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

Percentage Accurate: 85.5% → 92.1%

Time: 40.4s

Alternatives: 27

Speedup: 1.0×

• 51.3% 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: 85.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (-
           (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
           (* (* x 4.0) i))
          (* (* j 27.0) k))))
   (if (<= t_1 INFINITY) t_1 (* x (+ (* 18.0 (* z (* y t))) (* i -4.0))))))

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

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x * N[(N[(18.0 * N[(z * N[(y * t), $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 94.9%

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

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

   1. Initial program 0.0%

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

      1. associate--l- 0.0%

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

      2. associate-+l- 0.0%

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

      3. associate--l- 0.0%

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

      4. *-commutative 0.0%

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

      5. associate-*r* 0.0%

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

      6. associate-*l* 3.2%

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

      7. associate-*r* 6.5%

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

      8. *-commutative 6.5%

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

      9. associate-*l* 3.2%

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

      10. associate--l- 3.2%

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

   3. Simplified 19.6%

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

   4. Taylor expanded in a around 0 26.0%

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

      1. +-commutative 26.0%

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

      2. *-commutative 26.0%

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

      3. associate-*r* 29.0%

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

      4. associate-*l* 29.0%

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

      5. associate-*r* 29.0%

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

      6. *-commutative 29.0%

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

      7. associate-*r* 26.0%

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

      8. fma-def 26.0%

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

      9. *-commutative 26.0%

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

      10. associate-*l* 32.3%

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

      11. *-commutative 32.3%

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

      12. associate-*l* 32.3%

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

      13. *-commutative 32.3%

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

      14. associate-*r* 32.3%

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

      15. *-commutative 32.3%

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

      16. *-commutative 32.3%

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

      17. associate-*r* 32.3%

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

      18. associate-*l* 32.2%

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

      19. *-commutative 32.2%

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

   6. Simplified 32.2%

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

   7. Taylor expanded in x around inf 64.9%

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

      1. cancel-sign-sub-inv 64.9%

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

      2. metadata-eval 64.9%

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

      3. *-commutative 64.9%

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

      4. associate-*r* 64.9%

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

   9. Simplified 64.9%

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

4. Final simplification 91.3%

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

Alternative 2: 66.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_2 := b \cdot c + t_1\\ t_3 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ t_4 := t_1 + -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;b \cdot c \leq -5.7 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq -7.5 \cdot 10^{-98}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \cdot c \leq -4.8 \cdot 10^{-148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot c \leq -2.1 \cdot 10^{-185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-286}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{+203}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (+ (* t a) (* x i))))
        (t_2 (+ (* b c) t_1))
        (t_3 (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))
        (t_4 (+ t_1 (* -27.0 (* j k)))))
   (if (<= (* b c) -5.7e+135)
     t_2
     (if (<= (* b c) -7.5e-98)
       t_4
       (if (<= (* b c) -4.8e-148)
         t_3
         (if (<= (* b c) -2.1e-185)
           t_2
           (if (<= (* b c) -3.6e-286)
             t_3
             (if (<= (* b c) 9.5e+203) t_4 (* b c)))))))))

