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

Percentage Accurate: 85.2% → 91.2%

Time: 24.7s

Alternatives: 17

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% 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: 91.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(N[(N[(N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(t * N[(N[(N[(y * z), $MachinePrecision] * N[(x * 18.0), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 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 94.1%

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

      1. sub-neg 94.1%

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

      2. associate-+l- 94.1%

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

      3. sub-neg 94.1%

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

      4. sub-neg 94.1%

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

      5. distribute-rgt-out-- 94.1%

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

      6. associate-*l* 95.7%

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

      7. distribute-lft-neg-in 95.7%

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

      8. cancel-sign-sub 95.7%

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

      9. associate-*l* 95.7%

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

      10. associate-*l* 95.8%

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

   3. Simplified 95.8%

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

   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-- 16.7%

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

      6. associate-*l* 25.0%

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

      7. distribute-lft-neg-in 25.0%

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

      8. cancel-sign-sub 25.0%

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

      9. associate-*l* 25.0%

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

      10. associate-*l* 25.0%

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

   3. Simplified 25.0%

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

   4. Taylor expanded in x around inf 75.0%

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

4. Final simplification 93.8%

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

Alternative 2: 90.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	return fma(j, Float64(k * -27.0), fma(x, Float64(i * -4.0), fma(t, fma(x, Float64(18.0 * Float64(y * z)), Float64(-4.0 * a)), Float64(b * c))))
end

Wolfram

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

Derivation

1. Initial program 85.3%

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

   1. sub-neg 85.3%

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

   2. +-commutative 85.3%

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

   3. associate-*l* 85.3%

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

   4. distribute-rgt-neg-in 85.3%

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

   5. fma-def 85.7%

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

   6. *-commutative 85.7%

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

   7. distribute-rgt-neg-in 85.7%

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

   8. metadata-eval 85.7%

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

   9. sub-neg 85.7%

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

   10. +-commutative 85.7%

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

   11. associate-*l* 85.7%

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

   12. distribute-rgt-neg-in 85.7%

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

3. Simplified 93.4%

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

4. Final simplification 93.4%

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

Alternative 3: 78.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-18 \cdot \left(y \cdot \left(x \cdot \left(-z\right)\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 124000000000:\\ \;\;\;\;b \cdot c + \left(-27 \cdot \left(j \cdot k\right) + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) + i \cdot -4\right)\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+168}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (- (* -18.0 (* y (* x (- z)))) (* a 4.0)))))
   (if (<= t -5.2e+79)
     t_1
     (if (<= t 124000000000.0)
       (+
        (* b c)
        (+ (* -27.0 (* j k)) (* x (+ (* 18.0 (* y (* t z))) (* i -4.0)))))
       (if (<= t 2e+168)
         (- (+ (* b c) (* -4.0 (* t a))) (* 27.0 (* j k)))
         t_1)))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((-18.0 * (y * (x * -z))) - (a * 4.0));
	double tmp;
	if (t <= -5.2e+79) {
		tmp = t_1;
	} else if (t <= 124000000000.0) {
		tmp = (b * c) + ((-27.0 * (j * k)) + (x * ((18.0 * (y * (t * z))) + (i * -4.0))));
	} else if (t <= 2e+168) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (((-18.0d0) * (y * (x * -z))) - (a * 4.0d0))
    if (t <= (-5.2d+79)) then
        tmp = t_1
    else if (t <= 124000000000.0d0) then
        tmp = (b * c) + (((-27.0d0) * (j * k)) + (x * ((18.0d0 * (y * (t * z))) + (i * (-4.0d0)))))
    else if (t <= 2d+168) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (27.0d0 * (j * k))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((-18.0 * (y * (x * -z))) - (a * 4.0));
	double tmp;
	if (t <= -5.2e+79) {
		tmp = t_1;
	} else if (t <= 124000000000.0) {
		tmp = (b * c) + ((-27.0 * (j * k)) + (x * ((18.0 * (y * (t * z))) + (i * -4.0))));
	} else if (t <= 2e+168) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((-18.0 * (y * (x * -z))) - (a * 4.0))
	tmp = 0
	if t <= -5.2e+79:
		tmp = t_1
	elif t <= 124000000000.0:
		tmp = (b * c) + ((-27.0 * (j * k)) + (x * ((18.0 * (y * (t * z))) + (i * -4.0))))
	elif t <= 2e+168:
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k))
	else:
		tmp = t_1
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(-18.0 * Float64(y * Float64(x * Float64(-z)))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -5.2e+79)
		tmp = t_1;
	elseif (t <= 124000000000.0)
		tmp = Float64(Float64(b * c) + Float64(Float64(-27.0 * Float64(j * k)) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) + Float64(i * -4.0)))));
	elseif (t <= 2e+168)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((-18.0 * (y * (x * -z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -5.2e+79)
		tmp = t_1;
	elseif (t <= 124000000000.0)
		tmp = (b * c) + ((-27.0 * (j * k)) + (x * ((18.0 * (y * (t * z))) + (i * -4.0))));
	elseif (t <= 2e+168)
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(-18.0 * N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+79], t$95$1, If[LessEqual[t, 124000000000.0], N[(N[(b * c), $MachinePrecision] + N[(N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+168], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.20000000000000029e79 or 1.9999999999999999e168 < t

