neg-in 85.2%

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

      8. cancel-sign-sub 85.2%

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

      9. associate-*l* 85.2%

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

      10. associate-*l* 85.2%

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

   3. Simplified 85.2%

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

      1. associate--l+ 85.2%

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

      2. associate-*r* 86.3%

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

      3. associate-*r* 85.2%

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

      4. associate-*l* 85.2%

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

      5. fma-def 86.2%

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

      6. *-commutative 86.2%

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

      7. associate-*r* 86.2%

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

   5. Applied egg-rr 86.2%

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

   6. Taylor expanded in x around 0 55.2%

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

      1. associate-*r* 55.2%

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

      2. *-commutative 55.2%

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

   8. Simplified 55.2%

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

   9. Taylor expanded in a around inf 41.3%

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

   if -1.6499999999999999e69 < t < 7.7000000000000003e-283 or 2.05000000000000002e-72 < t < 1.70000000000000003e59

   1. Initial program 88.1%

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

      1. sub-neg 88.1%

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

      2. associate-+l- 88.1%

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

      3. sub-neg 88.1%

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

      4. sub-neg 88.1%

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

      5. distribute-rgt-out-- 88.1%

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

      6. associate-*l* 89.0%

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

      7. distribute-lft-neg-in 89.0%

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

      8. cancel-sign-sub 89.0%

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

      9. associate-*l* 89.0%

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

      10. associate-*l* 89.0%

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

   3. Simplified 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 x around inf 44.0%

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

   5. Taylor expanded in y around 0 34.9%

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

   if 7.7000000000000003e-283 < t < 2.05000000000000002e-72 or 1.70000000000000003e59 < t < 4.40000000000000006e86

   1. Initial program 87.1%

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

      1. sub-neg 87.1%

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

      2. associate-+l- 87.1%

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

      3. sub-neg 87.1%

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

      4. sub-neg 87.1%

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

      5. distribute-rgt-out-- 87.1%

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

      6. associate-*l* 83.5%

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

      7. distribute-lft-neg-in 83.5%

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

      8. cancel-sign-sub 83.5%

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

      9. associate-*l* 83.5%

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

      10. associate-*l* 83.6%

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

   3. Simplified 83.6%

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

      1. associate--l+ 83.6%

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

      2. associate-*r* 87.1%

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

      3. associate-*r* 83.6%

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

      4. associate-*l* 83.6%

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

      5. fma-def 83.6%

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

      6. *-commutative 83.6%

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

      7. associate-*r* 83.5%

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

   5. Applied egg-rr 83.5%

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

   6. Taylor expanded in b around inf 48.4%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+69}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;t \leq 7.7 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-72}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 12: 48.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+157}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{+150}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

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 (<= t -5e+157)
   (* 18.0 (* y (* z (* x t))))
   (if (<= t 1.1e+88)
     (- (* b c) (* 27.0 (* j k)))
     (if (<= t 3.25e+150) (* -4.0 (* t a)) (* 18.0 (* y (* t (* x z))))))))

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 <= -5e+157) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if (t <= 1.1e+88) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 3.25e+150) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = 18.0 * (y * (t * (x * z)));
	}
	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 <= (-5d+157)) then
        tmp = 18.0d0 * (y * (z * (x * t)))
    else if (t <= 1.1d+88) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (t <= 3.25d+150) then
        tmp = (-4.0d0) * (t * a)
    else
        tmp = 18.0d0 * (y * (t * (x * z)))
    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 <= -5e+157) {
		tmp = 18.0 * (y * (z * (x * t)));
	} else if (t <= 1.1e+88) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 3.25e+150) {
		tmp = -4.0 * (t * a);
	} else {
		tmp = 18.0 * (y * (t * (x * z)));
	}
	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 <= -5e+157:
		tmp = 18.0 * (y * (z * (x * t)))
	elif t <= 1.1e+88:
		tmp = (b * c) - (27.0 * (j * k))
	elif t <= 3.25e+150:
		tmp = -4.0 * (t * a)
	else:
		tmp = 18.0 * (y * (t * (x * z)))
	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 <= -5e+157)
		tmp = Float64(18.0 * Float64(y * Float64(z * Float64(x * t))));
	elseif (t <= 1.1e+88)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 3.25e+150)
		tmp = Float64(-4.0 * Float64(t * a));
	else
		tmp = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))));
	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 <= -5e+157)
		tmp = 18.0 * (y * (z * (x * t)));
	elseif (t <= 1.1e+88)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (t <= 3.25e+150)
		tmp = -4.0 * (t * a);
	else
		tmp = 18.0 * (y * (t * (x * z)));
	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[t, -5e+157], N[(18.0 * N[(y * N[(z * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+88], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.25e+150], N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision], N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.99999999999999976e157