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 = -4.0 * ((t * a) + (x * i));
	double t_2 = (b * c) + t_1;
	double t_3 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double t_4 = t_1 + (-27.0 * (j * k));
	double tmp;
	if ((b * c) <= -5.7e+135) {
		tmp = t_2;
	} else if ((b * c) <= -7.5e-98) {
		tmp = t_4;
	} else if ((b * c) <= -4.8e-148) {
		tmp = t_3;
	} else if ((b * c) <= -2.1e-185) {
		tmp = t_2;
	} else if ((b * c) <= -3.6e-286) {
		tmp = t_3;
	} else if ((b * c) <= 9.5e+203) {
		tmp = t_4;
	} else {
		tmp = b * c;
	}
	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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (-4.0d0) * ((t * a) + (x * i))
    t_2 = (b * c) + t_1
    t_3 = t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0)))
    t_4 = t_1 + ((-27.0d0) * (j * k))
    if ((b * c) <= (-5.7d+135)) then
        tmp = t_2
    else if ((b * c) <= (-7.5d-98)) then
        tmp = t_4
    else if ((b * c) <= (-4.8d-148)) then
        tmp = t_3
    else if ((b * c) <= (-2.1d-185)) then
        tmp = t_2
    else if ((b * c) <= (-3.6d-286)) then
        tmp = t_3
    else if ((b * c) <= 9.5d+203) then
        tmp = t_4
    else
        tmp = b * c
    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 = -4.0 * ((t * a) + (x * i));
	double t_2 = (b * c) + t_1;
	double t_3 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double t_4 = t_1 + (-27.0 * (j * k));
	double tmp;
	if ((b * c) <= -5.7e+135) {
		tmp = t_2;
	} else if ((b * c) <= -7.5e-98) {
		tmp = t_4;
	} else if ((b * c) <= -4.8e-148) {
		tmp = t_3;
	} else if ((b * c) <= -2.1e-185) {
		tmp = t_2;
	} else if ((b * c) <= -3.6e-286) {
		tmp = t_3;
	} else if ((b * c) <= 9.5e+203) {
		tmp = t_4;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * ((t * a) + (x * i))
	t_2 = (b * c) + t_1
	t_3 = t * ((18.0 * (x * (y * z))) + (a * -4.0))
	t_4 = t_1 + (-27.0 * (j * k))
	tmp = 0
	if (b * c) <= -5.7e+135:
		tmp = t_2
	elif (b * c) <= -7.5e-98:
		tmp = t_4
	elif (b * c) <= -4.8e-148:
		tmp = t_3
	elif (b * c) <= -2.1e-185:
		tmp = t_2
	elif (b * c) <= -3.6e-286:
		tmp = t_3
	elif (b * c) <= 9.5e+203:
		tmp = t_4
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0)))
	t_4 = Float64(t_1 + Float64(-27.0 * Float64(j * k)))
	tmp = 0.0
	if (Float64(b * c) <= -5.7e+135)
		tmp = t_2;
	elseif (Float64(b * c) <= -7.5e-98)
		tmp = t_4;
	elseif (Float64(b * c) <= -4.8e-148)
		tmp = t_3;
	elseif (Float64(b * c) <= -2.1e-185)
		tmp = t_2;
	elseif (Float64(b * c) <= -3.6e-286)
		tmp = t_3;
	elseif (Float64(b * c) <= 9.5e+203)
		tmp = t_4;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * ((t * a) + (x * i));
	t_2 = (b * c) + t_1;
	t_3 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	t_4 = t_1 + (-27.0 * (j * k));
	tmp = 0.0;
	if ((b * c) <= -5.7e+135)
		tmp = t_2;
	elseif ((b * c) <= -7.5e-98)
		tmp = t_4;
	elseif ((b * c) <= -4.8e-148)
		tmp = t_3;
	elseif ((b * c) <= -2.1e-185)
		tmp = t_2;
	elseif ((b * c) <= -3.6e-286)
		tmp = t_3;
	elseif ((b * c) <= 9.5e+203)
		tmp = t_4;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5.7e+135], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -7.5e-98], t$95$4, If[LessEqual[N[(b * c), $MachinePrecision], -4.8e-148], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], -2.1e-185], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -3.6e-286], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], 9.5e+203], t$95$4, N[(b * c), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -5.7000000000000002e135 or -4.8000000000000002e-148 < (*.f64 b c) < -2.1e-185

   1. Initial program 87.8%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in y around 0 90.2%

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

      1. associate-+r+ 90.2%

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

      2. +-commutative 90.2%

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

      3. distribute-lft-out 90.2%

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

      4. metadata-eval 90.2%

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

      5. cancel-sign-sub-inv 90.2%

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

      6. distribute-lft-out 90.2%

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

      7. fma-neg 92.7%

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

      8. distribute-lft-out 92.7%

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

      9. distribute-lft-neg-in 92.7%

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

      10. metadata-eval 92.7%

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

      11. +-commutative 92.7%

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

      12. *-commutative 92.7%

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

   6. Simplified 92.7%

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

   7. Taylor expanded in j around 0 85.6%

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

   if -5.7000000000000002e135 < (*.f64 b c) < -7.5000000000000006e-98 or -3.60000000000000013e-286 < (*.f64 b c) < 9.4999999999999995e203

   1. Initial program 85.0%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in y around 0 76.9%

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

      1. associate-+r+ 76.9%

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

      2. +-commutative 76.9%

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

      3. distribute-lft-out 76.9%

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

      4. metadata-eval 76.9%

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

      5. cancel-sign-sub-inv 76.9%

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

      6. distribute-lft-out 76.9%

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

      7. fma-neg 77.0%

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

      8. distribute-lft-out 77.0%

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

      9. distribute-lft-neg-in 77.0%

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

      10. metadata-eval 77.0%

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

      11. +-commutative 77.0%

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

      12. *-commutative 77.0%

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

   6. Simplified 77.0%

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

   7. Taylor expanded in b around 0 70.2%

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

   if -7.5000000000000006e-98 < (*.f64 b c) < -4.8000000000000002e-148 or -2.1e-185 < (*.f64 b c) < -3.60000000000000013e-286

   1. Initial program 84.3%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in b around 0 94.8%

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

   6. Simplified 94.9%

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

   7. Taylor expanded in t around inf 84.4%

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

   if 9.4999999999999995e203 < (*.f64 b c)