   1. Initial program 86.5%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in t around -inf 80.0%

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

   if -5.20000000000000029e79 < t < 1.24e11

   1. Initial program 84.3%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in a around 0 93.1%

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

   if 1.24e11 < t < 1.9999999999999999e168

   1. Initial program 86.9%

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

      1. sub-neg 86.9%

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

      2. associate-+l- 86.9%

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

      3. sub-neg 86.9%

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

      4. sub-neg 86.9%

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

      5. distribute-rgt-out-- 86.9%

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

      6. associate-*l* 80.8%

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

      7. distribute-lft-neg-in 80.8%

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

      8. cancel-sign-sub 80.8%

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

      9. associate-*l* 80.8%

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

      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 0 77.9%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(y \cdot \left(x \cdot \left(-z\right)\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 124000000000:\\ \;\;\;\;b \cdot c + \left(-27 \cdot \left(j \cdot k\right) + x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) + i \cdot -4\right)\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+168}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(y \cdot \left(x \cdot \left(-z\right)\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 4: 44.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;k \leq -1.5 \cdot 10^{-27}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.4 \cdot 10^{+27}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 9.6 \cdot 10^{+63}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 4.0 (* x i)))))
   (if (<= k -1.5e-27)
     (* -27.0 (* j k))
     (if (<= k 2.3e-72)
       t_1
       (if (<= k 3.4e+27)
         (* 18.0 (* (* x z) (* t y)))
         (if (<= k 3.8e+50)
           t_1
           (if (<= k 9.6e+63)
             (* k (* j -27.0))
             (if (<= k 8.2e+145) t_1 (* j (* k -27.0))))))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double tmp;
	if (k <= -1.5e-27) {
		tmp = -27.0 * (j * k);
	} else if (k <= 2.3e-72) {
		tmp = t_1;
	} else if (k <= 3.4e+27) {
		tmp = 18.0 * ((x * z) * (t * y));
	} else if (k <= 3.8e+50) {
		tmp = t_1;
	} else if (k <= 9.6e+63) {
		tmp = k * (j * -27.0);
	} else if (k <= 8.2e+145) {
		tmp = t_1;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) - (4.0d0 * (x * i))
    if (k <= (-1.5d-27)) then
        tmp = (-27.0d0) * (j * k)
    else if (k <= 2.3d-72) then
        tmp = t_1
    else if (k <= 3.4d+27) then
        tmp = 18.0d0 * ((x * z) * (t * y))
    else if (k <= 3.8d+50) then
        tmp = t_1
    else if (k <= 9.6d+63) then
        tmp = k * (j * (-27.0d0))
    else if (k <= 8.2d+145) then
        tmp = t_1
    else
        tmp = j * (k * (-27.0d0))
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (4.0 * (x * i));
	double tmp;
	if (k <= -1.5e-27) {
		tmp = -27.0 * (j * k);
	} else if (k <= 2.3e-72) {
		tmp = t_1;
	} else if (k <= 3.4e+27) {
		tmp = 18.0 * ((x * z) * (t * y));
	} else if (k <= 3.8e+50) {
		tmp = t_1;
	} else if (k <= 9.6e+63) {
		tmp = k * (j * -27.0);
	} else if (k <= 8.2e+145) {
		tmp = t_1;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (4.0 * (x * i))
	tmp = 0
	if k <= -1.5e-27:
		tmp = -27.0 * (j * k)
	elif k <= 2.3e-72:
		tmp = t_1
	elif k <= 3.4e+27:
		tmp = 18.0 * ((x * z) * (t * y))
	elif k <= 3.8e+50:
		tmp = t_1
	elif k <= 9.6e+63:
		tmp = k * (j * -27.0)
	elif k <= 8.2e+145:
		tmp = t_1
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)))
	tmp = 0.0
	if (k <= -1.5e-27)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (k <= 2.3e-72)
		tmp = t_1;
	elseif (k <= 3.4e+27)
		tmp = Float64(18.0 * Float64(Float64(x * z) * Float64(t * y)));
	elseif (k <= 3.8e+50)
		tmp = t_1;
	elseif (k <= 9.6e+63)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (k <= 8.2e+145)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (4.0 * (x * i));
	tmp = 0.0;
	if (k <= -1.5e-27)
		tmp = -27.0 * (j * k);
	elseif (k <= 2.3e-72)
		tmp = t_1;
	elseif (k <= 3.4e+27)
		tmp = 18.0 * ((x * z) * (t * y));
	elseif (k <= 3.8e+50)
		tmp = t_1;
	elseif (k <= 9.6e+63)
		tmp = k * (j * -27.0);
	elseif (k <= 8.2e+145)
		tmp = t_1;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -1.5e-27], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.3e-72], t$95$1, If[LessEqual[k, 3.4e+27], N[(18.0 * N[(N[(x * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.8e+50], t$95$1, If[LessEqual[k, 9.6e+63], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 8.2e+145], t$95$1, N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -1.5000000000000001e-27

   1. Initial program 90.1%

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

      1. sub-neg 90.1%

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

      2. +-commutative 90.1%

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

      3. associate-*l* 90.2%

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

      4. distribute-rgt-neg-in 90.2%

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

      5. fma-def 91.8%

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

      6. *-commutative 91.8%

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

      7. distribute-rgt-neg-in 91.8%

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

      8. metadata-eval 91.8%

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

      9. sub-neg 91.8%

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

      10. +-commutative 91.8%

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

      11. associate-*l* 91.8%

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

      12. distribute-rgt-neg-in 91.8%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in j around inf 44.7%

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

   if -1.5000000000000001e-27 < k < 2.29999999999999995e-72 or 3.4e27 < k < 3.79999999999999987e50 or 9.6e63 < k < 8.2000000000000003e145

   1. Initial program 83.7%

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

   2. Taylor expanded in t around 0 55.9%

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

   3. Taylor expanded in j around 0 50.3%

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

   if 2.29999999999999995e-72 < k < 3.4e27

   1. Initial program 86.5%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in a around 0 80.8%

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

   5. Taylor expanded in k around 0 55.0%

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

   6. Taylor expanded in y around inf 52.5%

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

      1. *-commutative 52.5%

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

      2. associate-*r* 53.1%

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

      3. *-commutative 53.1%

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

   8. Simplified 53.1%

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

   if 3.79999999999999987e50 < k < 9.6e63

   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* 99.6%

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

      4. distribute-rgt-neg-in 99.6%

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

      5. fma-def 99.6%

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

      6. *-commutative 99.6%

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

      7. distribute-rgt-neg-in 99.6%

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

      8. metadata-eval 99.6%

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

      9. sub-neg 99.6%

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

      10. +-commutative 99.6%

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

      11. associate-*l* 99.6%

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

      12. distribute-rgt-neg-in 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in j around inf 99.2%

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

      1. *-commutative 99.2%

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

      2. associate-*r* 100.0%

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

      3. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   if 8.2000000000000003e145 < k

   1. Initial program 81.1%

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

      1. sub-neg 81.1%

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

      2. +-commutative 81.1%

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

      3. associate-*l* 81.1%

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

      4. distribute-rgt-neg-in 81.1%

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

      5. fma-def 81.1%

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

      6. *-commutative 81.1%

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

      7. distribute-rgt-neg-in 81.1%

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

      8. metadata-eval 81.1%

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

      9. sub-neg 81.1%

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

      10. +-commutative 81.1%

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

      11. associate-*l* 81.1%

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

      12. distribute-rgt-neg-in 81.1%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in j around inf 56.5%