   1. Initial program 82.8%

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

      1. sub-neg 82.8%

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

      2. associate-+l- 82.8%

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

      3. sub-neg 82.8%

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

      4. sub-neg 82.8%

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

      5. distribute-rgt-out-- 91.4%

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

      6. associate-*l* 88.5%

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

      7. distribute-lft-neg-in 88.5%

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

      8. cancel-sign-sub 88.5%

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

      9. associate-*l* 88.5%

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

      10. associate-*l* 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in i around 0 91.5%

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

   5. Taylor expanded in a around 0 60.7%

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

   6. Taylor expanded in y around inf 58.3%

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

      1. *-commutative 58.3%

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

      2. *-commutative 58.3%

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

      3. *-commutative 58.3%

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

      4. associate-*l* 66.6%

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

   8. Simplified 66.6%

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

   if -4.99999999999999976e157 < t < 1.10000000000000004e88

   1. Initial program 87.4%

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

      1. sub-neg 87.4%

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

      2. associate-+l- 87.4%

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

      3. sub-neg 87.4%

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

      4. sub-neg 87.4%

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

      5. distribute-rgt-out-- 87.9%

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

      6. associate-*l* 87.4%

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

      7. distribute-lft-neg-in 87.4%

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

      8. cancel-sign-sub 87.4%

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

      9. associate-*l* 87.4%

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

      10. associate-*l* 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in x around 0 63.7%

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

   5. Taylor expanded in a around 0 53.8%

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

   if 1.10000000000000004e88 < t < 3.25000000000000016e150

   1. Initial program 90.0%

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

      1. sub-neg 90.0%

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

      2. associate-+l- 90.0%

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

      3. sub-neg 90.0%

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

      4. sub-neg 90.0%

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

      5. distribute-rgt-out-- 90.0%

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

      6. associate-*l* 90.0%

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

      7. distribute-lft-neg-in 90.0%

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

      8. cancel-sign-sub 90.0%

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

      9. associate-*l* 90.0%

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

      10. associate-*l* 90.0%

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

   3. Simplified 90.0%

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

      1. associate--l+ 90.0%

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

      2. associate-*r* 90.0%

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

      3. associate-*r* 90.0%

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

      4. associate-*l* 90.0%

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

      5. fma-def 90.0%

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

      6. *-commutative 90.0%

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

      7. associate-*r* 90.0%

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

   5. Applied egg-rr 90.0%

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

   6. Taylor expanded in x around 0 80.5%

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

      1. associate-*r* 80.5%

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

      2. *-commutative 80.5%

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

   8. Simplified 80.5%

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

   9. Taylor expanded in a around inf 70.5%

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

   if 3.25000000000000016e150 < t

   1. Initial program 66.7%

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

      1. sub-neg 66.7%

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

      2. associate-+l- 66.7%

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

      3. sub-neg 66.7%

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

      4. sub-neg 66.7%

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

      5. distribute-rgt-out-- 75.0%

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

      6. associate-*l* 75.0%

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

      7. distribute-lft-neg-in 75.0%

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

      8. cancel-sign-sub 75.0%

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

      9. associate-*l* 75.0%

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

      10. associate-*l* 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in x around inf 68.1%