   1. Initial program 60.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in y around 0 64.0%

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

      1. associate-+r+ 64.0%

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

      2. +-commutative 64.0%

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

      3. distribute-lft-out 64.0%

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

      4. metadata-eval 64.0%

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

      5. cancel-sign-sub-inv 64.0%

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

      6. distribute-lft-out 64.0%

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

      7. fma-neg 74.0%

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

      8. distribute-lft-out 74.0%

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

      9. distribute-lft-neg-in 74.0%

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

      10. metadata-eval 74.0%

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

      11. +-commutative 74.0%

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

      12. *-commutative 74.0%

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

   6. Simplified 74.0%

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

   7. Taylor expanded in b around inf 78.7%

      \[\leadsto \color{blue}{b \cdot c} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.7 \cdot 10^{+135}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -7.5 \cdot 10^{-98}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -4.8 \cdot 10^{-148}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -2.1 \cdot 10^{-185}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-286}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 9.5 \cdot 10^{+203}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 3: 66.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_2 := b \cdot c + t_1\\ t_3 := t_1 + -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;b \cdot c \leq -3.2 \cdot 10^{+137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq -6.6 \cdot 10^{-97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot c \leq -9.6 \cdot 10^{-148}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -6.2 \cdot 10^{-185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq -1.32 \cdot 10^{-307}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2.05 \cdot 10^{+201}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (+ (* t a) (* x i))))
        (t_2 (+ (* b c) t_1))
        (t_3 (+ t_1 (* -27.0 (* j k)))))
   (if (<= (* b c) -3.2e+137)
     t_2
     (if (<= (* b c) -6.6e-97)
       t_3
       (if (<= (* b c) -9.6e-148)
         (* t (+ (* 18.0 (* x (* y z))) (* a -4.0)))
         (if (<= (* b c) -6.2e-185)
           t_2
           (if (<= (* b c) -1.32e-307)
             (+ (* j (* k -27.0)) (* 18.0 (* t (* z (* x y)))))
             (if (<= (* b c) 2.05e+201) t_3 (* b c)))))))))

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 = -4.0 * ((t * a) + (x * i));
	double t_2 = (b * c) + t_1;
	double t_3 = t_1 + (-27.0 * (j * k));
	double tmp;
	if ((b * c) <= -3.2e+137) {
		tmp = t_2;
	} else if ((b * c) <= -6.6e-97) {
		tmp = t_3;
	} else if ((b * c) <= -9.6e-148) {
		tmp = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	} else if ((b * c) <= -6.2e-185) {
		tmp = t_2;
	} else if ((b * c) <= -1.32e-307) {
		tmp = (j * (k * -27.0)) + (18.0 * (t * (z * (x * y))));
	} else if ((b * c) <= 2.05e+201) {
		tmp = t_3;
	} else {
		tmp = b * c;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (-4.0d0) * ((t * a) + (x * i))
    t_2 = (b * c) + t_1
    t_3 = t_1 + ((-27.0d0) * (j * k))
    if ((b * c) <= (-3.2d+137)) then
        tmp = t_2
    else if ((b * c) <= (-6.6d-97)) then
        tmp = t_3
    else if ((b * c) <= (-9.6d-148)) then
        tmp = t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0)))
    else if ((b * c) <= (-6.2d-185)) then
        tmp = t_2
    else if ((b * c) <= (-1.32d-307)) then
        tmp = (j * (k * (-27.0d0))) + (18.0d0 * (t * (z * (x * y))))
    else if ((b * c) <= 2.05d+201) then
        tmp = t_3
    else
        tmp = b * c
    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 = -4.0 * ((t * a) + (x * i));
	double t_2 = (b * c) + t_1;
	double t_3 = t_1 + (-27.0 * (j * k));
	double tmp;
	if ((b * c) <= -3.2e+137) {
		tmp = t_2;
	} else if ((b * c) <= -6.6e-97) {
		tmp = t_3;
	} else if ((b * c) <= -9.6e-148) {
		tmp = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	} else if ((b * c) <= -6.2e-185) {
		tmp = t_2;
	} else if ((b * c) <= -1.32e-307) {
		tmp = (j * (k * -27.0)) + (18.0 * (t * (z * (x * y))));
	} else if ((b * c) <= 2.05e+201) {
		tmp = t_3;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * ((t * a) + (x * i))
	t_2 = (b * c) + t_1
	t_3 = t_1 + (-27.0 * (j * k))
	tmp = 0
	if (b * c) <= -3.2e+137:
		tmp = t_2
	elif (b * c) <= -6.6e-97:
		tmp = t_3
	elif (b * c) <= -9.6e-148:
		tmp = t * ((18.0 * (x * (y * z))) + (a * -4.0))
	elif (b * c) <= -6.2e-185:
		tmp = t_2
	elif (b * c) <= -1.32e-307:
		tmp = (j * (k * -27.0)) + (18.0 * (t * (z * (x * y))))
	elif (b * c) <= 2.05e+201:
		tmp = t_3
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)))
	t_2 = Float64(Float64(b * c) + t_1)
	t_3 = Float64(t_1 + Float64(-27.0 * Float64(j * k)))
	tmp = 0.0
	if (Float64(b * c) <= -3.2e+137)
		tmp = t_2;
	elseif (Float64(b * c) <= -6.6e-97)
		tmp = t_3;
	elseif (Float64(b * c) <= -9.6e-148)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0)));
	elseif (Float64(b * c) <= -6.2e-185)
		tmp = t_2;
	elseif (Float64(b * c) <= -1.32e-307)
		tmp = Float64(Float64(j * Float64(k * -27.0)) + Float64(18.0 * Float64(t * Float64(z * Float64(x * y)))));
	elseif (Float64(b * c) <= 2.05e+201)
		tmp = t_3;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * ((t * a) + (x * i));
	t_2 = (b * c) + t_1;
	t_3 = t_1 + (-27.0 * (j * k));
	tmp = 0.0;
	if ((b * c) <= -3.2e+137)
		tmp = t_2;
	elseif ((b * c) <= -6.6e-97)
		tmp = t_3;
	elseif ((b * c) <= -9.6e-148)
		tmp = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	elseif ((b * c) <= -6.2e-185)
		tmp = t_2;
	elseif ((b * c) <= -1.32e-307)
		tmp = (j * (k * -27.0)) + (18.0 * (t * (z * (x * y))));
	elseif ((b * c) <= 2.05e+201)
		tmp = t_3;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -3.2e+137], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -6.6e-97], t$95$3, If[LessEqual[N[(b * c), $MachinePrecision], -9.6e-148], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -6.2e-185], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -1.32e-307], N[(N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision] + N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.05e+201], t$95$3, N[(b * c), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -3.20000000000000019e137 or -9.6000000000000005e-148 < (*.f64 b c) < -6.1999999999999994e-185