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

      1. associate-*r* 59.4%

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

      2. *-commutative 59.4%

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

      3. *-commutative 59.4%

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

      4. *-commutative 59.4%

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

   6. Simplified 59.4%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.5 \cdot 10^{-27}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{-72}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 3.4 \cdot 10^{+27}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;k \leq 3.8 \cdot 10^{+50}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 9.6 \cdot 10^{+63}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;k \leq 8.2 \cdot 10^{+145}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 5: 58.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-243}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-302}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-57}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (- (* 18.0 (* y (* t z))) (* i 4.0)))))
   (if (<= x -2.7e+57)
     t_1
     (if (<= x -4.1e-243)
       (- (* b c) (* k (* j 27.0)))
       (if (<= x -2.1e-302)
         (* t (* a (- 4.0)))
         (if (<= x 2e-57) (- (* b c) (* 27.0 (* j k))) t_1))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	double tmp;
	if (x <= -2.7e+57) {
		tmp = t_1;
	} else if (x <= -4.1e-243) {
		tmp = (b * c) - (k * (j * 27.0));
	} else if (x <= -2.1e-302) {
		tmp = t * (a * -4.0);
	} else if (x <= 2e-57) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((18.0d0 * (y * (t * z))) - (i * 4.0d0))
    if (x <= (-2.7d+57)) then
        tmp = t_1
    else if (x <= (-4.1d-243)) then
        tmp = (b * c) - (k * (j * 27.0d0))
    else if (x <= (-2.1d-302)) then
        tmp = t * (a * -4.0d0)
    else if (x <= 2d-57) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	double tmp;
	if (x <= -2.7e+57) {
		tmp = t_1;
	} else if (x <= -4.1e-243) {
		tmp = (b * c) - (k * (j * 27.0));
	} else if (x <= -2.1e-302) {
		tmp = t * (a * -4.0);
	} else if (x <= 2e-57) {
		tmp = (b * c) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = x * ((18.0 * (y * (t * z))) - (i * 4.0))
	tmp = 0
	if x <= -2.7e+57:
		tmp = t_1
	elif x <= -4.1e-243:
		tmp = (b * c) - (k * (j * 27.0))
	elif x <= -2.1e-302:
		tmp = t * (a * -4.0)
	elif x <= 2e-57:
		tmp = (b * c) - (27.0 * (j * k))
	else:
		tmp = t_1
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(i * 4.0)))
	tmp = 0.0
	if (x <= -2.7e+57)
		tmp = t_1;
	elseif (x <= -4.1e-243)
		tmp = Float64(Float64(b * c) - Float64(k * Float64(j * 27.0)));
	elseif (x <= -2.1e-302)
		tmp = Float64(t * Float64(a * Float64(-4.0)));
	elseif (x <= 2e-57)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	tmp = 0.0;
	if (x <= -2.7e+57)
		tmp = t_1;
	elseif (x <= -4.1e-243)
		tmp = (b * c) - (k * (j * 27.0));
	elseif (x <= -2.1e-302)
		tmp = t * (a * -4.0);
	elseif (x <= 2e-57)
		tmp = (b * c) - (27.0 * (j * k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e+57], t$95$1, If[LessEqual[x, -4.1e-243], N[(N[(b * c), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.1e-302], N[(t * N[(a * (-4.0)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e-57], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.6999999999999998e57 or 1.99999999999999991e-57 < x

   1. Initial program 73.7%

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

      1. sub-neg 73.7%

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

      2. associate-+l- 73.7%

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

      3. sub-neg 73.7%

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

      4. sub-neg 73.7%

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

      5. distribute-rgt-out-- 76.1%

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

      6. associate-*l* 85.5%

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

      7. distribute-lft-neg-in 85.5%

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

      8. cancel-sign-sub 85.5%

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

      9. associate-*l* 85.5%

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

      10. associate-*l* 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in x around inf 70.3%

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

   if -2.6999999999999998e57 < x < -4.09999999999999981e-243

   1. Initial program 94.3%

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

   2. Taylor expanded in t around 0 63.1%

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

   3. Taylor expanded in i around 0 56.6%

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

      1. expm1-log1p-u 35.0%

         \[\leadsto c \cdot b - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(27 \cdot \left(k \cdot j\right)\right)\right)} \]

      2. expm1-udef 34.7%

         \[\leadsto c \cdot b - \color{blue}{\left(e^{\mathsf{log1p}\left(27 \cdot \left(k \cdot j\right)\right)} - 1\right)} \]

      3. *-commutative 34.7%

         \[\leadsto c \cdot b - \left(e^{\mathsf{log1p}\left(\color{blue}{\left(k \cdot j\right) \cdot 27}\right)} - 1\right) \]

   5. Applied egg-rr 34.7%

      \[\leadsto c \cdot b - \color{blue}{\left(e^{\mathsf{log1p}\left(\left(k \cdot j\right) \cdot 27\right)} - 1\right)} \]
   6. Step-by-step derivation

      1. expm1-def 35.0%

         \[\leadsto c \cdot b - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(k \cdot j\right) \cdot 27\right)\right)} \]

      2. expm1-log1p 56.6%

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

      3. associate-*l* 56.6%

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

   7. Simplified 56.6%

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

   if -4.09999999999999981e-243 < x < -2.10000000000000013e-302

   1. Initial program 99.9%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in t around -inf 72.8%

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

   5. Taylor expanded in y around 0 72.8%

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

      1. *-commutative 72.8%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(a \cdot 4\right)} \cdot t\right) \]

   7. Simplified 72.8%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(a \cdot 4\right)} \cdot t\right) \]

   if -2.10000000000000013e-302 < x < 1.99999999999999991e-57

   1. Initial program 97.7%

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

   2. Taylor expanded in t around 0 75.5%

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

   3. Taylor expanded in i around 0 71.4%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-243}:\\ \;\;\;\;b \cdot c - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-302}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-57}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \end{array} \]

Alternative 6: 72.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-18 \cdot \left(y \cdot \left(x \cdot \left(-z\right)\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 380000000:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+168}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (- (* -18.0 (* y (* x (- z)))) (* a 4.0)))))
   (if (<= t -5.6e+81)
     t_1
     (if (<= t 380000000.0)
       (- (- (* b c) (* 4.0 (* x i))) (* k (* j 27.0)))
       (if (<= t 1.95e+168)
         (- (+ (* b c) (* -4.0 (* t a))) (* 27.0 (* j k)))
         t_1)))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((-18.0 * (y * (x * -z))) - (a * 4.0));
	double tmp;
	if (t <= -5.6e+81) {
		tmp = t_1;
	} else if (t <= 380000000.0) {
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	} else if (t <= 1.95e+168) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (((-18.0d0) * (y * (x * -z))) - (a * 4.0d0))
    if (t <= (-5.6d+81)) then
        tmp = t_1
    else if (t <= 380000000.0d0) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - (k * (j * 27.0d0))
    else if (t <= 1.95d+168) then
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (27.0d0 * (j * k))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((-18.0 * (y * (x * -z))) - (a * 4.0));
	double tmp;
	if (t <= -5.6e+81) {
		tmp = t_1;
	} else if (t <= 380000000.0) {
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	} else if (t <= 1.95e+168) {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((-18.0 * (y * (x * -z))) - (a * 4.0))
	tmp = 0
	if t <= -5.6e+81:
		tmp = t_1
	elif t <= 380000000.0:
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0))
	elif t <= 1.95e+168:
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k))
	else:
		tmp = t_1
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(-18.0 * Float64(y * Float64(x * Float64(-z)))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -5.6e+81)
		tmp = t_1;
	elseif (t <= 380000000.0)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(k * Float64(j * 27.0)));
	elseif (t <= 1.95e+168)
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(27.0 * Float64(j * k)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((-18.0 * (y * (x * -z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -5.6e+81)
		tmp = t_1;
	elseif (t <= 380000000.0)
		tmp = ((b * c) - (4.0 * (x * i))) - (k * (j * 27.0));
	elseif (t <= 1.95e+168)
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(-18.0 * N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+81], t$95$1, If[LessEqual[t, 380000000.0], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+168], N[(N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5999999999999999e81 or 1.95e168 < t