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

   5. Taylor expanded in y around inf 68.1%

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

      1. *-commutative 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in y around 0 71.9%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+157}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(z \cdot \left(x \cdot t\right)\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+88}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{+150}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 13: 33.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -3.2 \cdot 10^{-63} \lor \neg \left(k \leq 4.65 \cdot 10^{+111}\right):\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

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 (or (<= k -3.2e-63) (not (<= k 4.65e+111))) (* (* 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 ((k <= -3.2e-63) || !(k <= 4.65e+111)) {
		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 ((k <= (-3.2d-63)) .or. (.not. (k <= 4.65d+111))) 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 ((k <= -3.2e-63) || !(k <= 4.65e+111)) {
		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 (k <= -3.2e-63) or not (k <= 4.65e+111):
		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 ((k <= -3.2e-63) || !(k <= 4.65e+111))
		tmp = Float64(Float64(j * 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 ((k <= -3.2e-63) || ~((k <= 4.65e+111)))
		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[Or[LessEqual[k, -3.2e-63], N[Not[LessEqual[k, 4.65e+111]], $MachinePrecision]], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], N[(b * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -3.19999999999999989e-63 or 4.65000000000000006e111 < k

   1. Initial program 79.0%

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

      1. sub-neg 79.0%

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

      2. +-commutative 79.0%

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

      3. associate-*l* 79.0%

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

      4. distribute-rgt-neg-in 79.0%

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

      5. fma-def 82.3%

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

      6. *-commutative 82.3%

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

      7. distribute-rgt-neg-in 82.3%

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

      8. metadata-eval 82.3%

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

      9. sub-neg 82.3%

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

      10. +-commutative 82.3%

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

      11. associate-*l* 82.3%

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

      12. distribute-rgt-neg-in 82.3%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in j around inf 37.8%

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

   if -3.19999999999999989e-63 < k < 4.65000000000000006e111

   1. Initial program 90.4%

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

      1. sub-neg 90.4%

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

      2. associate-+l- 90.4%

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

      3. sub-neg 90.4%

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

      4. sub-neg 90.4%

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

      5. distribute-rgt-out-- 92.6%

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

      6. associate-*l* 90.4%

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

      7. distribute-lft-neg-in 90.4%

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

      8. cancel-sign-sub 90.4%

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

      9. associate-*l* 90.4%

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

      10. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

      1. associate--l+ 90.4%

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

      2. associate-*r* 92.6%

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

      3. associate-*r* 90.4%

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

      4. associate-*l* 90.4%

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

      5. fma-def 90.4%

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

      6. *-commutative 90.4%

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

      7. associate-*r* 90.4%

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

   5. Applied egg-rr 90.4%

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

   6. Taylor expanded in b around inf 32.0%

      \[\leadsto \color{blue}{c \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.2 \cdot 10^{-63} \lor \neg \left(k \leq 4.65 \cdot 10^{+111}\right):\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 14: 33.8% accurate, 3.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -3.2 \cdot 10^{-63}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{+110}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

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
 (if (<= k -3.2e-63)
   (* (* j k) -27.0)
   (if (<= k 3.8e+110) (* b c) (* 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 tmp;
	if (k <= -3.2e-63) {
		tmp = (j * k) * -27.0;
	} else if (k <= 3.8e+110) {
		tmp = b * c;
	} 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) :: tmp
    if (k <= (-3.2d-63)) then
        tmp = (j * k) * (-27.0d0)
    else if (k <= 3.8d+110) then
        tmp = b * c
    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 tmp;
	if (k <= -3.2e-63) {
		tmp = (j * k) * -27.0;
	} else if (k <= 3.8e+110) {
		tmp = b * c;
	} 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):
	tmp = 0
	if k <= -3.2e-63:
		tmp = (j * k) * -27.0
	elif k <= 3.8e+110:
		tmp = b * c
	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)
	tmp = 0.0
	if (k <= -3.2e-63)
		tmp = Float64(Float64(j * k) * -27.0);
	elseif (k <= 3.8e+110)
		tmp = Float64(b * c);
	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)
	tmp = 0.0;
	if (k <= -3.2e-63)
		tmp = (j * k) * -27.0;
	elseif (k <= 3.8e+110)
		tmp = b * c;
	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_] := If[LessEqual[k, -3.2e-63], N[(N[(j * k), $MachinePrecision] * -27.0), $MachinePrecision], If[LessEqual[k, 3.8e+110], N[(b * c), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -3.19999999999999989e-63