   1. Initial program 87.8%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in y around 0 90.2%

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

      1. associate-+r+ 90.2%

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

      2. +-commutative 90.2%

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

      3. distribute-lft-out 90.2%

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

      4. metadata-eval 90.2%

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

      5. cancel-sign-sub-inv 90.2%

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

      6. distribute-lft-out 90.2%

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

      7. fma-neg 92.7%

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

      8. distribute-lft-out 92.7%

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

      9. distribute-lft-neg-in 92.7%

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

      10. metadata-eval 92.7%

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

      11. +-commutative 92.7%

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

      12. *-commutative 92.7%

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

   6. Simplified 92.7%

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

   7. Taylor expanded in j around 0 85.6%

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

   if -3.20000000000000019e137 < (*.f64 b c) < -6.6000000000000002e-97 or -1.3199999999999999e-307 < (*.f64 b c) < 2.0500000000000001e201

   1. Initial program 84.6%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in y around 0 77.6%

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

      1. associate-+r+ 77.6%

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

      2. +-commutative 77.6%

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

      3. distribute-lft-out 77.6%

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

      4. metadata-eval 77.6%

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

      5. cancel-sign-sub-inv 77.6%

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

      6. distribute-lft-out 77.6%

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

      7. fma-neg 77.6%

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

      8. distribute-lft-out 77.6%

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

      9. distribute-lft-neg-in 77.6%

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

      10. metadata-eval 77.6%

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

      11. +-commutative 77.6%

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

      12. *-commutative 77.6%

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

   6. Simplified 77.6%

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

   7. Taylor expanded in b around 0 70.6%

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

   if -6.6000000000000002e-97 < (*.f64 b c) < -9.6000000000000005e-148

   1. Initial program 75.4%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in b around 0 87.9%

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

   6. Simplified 87.9%

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

   7. Taylor expanded in t around inf 87.9%

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

   if -6.1999999999999994e-185 < (*.f64 b c) < -1.3199999999999999e-307

   1. Initial program 93.2%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in y around inf 68.5%

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

      1. *-commutative 68.5%

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

      2. *-commutative 68.5%

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

      3. associate-*l* 62.1%

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

      4. *-commutative 62.1%

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

      5. associate-*r* 62.1%

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

      6. associate-*r* 62.1%

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

      7. associate-*l* 62.2%

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

      8. *-commutative 62.2%

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

   6. Simplified 62.2%

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

   7. Taylor expanded in x around 0 68.5%

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

      1. associate-*r* 74.9%

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

   9. Simplified 74.9%

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

   if 2.0500000000000001e201 < (*.f64 b c)