   1. Initial program 87.5%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in t around -inf 81.0%

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

   if -5.5999999999999999e81 < t < 3.8e8

   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. Taylor expanded in t around 0 82.7%

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

   if 3.8e8 < t < 1.95e168

   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-- 87.4%

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

      6. associate-*l* 81.3%

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

      7. distribute-lft-neg-in 81.3%

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

      8. cancel-sign-sub 81.3%

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

      9. associate-*l* 81.3%

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

      10. associate-*l* 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in x around 0 75.7%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(y \cdot \left(x \cdot \left(-z\right)\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 380000000:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+168}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(y \cdot \left(x \cdot \left(-z\right)\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 7: 48.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := 27 \cdot \left(j \cdot \left(-k\right)\right) - 4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right)\right)\\ \mathbf{elif}\;b \leq 8000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* 27.0 (* j (- k))) (* 4.0 (* x i))))
        (t_2 (- (* b c) (* 27.0 (* j k)))))
   (if (<= b -3.2e+190)
     t_2
     (if (<= b -4.6e+105)
       t_1
       (if (<= b -1.35e+39) (* t (* a (- 4.0))) (if (<= b 8000.0) t_1 t_2))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (27.0 * (j * -k)) - (4.0 * (x * i));
	double t_2 = (b * c) - (27.0 * (j * k));
	double tmp;
	if (b <= -3.2e+190) {
		tmp = t_2;
	} else if (b <= -4.6e+105) {
		tmp = t_1;
	} else if (b <= -1.35e+39) {
		tmp = t * (a * -4.0);
	} else if (b <= 8000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (27.0d0 * (j * -k)) - (4.0d0 * (x * i))
    t_2 = (b * c) - (27.0d0 * (j * k))
    if (b <= (-3.2d+190)) then
        tmp = t_2
    else if (b <= (-4.6d+105)) then
        tmp = t_1
    else if (b <= (-1.35d+39)) then
        tmp = t * (a * -4.0d0)
    else if (b <= 8000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (27.0 * (j * -k)) - (4.0 * (x * i));
	double t_2 = (b * c) - (27.0 * (j * k));
	double tmp;
	if (b <= -3.2e+190) {
		tmp = t_2;
	} else if (b <= -4.6e+105) {
		tmp = t_1;
	} else if (b <= -1.35e+39) {
		tmp = t * (a * -4.0);
	} else if (b <= 8000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (27.0 * (j * -k)) - (4.0 * (x * i))
	t_2 = (b * c) - (27.0 * (j * k))
	tmp = 0
	if b <= -3.2e+190:
		tmp = t_2
	elif b <= -4.6e+105:
		tmp = t_1
	elif b <= -1.35e+39:
		tmp = t * (a * -4.0)
	elif b <= 8000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(27.0 * Float64(j * Float64(-k))) - Float64(4.0 * Float64(x * i)))
	t_2 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	tmp = 0.0
	if (b <= -3.2e+190)
		tmp = t_2;
	elseif (b <= -4.6e+105)
		tmp = t_1;
	elseif (b <= -1.35e+39)
		tmp = Float64(t * Float64(a * Float64(-4.0)));
	elseif (b <= 8000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (27.0 * (j * -k)) - (4.0 * (x * i));
	t_2 = (b * c) - (27.0 * (j * k));
	tmp = 0.0;
	if (b <= -3.2e+190)
		tmp = t_2;
	elseif (b <= -4.6e+105)
		tmp = t_1;
	elseif (b <= -1.35e+39)
		tmp = t * (a * -4.0);
	elseif (b <= 8000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(27.0 * N[(j * (-k)), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+190], t$95$2, If[LessEqual[b, -4.6e+105], t$95$1, If[LessEqual[b, -1.35e+39], N[(t * N[(a * (-4.0)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.2000000000000001e190 or 8e3 < b

   1. Initial program 85.2%

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

   2. Taylor expanded in t around 0 69.9%

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

   3. Taylor expanded in i around 0 59.3%

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

   if -3.2000000000000001e190 < b < -4.5999999999999996e105 or -1.35000000000000002e39 < b < 8e3

   1. Initial program 85.1%

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

   2. Taylor expanded in t around 0 58.3%

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

   3. Taylor expanded in c around 0 53.6%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]

   if -4.5999999999999996e105 < b < -1.35000000000000002e39

   1. Initial program 87.2%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in t around -inf 55.4%

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

   5. Taylor expanded in y around 0 38.7%

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

      1. *-commutative 38.7%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(a \cdot 4\right)} \cdot t\right) \]

   7. Simplified 38.7%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(a \cdot 4\right)} \cdot t\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+190}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{+105}:\\ \;\;\;\;27 \cdot \left(j \cdot \left(-k\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right)\right)\\ \mathbf{elif}\;b \leq 8000:\\ \;\;\;\;27 \cdot \left(j \cdot \left(-k\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 8: 59.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(-18 \cdot \left(y \cdot \left(x \cdot \left(-z\right)\right)\right) - a \cdot 4\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-266}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 110000000:\\ \;\;\;\;27 \cdot \left(j \cdot \left(-k\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (- (* -18.0 (* y (* x (- z)))) (* a 4.0)))))
   (if (<= t -3.3e-49)
     t_1
     (if (<= t 9.6e-266)
       (- (* b c) (* 27.0 (* j k)))
       (if (<= t 110000000.0) (- (* 27.0 (* j (- k))) (* 4.0 (* x i))) t_1)))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((-18.0 * (y * (x * -z))) - (a * 4.0));
	double tmp;
	if (t <= -3.3e-49) {
		tmp = t_1;
	} else if (t <= 9.6e-266) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 110000000.0) {
		tmp = (27.0 * (j * -k)) - (4.0 * (x * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (((-18.0d0) * (y * (x * -z))) - (a * 4.0d0))
    if (t <= (-3.3d-49)) then
        tmp = t_1
    else if (t <= 9.6d-266) then
        tmp = (b * c) - (27.0d0 * (j * k))
    else if (t <= 110000000.0d0) then
        tmp = (27.0d0 * (j * -k)) - (4.0d0 * (x * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * ((-18.0 * (y * (x * -z))) - (a * 4.0));
	double tmp;
	if (t <= -3.3e-49) {
		tmp = t_1;
	} else if (t <= 9.6e-266) {
		tmp = (b * c) - (27.0 * (j * k));
	} else if (t <= 110000000.0) {
		tmp = (27.0 * (j * -k)) - (4.0 * (x * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((-18.0 * (y * (x * -z))) - (a * 4.0))
	tmp = 0
	if t <= -3.3e-49:
		tmp = t_1
	elif t <= 9.6e-266:
		tmp = (b * c) - (27.0 * (j * k))
	elif t <= 110000000.0:
		tmp = (27.0 * (j * -k)) - (4.0 * (x * i))
	else:
		tmp = t_1
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(-18.0 * Float64(y * Float64(x * Float64(-z)))) - Float64(a * 4.0)))
	tmp = 0.0
	if (t <= -3.3e-49)
		tmp = t_1;
	elseif (t <= 9.6e-266)
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	elseif (t <= 110000000.0)
		tmp = Float64(Float64(27.0 * Float64(j * Float64(-k))) - Float64(4.0 * Float64(x * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((-18.0 * (y * (x * -z))) - (a * 4.0));
	tmp = 0.0;
	if (t <= -3.3e-49)
		tmp = t_1;
	elseif (t <= 9.6e-266)
		tmp = (b * c) - (27.0 * (j * k));
	elseif (t <= 110000000.0)
		tmp = (27.0 * (j * -k)) - (4.0 * (x * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(-18.0 * N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e-49], t$95$1, If[LessEqual[t, 9.6e-266], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 110000000.0], N[(N[(27.0 * N[(j * (-k)), $MachinePrecision]), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3e-49 or 1.1e8 < t