   1. Initial program 78.5%

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

      1. sub-neg 78.5%

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

      2. +-commutative 78.5%

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

      3. associate-*l* 78.5%

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

      4. distribute-rgt-neg-in 78.5%

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

      5. fma-def 79.8%

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

      6. *-commutative 79.8%

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

      7. distribute-rgt-neg-in 79.8%

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

      8. metadata-eval 79.8%

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

      9. sub-neg 79.8%

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

      10. +-commutative 79.8%

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

      11. associate-*l* 79.8%

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

      12. distribute-rgt-neg-in 79.8%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in j around inf 31.7%

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

   if -3.19999999999999989e-63 < k < 3.79999999999999989e110

   1. Initial program 90.4%

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

      1. sub-neg 90.4%

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

      2. associate-+l- 90.4%

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

      3. sub-neg 90.4%

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

      4. sub-neg 90.4%

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

      5. distribute-rgt-out-- 92.6%

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

      6. associate-*l* 90.4%

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

      7. distribute-lft-neg-in 90.4%

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

      8. cancel-sign-sub 90.4%

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

      9. associate-*l* 90.4%

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

      10. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

      1. associate--l+ 90.4%

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

      2. associate-*r* 92.6%

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

      3. associate-*r* 90.4%

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

      4. associate-*l* 90.4%

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

      5. fma-def 90.4%

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

      6. *-commutative 90.4%

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

      7. associate-*r* 90.4%

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

   5. Applied egg-rr 90.4%

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

   6. Taylor expanded in b around inf 32.0%

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

   if 3.79999999999999989e110 < k

   1. Initial program 79.9%

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

      1. sub-neg 79.9%

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

      2. +-commutative 79.9%

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

      3. associate-*l* 80.0%

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

      4. distribute-rgt-neg-in 80.0%

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

      5. fma-def 86.7%

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

      6. *-commutative 86.7%

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

      7. distribute-rgt-neg-in 86.7%

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

      8. metadata-eval 86.7%

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

      9. sub-neg 86.7%

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

      10. +-commutative 86.7%

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

      11. associate-*l* 86.7%

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

      12. distribute-rgt-neg-in 86.7%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in j around inf 48.3%

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

      1. associate-*r* 48.3%

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

      2. *-commutative 48.3%

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

      3. *-commutative 48.3%

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

      4. *-commutative 48.3%

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

   6. Simplified 48.3%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3.2 \cdot 10^{-63}:\\ \;\;\;\;\left(j \cdot k\right) \cdot -27\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{+110}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 15: 23.8% 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 84.9%

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

   1. sub-neg 84.9%

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

   2. associate-+l- 84.9%

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

   3. sub-neg 84.9%

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

   4. sub-neg 84.9%

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

   5. distribute-rgt-out-- 87.2%

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

   6. associate-*l* 86.5%

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

   7. distribute-lft-neg-in 86.5%

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

   8. cancel-sign-sub 86.5%

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

   9. associate-*l* 86.5%

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

   10. associate-*l* 86.5%

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

3. Simplified 86.5%

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

   1. associate--l+ 86.5%

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

   2. associate-*r* 87.3%

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

   3. associate-*r* 86.5%

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

   4. associate-*l* 86.5%

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

   5. fma-def 87.3%

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

   6. *-commutative 87.3%

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

   7. associate-*r* 87.2%

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

5. Applied egg-rr 87.2%

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

6. Taylor expanded in b around inf 25.1%

   \[\leadsto \color{blue}{c \cdot b} \]

7. Final simplification 25.1%

   \[\leadsto b \cdot c \]

Developer target: 89.0% 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 2023224 
(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)))