   1. Initial program 60.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in y around 0 64.0%

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

      1. associate-+r+ 64.0%

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

      2. +-commutative 64.0%

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

      3. distribute-lft-out 64.0%

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

      4. metadata-eval 64.0%

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

      5. cancel-sign-sub-inv 64.0%

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

      6. distribute-lft-out 64.0%

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

      7. fma-neg 74.0%

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

      8. distribute-lft-out 74.0%

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

      9. distribute-lft-neg-in 74.0%

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

      10. metadata-eval 74.0%

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

      11. +-commutative 74.0%

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

      12. *-commutative 74.0%

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

   6. Simplified 74.0%

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

   7. Taylor expanded in b around inf 78.7%

      \[\leadsto \color{blue}{b \cdot c} \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.2 \cdot 10^{+137}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -6.6 \cdot 10^{-97}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -9.6 \cdot 10^{-148}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -6.2 \cdot 10^{-185}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1.32 \cdot 10^{-307}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2.05 \cdot 10^{+201}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 4: 53.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -4.9 \cdot 10^{+110}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1.9 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq -4.2 \cdot 10^{-237}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.15 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 9.8 \cdot 10^{-117}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(t \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.7 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ t_1 (* -4.0 (* t a)))))
   (if (<= (* b c) -4.9e+110)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= (* b c) -1.9e-114)
       t_2
       (if (<= (* b c) -4.2e-237)
         (* -4.0 (+ (* t a) (* x i)))
         (if (<= (* b c) 1.15e-172)
           t_2
           (if (<= (* b c) 9.8e-117)
             (* 18.0 (* z (* t (* x y))))
             (if (<= (* b c) 3.7e-20) t_2 (+ (* b c) t_1)))))))))

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 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (t * a));
	double tmp;
	if ((b * c) <= -4.9e+110) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -1.9e-114) {
		tmp = t_2;
	} else if ((b * c) <= -4.2e-237) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else if ((b * c) <= 1.15e-172) {
		tmp = t_2;
	} else if ((b * c) <= 9.8e-117) {
		tmp = 18.0 * (z * (t * (x * y)));
	} else if ((b * c) <= 3.7e-20) {
		tmp = t_2;
	} else {
		tmp = (b * c) + t_1;
	}
	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 = j * (k * (-27.0d0))
    t_2 = t_1 + ((-4.0d0) * (t * a))
    if ((b * c) <= (-4.9d+110)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if ((b * c) <= (-1.9d-114)) then
        tmp = t_2
    else if ((b * c) <= (-4.2d-237)) then
        tmp = (-4.0d0) * ((t * a) + (x * i))
    else if ((b * c) <= 1.15d-172) then
        tmp = t_2
    else if ((b * c) <= 9.8d-117) then
        tmp = 18.0d0 * (z * (t * (x * y)))
    else if ((b * c) <= 3.7d-20) then
        tmp = t_2
    else
        tmp = (b * c) + t_1
    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 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (t * a));
	double tmp;
	if ((b * c) <= -4.9e+110) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -1.9e-114) {
		tmp = t_2;
	} else if ((b * c) <= -4.2e-237) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else if ((b * c) <= 1.15e-172) {
		tmp = t_2;
	} else if ((b * c) <= 9.8e-117) {
		tmp = 18.0 * (z * (t * (x * y)));
	} else if ((b * c) <= 3.7e-20) {
		tmp = t_2;
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (-4.0 * (t * a))
	tmp = 0
	if (b * c) <= -4.9e+110:
		tmp = (b * c) - (4.0 * (x * i))
	elif (b * c) <= -1.9e-114:
		tmp = t_2
	elif (b * c) <= -4.2e-237:
		tmp = -4.0 * ((t * a) + (x * i))
	elif (b * c) <= 1.15e-172:
		tmp = t_2
	elif (b * c) <= 9.8e-117:
		tmp = 18.0 * (z * (t * (x * y)))
	elif (b * c) <= 3.7e-20:
		tmp = t_2
	else:
		tmp = (b * c) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (Float64(b * c) <= -4.9e+110)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= -1.9e-114)
		tmp = t_2;
	elseif (Float64(b * c) <= -4.2e-237)
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	elseif (Float64(b * c) <= 1.15e-172)
		tmp = t_2;
	elseif (Float64(b * c) <= 9.8e-117)
		tmp = Float64(18.0 * Float64(z * Float64(t * Float64(x * y))));
	elseif (Float64(b * c) <= 3.7e-20)
		tmp = t_2;
	else
		tmp = Float64(Float64(b * c) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (-4.0 * (t * a));
	tmp = 0.0;
	if ((b * c) <= -4.9e+110)
		tmp = (b * c) - (4.0 * (x * i));
	elseif ((b * c) <= -1.9e-114)
		tmp = t_2;
	elseif ((b * c) <= -4.2e-237)
		tmp = -4.0 * ((t * a) + (x * i));
	elseif ((b * c) <= 1.15e-172)
		tmp = t_2;
	elseif ((b * c) <= 9.8e-117)
		tmp = 18.0 * (z * (t * (x * y)));
	elseif ((b * c) <= 3.7e-20)
		tmp = t_2;
	else
		tmp = (b * c) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -4.9e+110], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.9e-114], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -4.2e-237], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.15e-172], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 9.8e-117], N[(18.0 * N[(z * N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.7e-20], t$95$2, N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -4.90000000000000002e110