   1. Initial program 87.4%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in t around -inf 71.0%

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

   if -3.3e-49 < t < 9.5999999999999999e-266

   1. Initial program 86.7%

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

   2. Taylor expanded in t around 0 89.4%

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

   3. Taylor expanded in i around 0 72.2%

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

   if 9.5999999999999999e-266 < t < 1.1e8

   1. Initial program 79.6%

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

   2. Taylor expanded in t around 0 80.9%

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

   3. Taylor expanded in c around 0 63.5%

      \[\leadsto \color{blue}{-1 \cdot \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(k \cdot j\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(y \cdot \left(x \cdot \left(-z\right)\right)\right) - a \cdot 4\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-266}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;t \leq 110000000:\\ \;\;\;\;27 \cdot \left(j \cdot \left(-k\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-18 \cdot \left(y \cdot \left(x \cdot \left(-z\right)\right)\right) - a \cdot 4\right)\\ \end{array} \]

Alternative 9: 70.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+153} \lor \neg \left(x \leq 2.85 \cdot 10^{-42}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: 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 -1.32e+153) (not (<= x 2.85e-42)))
   (* x (- (* 18.0 (* y (* t z))) (* i 4.0)))
   (- (+ (* b c) (* -4.0 (* t a))) (* 27.0 (* j k)))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -1.32e+153) || !(x <= 2.85e-42)) {
		tmp = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-1.32d+153)) .or. (.not. (x <= 2.85d-42))) then
        tmp = x * ((18.0d0 * (y * (t * z))) - (i * 4.0d0))
    else
        tmp = ((b * c) + ((-4.0d0) * (t * a))) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -1.32e+153) || !(x <= 2.85e-42)) {
		tmp = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	} else {
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -1.32e+153) or not (x <= 2.85e-42):
		tmp = x * ((18.0 * (y * (t * z))) - (i * 4.0))
	else:
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k))
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -1.32e+153) || !(x <= 2.85e-42))
		tmp = Float64(x * Float64(Float64(18.0 * Float64(y * Float64(t * z))) - Float64(i * 4.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a))) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -1.32e+153) || ~((x <= 2.85e-42)))
		tmp = x * ((18.0 * (y * (t * z))) - (i * 4.0));
	else
		tmp = ((b * c) + (-4.0 * (t * a))) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -1.32e+153], N[Not[LessEqual[x, 2.85e-42]], $MachinePrecision]], N[(x * N[(N[(18.0 * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * 4.0), $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 < -1.3200000000000001e153 or 2.85e-42 < x

   1. Initial program 71.5%

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

      1. sub-neg 71.5%

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

      2. associate-+l- 71.5%

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

      3. sub-neg 71.5%

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

      4. sub-neg 71.5%

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

      5. distribute-rgt-out-- 74.5%

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

      6. associate-*l* 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 x around inf 75.1%

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

   if -1.3200000000000001e153 < x < 2.85e-42

   1. Initial program 94.1%

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

      1. sub-neg 94.1%

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

      2. associate-+l- 94.1%

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

      3. sub-neg 94.1%

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

      4. sub-neg 94.1%

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

      5. distribute-rgt-out-- 94.8%

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

      6. associate-*l* 91.6%

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

      7. distribute-lft-neg-in 91.6%

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

      8. cancel-sign-sub 91.6%

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

      9. associate-*l* 91.6%

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

      10. associate-*l* 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in x around 0 80.7%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+153} \lor \neg \left(x \leq 2.85 \cdot 10^{-42}\right):\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(t \cdot z\right)\right) - i \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right) - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 10: 49.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -2.2 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{-72}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 5.8 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(z \cdot \left(x \cdot \left(y \cdot \left(--18\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* j k)))))
   (if (<= k -2.2e-49)
     t_1
     (if (<= k 2.3e-72)
       (- (* b c) (* 4.0 (* x i)))
       (if (<= k 5.8e+27) (* t (* z (* x (* y (- -18.0))))) t_1)))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double tmp;
	if (k <= -2.2e-49) {
		tmp = t_1;
	} else if (k <= 2.3e-72) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (k <= 5.8e+27) {
		tmp = t * (z * (x * (y * -(-18.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) - (27.0d0 * (j * k))
    if (k <= (-2.2d-49)) then
        tmp = t_1
    else if (k <= 2.3d-72) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (k <= 5.8d+27) then
        tmp = t * (z * (x * (y * -(-18.0d0))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double tmp;
	if (k <= -2.2e-49) {
		tmp = t_1;
	} else if (k <= 2.3e-72) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (k <= 5.8e+27) {
		tmp = t * (z * (x * (y * -(-18.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (27.0 * (j * k))
	tmp = 0
	if k <= -2.2e-49:
		tmp = t_1
	elif k <= 2.3e-72:
		tmp = (b * c) - (4.0 * (x * i))
	elif k <= 5.8e+27:
		tmp = t * (z * (x * (y * -(-18.0))))
	else:
		tmp = t_1
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	tmp = 0.0
	if (k <= -2.2e-49)
		tmp = t_1;
	elseif (k <= 2.3e-72)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (k <= 5.8e+27)
		tmp = Float64(t * Float64(z * Float64(x * Float64(y * Float64(-(-18.0))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (27.0 * (j * k));
	tmp = 0.0;
	if (k <= -2.2e-49)
		tmp = t_1;
	elseif (k <= 2.3e-72)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (k <= 5.8e+27)
		tmp = t * (z * (x * (y * -(-18.0))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -2.2e-49], t$95$1, If[LessEqual[k, 2.3e-72], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5.8e+27], N[(t * N[(z * N[(x * N[(y * (--18.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if k < -2.1999999999999999e-49 or 5.8000000000000002e27 < k

   1. Initial program 86.7%

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

   2. Taylor expanded in t around 0 70.2%

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

   3. Taylor expanded in i around 0 57.2%

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

   if -2.1999999999999999e-49 < k < 2.29999999999999995e-72

   1. Initial program 83.4%

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

   2. Taylor expanded in t around 0 53.1%

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

   3. Taylor expanded in j around 0 51.7%

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

   if 2.29999999999999995e-72 < k < 5.8000000000000002e27

   1. Initial program 87.3%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in t around -inf 61.8%

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

   5. Taylor expanded in y around inf 49.7%

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

      1. associate-*r* 49.7%

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

      2. *-commutative 49.7%

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

      3. *-commutative 49.7%

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

   7. Simplified 49.7%

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

   8. Taylor expanded in z around 0 49.7%

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

      1. associate-*r* 49.7%

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

      2. *-commutative 49.7%

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

      3. *-commutative 49.7%

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

      4. associate-*l* 43.6%

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

   10. Simplified 43.6%

       \[\leadsto -1 \cdot \left(\color{blue}{\left(z \cdot \left(x \cdot \left(y \cdot -18\right)\right)\right)} \cdot t\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -2.2 \cdot 10^{-49}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{-72}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 5.8 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(z \cdot \left(x \cdot \left(y \cdot \left(--18\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 11: 49.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -9.5 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{-74}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 5.5 \cdot 10^{+27}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* b c) (* 27.0 (* j k)))))
   (if (<= k -9.5e-62)
     t_1
     (if (<= k 6.2e-74)
       (- (* b c) (* 4.0 (* x i)))
       (if (<= k 5.5e+27) (* 18.0 (* (* x z) (* t y))) t_1)))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double tmp;
	if (k <= -9.5e-62) {
		tmp = t_1;
	} else if (k <= 6.2e-74) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (k <= 5.5e+27) {
		tmp = 18.0 * ((x * z) * (t * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * c) - (27.0d0 * (j * k))
    if (k <= (-9.5d-62)) then
        tmp = t_1
    else if (k <= 6.2d-74) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (k <= 5.5d+27) then
        tmp = 18.0d0 * ((x * z) * (t * y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (b * c) - (27.0 * (j * k));
	double tmp;
	if (k <= -9.5e-62) {
		tmp = t_1;
	} else if (k <= 6.2e-74) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (k <= 5.5e+27) {
		tmp = 18.0 * ((x * z) * (t * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) - (27.0 * (j * k))
	tmp = 0
	if k <= -9.5e-62:
		tmp = t_1
	elif k <= 6.2e-74:
		tmp = (b * c) - (4.0 * (x * i))
	elif k <= 5.5e+27:
		tmp = 18.0 * ((x * z) * (t * y))
	else:
		tmp = t_1
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)))
	tmp = 0.0
	if (k <= -9.5e-62)
		tmp = t_1;
	elseif (k <= 6.2e-74)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (k <= 5.5e+27)
		tmp = Float64(18.0 * Float64(Float64(x * z) * Float64(t * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) - (27.0 * (j * k));
	tmp = 0.0;
	if (k <= -9.5e-62)
		tmp = t_1;
	elseif (k <= 6.2e-74)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (k <= 5.5e+27)
		tmp = 18.0 * ((x * z) * (t * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -9.5e-62], t$95$1, If[LessEqual[k, 6.2e-74], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 5.5e+27], N[(18.0 * N[(N[(x * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if k < -9.49999999999999951e-62 or 5.49999999999999966e27 < k

   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. Taylor expanded in t around 0 69.2%

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

   3. Taylor expanded in i around 0 56.0%

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

   if -9.49999999999999951e-62 < k < 6.2000000000000003e-74

   1. Initial program 82.6%

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

   2. Taylor expanded in t around 0 53.6%

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

   3. Taylor expanded in j around 0 52.2%

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

   if 6.2000000000000003e-74 < k < 5.49999999999999966e27

   1. Initial program 87.3%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in a around 0 82.0%

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

   5. Taylor expanded in k around 0 57.8%

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

   6. Taylor expanded in y around inf 49.6%

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

      1. *-commutative 49.6%

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

      2. associate-*r* 50.2%

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

      3. *-commutative 50.2%

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

   8. Simplified 50.2%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -9.5 \cdot 10^{-62}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 6.2 \cdot 10^{-74}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 5.5 \cdot 10^{+27}:\\ \;\;\;\;18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 12: 32.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot \left(-4\right)\right)\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-53}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-307}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 160000000:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a (- 4.0)))))
   (if (<= t -5.6e+203)
     t_1
     (if (<= t -4.8e-53)
       (* 18.0 (* y (* t (* x z))))
       (if (<= t -1.15e-307)
         (* j (* k -27.0))
         (if (<= t 160000000.0) (* -4.0 (* x i)) t_1))))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (t <= -5.6e+203) {
		tmp = t_1;
	} else if (t <= -4.8e-53) {
		tmp = 18.0 * (y * (t * (x * z)));
	} else if (t <= -1.15e-307) {
		tmp = j * (k * -27.0);
	} else if (t <= 160000000.0) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * -4.0d0)
    if (t <= (-5.6d+203)) then
        tmp = t_1
    else if (t <= (-4.8d-53)) then
        tmp = 18.0d0 * (y * (t * (x * z)))
    else if (t <= (-1.15d-307)) then
        tmp = j * (k * (-27.0d0))
    else if (t <= 160000000.0d0) then
        tmp = (-4.0d0) * (x * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (t <= -5.6e+203) {
		tmp = t_1;
	} else if (t <= -4.8e-53) {
		tmp = 18.0 * (y * (t * (x * z)));
	} else if (t <= -1.15e-307) {
		tmp = j * (k * -27.0);
	} else if (t <= 160000000.0) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if t <= -5.6e+203:
		tmp = t_1
	elif t <= -4.8e-53:
		tmp = 18.0 * (y * (t * (x * z)))
	elif t <= -1.15e-307:
		tmp = j * (k * -27.0)
	elif t <= 160000000.0:
		tmp = -4.0 * (x * i)
	else:
		tmp = t_1
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * Float64(-4.0)))
	tmp = 0.0
	if (t <= -5.6e+203)
		tmp = t_1;
	elseif (t <= -4.8e-53)
		tmp = Float64(18.0 * Float64(y * Float64(t * Float64(x * z))));
	elseif (t <= -1.15e-307)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (t <= 160000000.0)
		tmp = Float64(-4.0 * Float64(x * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (t <= -5.6e+203)
		tmp = t_1;
	elseif (t <= -4.8e-53)
		tmp = 18.0 * (y * (t * (x * z)));
	elseif (t <= -1.15e-307)
		tmp = j * (k * -27.0);
	elseif (t <= 160000000.0)
		tmp = -4.0 * (x * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * (-4.0)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+203], t$95$1, If[LessEqual[t, -4.8e-53], N[(18.0 * N[(y * N[(t * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.15e-307], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 160000000.0], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.5999999999999998e203 or 1.6e8 < t

   1. Initial program 85.3%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in t around -inf 73.6%

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

   5. Taylor expanded in y around 0 50.8%

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

      1. *-commutative 50.8%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(a \cdot 4\right)} \cdot t\right) \]