   1. Initial program 88.9%

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

   2. Taylor expanded in y around 0 88.9%

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

   3. Taylor expanded in a around 0 83.6%

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

      1. associate-*r* 83.6%

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

      2. *-commutative 83.6%

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

      3. *-commutative 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in j around 0 75.0%

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

   if -4.90000000000000002e110 < (*.f64 b c) < -1.8999999999999999e-114 or -4.2000000000000002e-237 < (*.f64 b c) < 1.14999999999999998e-172 or 9.7999999999999995e-117 < (*.f64 b c) < 3.7000000000000001e-20

   1. Initial program 84.4%

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

   3. Simplified 85.9%

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

   4. Taylor expanded in a around inf 64.0%

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

      1. *-commutative 64.0%

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

   6. Simplified 64.0%

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

   if -1.8999999999999999e-114 < (*.f64 b c) < -4.2000000000000002e-237

   1. Initial program 87.0%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in y around 0 62.7%

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

      1. associate-+r+ 62.7%

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

      2. +-commutative 62.7%

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

      3. distribute-lft-out 62.7%

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

      4. metadata-eval 62.7%

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

      5. cancel-sign-sub-inv 62.7%

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

      6. distribute-lft-out 62.7%

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

      7. fma-neg 62.7%

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

      8. distribute-lft-out 62.7%

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

      9. distribute-lft-neg-in 62.7%

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

      10. metadata-eval 62.7%

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

      11. +-commutative 62.7%

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

      12. *-commutative 62.7%

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

   6. Simplified 62.7%

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

   7. Taylor expanded in j around 0 62.7%

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

   8. Taylor expanded in b around 0 58.5%

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

   if 1.14999999999999998e-172 < (*.f64 b c) < 9.7999999999999995e-117

   1. Initial program 75.2%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in b around 0 67.4%

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

   6. Simplified 67.4%

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

   7. Taylor expanded in y around inf 42.7%

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

      1. associate-*r* 46.1%

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

      2. associate-*r* 54.1%

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

   9. Simplified 54.1%

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

   if 3.7000000000000001e-20 < (*.f64 b c)

   1. Initial program 78.4%

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

   3. Simplified 81.9%

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

   4. Taylor expanded in b around inf 56.9%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.9 \cdot 10^{+110}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1.9 \cdot 10^{-114}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -4.2 \cdot 10^{-237}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.15 \cdot 10^{-172}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 9.8 \cdot 10^{-117}:\\ \;\;\;\;18 \cdot \left(z \cdot \left(t \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.7 \cdot 10^{-20}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 5: 54.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;b \cdot c \leq -3.25 \cdot 10^{+109}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1.45 \cdot 10^{-28}:\\ \;\;\;\;t_2 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -7 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -2.1 \cdot 10^{-183}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -6.5 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 10^{-16}:\\ \;\;\;\;t_2 + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))
        (t_2 (* j (* k -27.0))))
   (if (<= (* b c) -3.25e+109)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= (* b c) -1.45e-28)
       (+ t_2 (* -4.0 (* t a)))
       (if (<= (* b c) -7e-147)
         t_1
         (if (<= (* b c) -2.1e-183)
           (* -4.0 (+ (* t a) (* x i)))
           (if (<= (* b c) -6.5e-287)
             t_1
             (if (<= (* b c) 1e-16)
               (+ t_2 (* x (* i -4.0)))
               (+ (* b c) 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 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double t_2 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -3.25e+109) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -1.45e-28) {
		tmp = t_2 + (-4.0 * (t * a));
	} else if ((b * c) <= -7e-147) {
		tmp = t_1;
	} else if ((b * c) <= -2.1e-183) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else if ((b * c) <= -6.5e-287) {
		tmp = t_1;
	} else if ((b * c) <= 1e-16) {
		tmp = t_2 + (x * (i * -4.0));
	} else {
		tmp = (b * c) + 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 = t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0)))
    t_2 = j * (k * (-27.0d0))
    if ((b * c) <= (-3.25d+109)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if ((b * c) <= (-1.45d-28)) then
        tmp = t_2 + ((-4.0d0) * (t * a))
    else if ((b * c) <= (-7d-147)) then
        tmp = t_1
    else if ((b * c) <= (-2.1d-183)) then
        tmp = (-4.0d0) * ((t * a) + (x * i))
    else if ((b * c) <= (-6.5d-287)) then
        tmp = t_1
    else if ((b * c) <= 1d-16) then
        tmp = t_2 + (x * (i * (-4.0d0)))
    else
        tmp = (b * c) + 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 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double t_2 = j * (k * -27.0);
	double tmp;
	if ((b * c) <= -3.25e+109) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -1.45e-28) {
		tmp = t_2 + (-4.0 * (t * a));
	} else if ((b * c) <= -7e-147) {
		tmp = t_1;
	} else if ((b * c) <= -2.1e-183) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else if ((b * c) <= -6.5e-287) {
		tmp = t_1;
	} else if ((b * c) <= 1e-16) {
		tmp = t_2 + (x * (i * -4.0));
	} else {
		tmp = (b * c) + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = t * ((18.0 * (x * (y * z))) + (a * -4.0))
	t_2 = j * (k * -27.0)
	tmp = 0
	if (b * c) <= -3.25e+109:
		tmp = (b * c) - (4.0 * (x * i))
	elif (b * c) <= -1.45e-28:
		tmp = t_2 + (-4.0 * (t * a))
	elif (b * c) <= -7e-147:
		tmp = t_1
	elif (b * c) <= -2.1e-183:
		tmp = -4.0 * ((t * a) + (x * i))
	elif (b * c) <= -6.5e-287:
		tmp = t_1
	elif (b * c) <= 1e-16:
		tmp = t_2 + (x * (i * -4.0))
	else:
		tmp = (b * c) + t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0)))
	t_2 = Float64(j * Float64(k * -27.0))
	tmp = 0.0
	if (Float64(b * c) <= -3.25e+109)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= -1.45e-28)
		tmp = Float64(t_2 + Float64(-4.0 * Float64(t * a)));
	elseif (Float64(b * c) <= -7e-147)
		tmp = t_1;
	elseif (Float64(b * c) <= -2.1e-183)
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	elseif (Float64(b * c) <= -6.5e-287)
		tmp = t_1;
	elseif (Float64(b * c) <= 1e-16)
		tmp = Float64(t_2 + Float64(x * Float64(i * -4.0)));
	else
		tmp = Float64(Float64(b * c) + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	t_2 = j * (k * -27.0);
	tmp = 0.0;
	if ((b * c) <= -3.25e+109)
		tmp = (b * c) - (4.0 * (x * i));
	elseif ((b * c) <= -1.45e-28)
		tmp = t_2 + (-4.0 * (t * a));
	elseif ((b * c) <= -7e-147)
		tmp = t_1;
	elseif ((b * c) <= -2.1e-183)
		tmp = -4.0 * ((t * a) + (x * i));
	elseif ((b * c) <= -6.5e-287)
		tmp = t_1;
	elseif ((b * c) <= 1e-16)
		tmp = t_2 + (x * (i * -4.0));
	else
		tmp = (b * c) + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -3.25e+109], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.45e-28], N[(t$95$2 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -7e-147], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -2.1e-183], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -6.5e-287], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1e-16], N[(t$95$2 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 b c) < -3.25e109

   1. Initial program 88.9%

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

   2. Taylor expanded in y around 0 88.9%

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

   3. Taylor expanded in a around 0 83.6%

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

      1. associate-*r* 83.6%

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

      2. *-commutative 83.6%

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

      3. *-commutative 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in j around 0 75.0%

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

   if -3.25e109 < (*.f64 b c) < -1.45000000000000006e-28

   1. Initial program 83.7%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in a around inf 71.5%

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

      1. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   if -1.45000000000000006e-28 < (*.f64 b c) < -7.00000000000000007e-147 or -2.1000000000000002e-183 < (*.f64 b c) < -6.4999999999999999e-287

   1. Initial program 88.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in b around 0 96.1%

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

   6. Simplified 96.1%

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

   7. Taylor expanded in t around inf 80.4%

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

   if -7.00000000000000007e-147 < (*.f64 b c) < -2.1000000000000002e-183

   1. Initial program 80.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in y around 0 90.0%

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

      1. associate-+r+ 90.0%

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

      2. +-commutative 90.0%

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

      3. distribute-lft-out 90.0%

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

      4. metadata-eval 90.0%

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

      5. cancel-sign-sub-inv 90.0%

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

      6. distribute-lft-out 90.0%

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

      7. fma-neg 90.0%

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

      8. distribute-lft-out 90.0%

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

      9. distribute-lft-neg-in 90.0%

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

      10. metadata-eval 90.0%

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

      11. +-commutative 90.0%

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

      12. *-commutative 90.0%

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

   6. Simplified 90.0%

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

   7. Taylor expanded in j around 0 90.0%

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

   8. Taylor expanded in b around 0 80.4%

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

   if -6.4999999999999999e-287 < (*.f64 b c) < 9.9999999999999998e-17

   1. Initial program 83.9%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in i around inf 58.3%

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

      1. associate-*r* 58.3%

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

      2. *-commutative 58.3%

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

   6. Simplified 58.3%

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

   if 9.9999999999999998e-17 < (*.f64 b c)