   7. Simplified 50.8%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(a \cdot 4\right)} \cdot t\right) \]

   if -5.5999999999999998e203 < t < -4.80000000000000015e-53

   1. Initial program 92.3%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in a around 0 75.9%

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

   5. Taylor expanded in k around 0 63.9%

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

   6. Taylor expanded in y around inf 41.3%

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

   if -4.80000000000000015e-53 < t < -1.1499999999999999e-307

   1. Initial program 87.0%

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

      1. sub-neg 87.0%

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

      2. +-commutative 87.0%

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

      3. associate-*l* 87.0%

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

      4. distribute-rgt-neg-in 87.0%

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

      5. fma-def 87.0%

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

      6. *-commutative 87.0%

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

      7. distribute-rgt-neg-in 87.0%

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

      8. metadata-eval 87.0%

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

      9. sub-neg 87.0%

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

      10. +-commutative 87.0%

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

      11. associate-*l* 87.0%

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

      12. distribute-rgt-neg-in 87.0%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in j around inf 47.4%

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

      1. associate-*r* 47.4%

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

      2. *-commutative 47.4%

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

      3. *-commutative 47.4%

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

      4. *-commutative 47.4%

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

   6. Simplified 47.4%

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

   if -1.1499999999999999e-307 < t < 1.6e8

   1. Initial program 80.3%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in a around 0 90.6%

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

   5. Taylor expanded in k around 0 68.2%

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

   6. Taylor expanded in i around inf 39.3%

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

      1. *-commutative 39.3%

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

   8. Simplified 39.3%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+203}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right)\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-53}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-307}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 160000000:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right)\right)\\ \end{array} \]

Alternative 13: 31.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot \left(-4\right)\right)\\ \mathbf{if}\;t \leq -6.6 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-307}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 115000000:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (* a (- 4.0)))))
   (if (<= t -6.6e+33)
     t_1
     (if (<= t -1.3e-307)
       (* j (* k -27.0))
       (if (<= t 115000000.0) (* -4.0 (* x i)) t_1)))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (t <= -6.6e+33) {
		tmp = t_1;
	} else if (t <= -1.3e-307) {
		tmp = j * (k * -27.0);
	} else if (t <= 115000000.0) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * -4.0d0)
    if (t <= (-6.6d+33)) then
        tmp = t_1
    else if (t <= (-1.3d-307)) then
        tmp = j * (k * (-27.0d0))
    else if (t <= 115000000.0d0) then
        tmp = (-4.0d0) * (x * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (t <= -6.6e+33) {
		tmp = t_1;
	} else if (t <= -1.3e-307) {
		tmp = j * (k * -27.0);
	} else if (t <= 115000000.0) {
		tmp = -4.0 * (x * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * (a * -4.0)
	tmp = 0
	if t <= -6.6e+33:
		tmp = t_1
	elif t <= -1.3e-307:
		tmp = j * (k * -27.0)
	elif t <= 115000000.0:
		tmp = -4.0 * (x * i)
	else:
		tmp = t_1
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(a * Float64(-4.0)))
	tmp = 0.0
	if (t <= -6.6e+33)
		tmp = t_1;
	elseif (t <= -1.3e-307)
		tmp = Float64(j * Float64(k * -27.0));
	elseif (t <= 115000000.0)
		tmp = Float64(-4.0 * Float64(x * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (t <= -6.6e+33)
		tmp = t_1;
	elseif (t <= -1.3e-307)
		tmp = j * (k * -27.0);
	elseif (t <= 115000000.0)
		tmp = -4.0 * (x * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(a * (-4.0)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.6e+33], t$95$1, If[LessEqual[t, -1.3e-307], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 115000000.0], N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.59999999999999953e33 or 1.15e8 < t

   1. Initial program 87.5%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in t around -inf 71.7%

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

   5. Taylor expanded in y around 0 46.8%

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

      1. *-commutative 46.8%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(a \cdot 4\right)} \cdot t\right) \]

   7. Simplified 46.8%

      \[\leadsto -1 \cdot \left(\color{blue}{\left(a \cdot 4\right)} \cdot t\right) \]

   if -6.59999999999999953e33 < t < -1.29999999999999998e-307

   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. +-commutative 87.1%

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

      3. associate-*l* 87.1%

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

      4. distribute-rgt-neg-in 87.1%

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

      5. fma-def 87.1%

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

      6. *-commutative 87.1%

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

      7. distribute-rgt-neg-in 87.1%

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

      8. metadata-eval 87.1%

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

      9. sub-neg 87.1%

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

      10. +-commutative 87.1%

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

      11. associate-*l* 87.1%

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

      12. distribute-rgt-neg-in 87.1%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in j around inf 43.0%

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

      1. associate-*r* 43.0%

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

      2. *-commutative 43.0%

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

      3. *-commutative 43.0%

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

      4. *-commutative 43.0%

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

   6. Simplified 43.0%

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

   if -1.29999999999999998e-307 < t < 1.15e8

   1. Initial program 80.3%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in a around 0 90.6%

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

   5. Taylor expanded in k around 0 68.2%

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

   6. Taylor expanded in i around inf 39.3%

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

      1. *-commutative 39.3%

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

   8. Simplified 39.3%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right)\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-307}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 115000000:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-4\right)\right)\\ \end{array} \]

Alternative 14: 31.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;x \leq -5.3 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-197}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* x i))))
   (if (<= x -5.3e+85)
     t_1
     (if (<= x -9.2e-197) (* b c) (if (<= x 5e-21) (* j (* k -27.0)) t_1)))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (x <= -5.3e+85) {
		tmp = t_1;
	} else if (x <= -9.2e-197) {
		tmp = b * c;
	} else if (x <= 5e-21) {
		tmp = j * (k * -27.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (x * i)
    if (x <= (-5.3d+85)) then
        tmp = t_1
    else if (x <= (-9.2d-197)) then
        tmp = b * c
    else if (x <= 5d-21) then
        tmp = j * (k * (-27.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (x * i);
	double tmp;
	if (x <= -5.3e+85) {
		tmp = t_1;
	} else if (x <= -9.2e-197) {
		tmp = b * c;
	} else if (x <= 5e-21) {
		tmp = j * (k * -27.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (x * i)
	tmp = 0
	if x <= -5.3e+85:
		tmp = t_1
	elif x <= -9.2e-197:
		tmp = b * c
	elif x <= 5e-21:
		tmp = j * (k * -27.0)
	else:
		tmp = t_1
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(x * i))
	tmp = 0.0
	if (x <= -5.3e+85)
		tmp = t_1;
	elseif (x <= -9.2e-197)
		tmp = Float64(b * c);
	elseif (x <= 5e-21)
		tmp = Float64(j * Float64(k * -27.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (x * i);
	tmp = 0.0;
	if (x <= -5.3e+85)
		tmp = t_1;
	elseif (x <= -9.2e-197)
		tmp = b * c;
	elseif (x <= 5e-21)
		tmp = j * (k * -27.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.3e+85], t$95$1, If[LessEqual[x, -9.2e-197], N[(b * c), $MachinePrecision], If[LessEqual[x, 5e-21], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.2999999999999999e85 or 4.99999999999999973e-21 < x

   1. Initial program 72.6%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in a around 0 88.1%

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

   5. Taylor expanded in k around 0 77.8%

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

   6. Taylor expanded in i around inf 42.4%

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

      1. *-commutative 42.4%

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

   8. Simplified 42.4%

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

   if -5.2999999999999999e85 < x < -9.2000000000000002e-197

   1. Initial program 91.4%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in a around 0 72.1%

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

   5. Taylor expanded in c around inf 30.8%

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

   if -9.2000000000000002e-197 < x < 4.99999999999999973e-21

   1. Initial program 97.4%

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

      1. sub-neg 97.4%

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

      2. +-commutative 97.4%

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

      3. associate-*l* 97.4%

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

      4. distribute-rgt-neg-in 97.4%

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

      5. fma-def 97.4%

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

      6. *-commutative 97.4%

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

      7. distribute-rgt-neg-in 97.4%

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

      8. metadata-eval 97.4%

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

      9. sub-neg 97.4%

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

      10. +-commutative 97.4%

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

      11. associate-*l* 97.4%

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

      12. distribute-rgt-neg-in 97.4%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in j around inf 43.0%

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

      1. associate-*r* 43.0%

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

      2. *-commutative 43.0%

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

      3. *-commutative 43.0%

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

      4. *-commutative 43.0%

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

   6. Simplified 43.0%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{+85}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-197}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 15: 33.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -9.5 \cdot 10^{-28} \lor \neg \left(k \leq 3.3 \cdot 10^{-19}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= k -9.5e-28) (not (<= k 3.3e-19))) (* -27.0 (* j k)) (* b c)))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((k <= -9.5e-28) || !(k <= 3.3e-19)) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((k <= (-9.5d-28)) .or. (.not. (k <= 3.3d-19))) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((k <= -9.5e-28) || !(k <= 3.3e-19)) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (k <= -9.5e-28) or not (k <= 3.3e-19):
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((k <= -9.5e-28) || !(k <= 3.3e-19))
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((k <= -9.5e-28) || ~((k <= 3.3e-19)))
		tmp = -27.0 * (j * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[k, -9.5e-28], N[Not[LessEqual[k, 3.3e-19]], $MachinePrecision]], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if k < -9.50000000000000001e-28 or 3.2999999999999998e-19 < k

   1. Initial program 86.8%

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

      1. sub-neg 86.8%

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

      2. +-commutative 86.8%

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

      3. associate-*l* 86.8%

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

      4. distribute-rgt-neg-in 86.8%

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

      5. fma-def 87.5%

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

      6. *-commutative 87.5%

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

      7. distribute-rgt-neg-in 87.5%

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

      8. metadata-eval 87.5%

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

      9. sub-neg 87.5%

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

      10. +-commutative 87.5%

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

      11. associate-*l* 87.5%

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

      12. distribute-rgt-neg-in 87.5%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in j around inf 42.7%

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

   if -9.50000000000000001e-28 < k < 3.2999999999999998e-19

   1. Initial program 83.6%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in a around 0 74.6%

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

   5. Taylor expanded in c around inf 24.2%

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

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -9.5 \cdot 10^{-28} \lor \neg \left(k \leq 3.3 \cdot 10^{-19}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 16: 33.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ \begin{array}{l} \mathbf{if}\;k \leq -1.5 \cdot 10^{-27}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{-18}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k -1.5e-27)
   (* -27.0 (* j k))
   (if (<= k 2.3e-18) (* b c) (* j (* k -27.0)))))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -1.5e-27) {
		tmp = -27.0 * (j * k);
	} else if (k <= 2.3e-18) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (k <= (-1.5d-27)) then
        tmp = (-27.0d0) * (j * k)
    else if (k <= 2.3d-18) then
        tmp = b * c
    else
        tmp = j * (k * (-27.0d0))
    end if
    code = tmp
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= -1.5e-27) {
		tmp = -27.0 * (j * k);
	} else if (k <= 2.3e-18) {
		tmp = b * c;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

[j, k] = sort([j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if k <= -1.5e-27:
		tmp = -27.0 * (j * k)
	elif k <= 2.3e-18:
		tmp = b * c
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

j, k = sort([j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= -1.5e-27)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (k <= 2.3e-18)
		tmp = Float64(b * c);
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

j, k = num2cell(sort([j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (k <= -1.5e-27)
		tmp = -27.0 * (j * k);
	elseif (k <= 2.3e-18)
		tmp = b * c;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, -1.5e-27], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 2.3e-18], N[(b * c), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < -1.5000000000000001e-27

   1. Initial program 90.1%

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

      1. sub-neg 90.1%

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

      2. +-commutative 90.1%

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

      3. associate-*l* 90.2%

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

      4. distribute-rgt-neg-in 90.2%

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

      5. fma-def 91.8%

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

      6. *-commutative 91.8%

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

      7. distribute-rgt-neg-in 91.8%

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

      8. metadata-eval 91.8%

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

      9. sub-neg 91.8%

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

      10. +-commutative 91.8%

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

      11. associate-*l* 91.8%

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

      12. distribute-rgt-neg-in 91.8%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in j around inf 44.7%

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

   if -1.5000000000000001e-27 < k < 2.3000000000000001e-18

   1. Initial program 83.8%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in a around 0 74.8%

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

   5. Taylor expanded in c around inf 24.8%

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

   if 2.3000000000000001e-18 < k

   1. Initial program 83.9%

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

      1. sub-neg 83.9%

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

      2. +-commutative 83.9%

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

      3. associate-*l* 83.8%

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

      4. distribute-rgt-neg-in 83.8%

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

      5. fma-def 83.9%

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

      6. *-commutative 83.9%

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

      7. distribute-rgt-neg-in 83.9%

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

      8. metadata-eval 83.9%

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

      9. sub-neg 83.9%

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

      10. +-commutative 83.9%

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

      11. associate-*l* 83.9%

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

      12. distribute-rgt-neg-in 83.9%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in j around inf 41.6%

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

      1. associate-*r* 42.9%

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

      2. *-commutative 42.9%

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

      3. *-commutative 42.9%

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

      4. *-commutative 42.9%

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

   6. Simplified 42.9%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.5 \cdot 10^{-27}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 2.3 \cdot 10^{-18}:\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 17: 23.0% accurate, 10.3× speedup

Math

\[\begin{array}{l} [j, k] = \mathsf{sort}([j, k])\\ \\ b \cdot c \end{array} \]

FPCore

NOTE: j and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k) :precision binary64 (* b c))

C

assert(j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Fortran

NOTE: j and k should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = b * c
end function

Java

assert j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return b * c;
}

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: j and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(b * c), $MachinePrecision]

Derivation

1. Initial program 85.3%

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

3. Simplified 91.5%

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

4. Taylor expanded in a around 0 77.5%

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

5. Taylor expanded in c around inf 19.9%

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

6. Final simplification 19.9%

   \[\leadsto b \cdot c \]

Developer target: 89.4% 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 2023195 
(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)))