   1. Initial program 77.7%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in b around inf 57.0%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -3.25 \cdot 10^{+109}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1.45 \cdot 10^{-28}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -7 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq -2.1 \cdot 10^{-183}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -6.5 \cdot 10^{-287}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 10^{-16}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 6: 82.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 4 \cdot \left(x \cdot i\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-15} \lor \neg \left(t_2 \leq 10^{+17}\right):\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + t_1\right)\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 4.0 (* x i))) (t_2 (* (* j 27.0) k)))
   (if (or (<= t_2 -5e-15) (not (<= t_2 1e+17)))
     (- (- (* b c) (+ (* 4.0 (* t a)) t_1)) t_2)
     (- (+ (* b c) (* t (- (* 18.0 (* x (* y z))) (* a 4.0)))) t_1))))

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 = 4.0 * (x * i);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if ((t_2 <= -5e-15) || !(t_2 <= 1e+17)) {
		tmp = ((b * c) - ((4.0 * (t * a)) + t_1)) - t_2;
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	}
	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 = 4.0d0 * (x * i)
    t_2 = (j * 27.0d0) * k
    if ((t_2 <= (-5d-15)) .or. (.not. (t_2 <= 1d+17))) then
        tmp = ((b * c) - ((4.0d0 * (t * a)) + t_1)) - t_2
    else
        tmp = ((b * c) + (t * ((18.0d0 * (x * (y * z))) - (a * 4.0d0)))) - t_1
    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 = 4.0 * (x * i);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if ((t_2 <= -5e-15) || !(t_2 <= 1e+17)) {
		tmp = ((b * c) - ((4.0 * (t * a)) + t_1)) - t_2;
	} else {
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 4.0 * (x * i)
	t_2 = (j * 27.0) * k
	tmp = 0
	if (t_2 <= -5e-15) or not (t_2 <= 1e+17):
		tmp = ((b * c) - ((4.0 * (t * a)) + t_1)) - t_2
	else:
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(4.0 * Float64(x * i))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_2 <= -5e-15) || !(t_2 <= 1e+17))
		tmp = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + t_1)) - t_2);
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) - Float64(a * 4.0)))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 4.0 * (x * i);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if ((t_2 <= -5e-15) || ~((t_2 <= 1e+17)))
		tmp = ((b * c) - ((4.0 * (t * a)) + t_1)) - t_2;
	else
		tmp = ((b * c) + (t * ((18.0 * (x * (y * z))) - (a * 4.0)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -5e-15], N[Not[LessEqual[t$95$2, 1e+17]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j 27) k) < -4.99999999999999999e-15 or 1e17 < (*.f64 (*.f64 j 27) k)

   1. Initial program 83.5%

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

   2. Taylor expanded in y around 0 83.1%

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

   if -4.99999999999999999e-15 < (*.f64 (*.f64 j 27) k) < 1e17

   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. Step-by-step derivation

      1. associate--l- 83.4%

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

      2. associate-+l- 83.4%

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

      3. associate--l- 83.4%

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

      4. *-commutative 83.4%

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

      5. associate-*r* 83.3%

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

      6. associate-*l* 83.3%

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

      7. associate-*r* 84.1%

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

      8. *-commutative 84.1%

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

      9. associate-*l* 84.1%

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

      10. associate--l- 84.1%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in j around 0 85.3%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{-15} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 10^{+17}\right):\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - a \cdot 4\right)\right) - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 7: 54.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t_1 + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -1.1 \cdot 10^{+111}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq -8 \cdot 10^{-239}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.8 \cdot 10^{-229}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 3.3 \cdot 10^{-15}:\\ \;\;\;\;t_1 + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0))) (t_2 (+ t_1 (* -4.0 (* t a)))))
   (if (<= (* b c) -1.1e+111)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= (* b c) -3.6e-112)
       t_2
       (if (<= (* b c) -8e-239)
         (* -4.0 (+ (* t a) (* x i)))
         (if (<= (* b c) 1.8e-229)
           t_2
           (if (<= (* b c) 3.3e-15)
             (+ t_1 (* x (* i -4.0)))
             (+ (* b c) t_1))))))))

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 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (t * a));
	double tmp;
	if ((b * c) <= -1.1e+111) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -3.6e-112) {
		tmp = t_2;
	} else if ((b * c) <= -8e-239) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else if ((b * c) <= 1.8e-229) {
		tmp = t_2;
	} else if ((b * c) <= 3.3e-15) {
		tmp = t_1 + (x * (i * -4.0));
	} else {
		tmp = (b * c) + t_1;
	}
	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 = j * (k * (-27.0d0))
    t_2 = t_1 + ((-4.0d0) * (t * a))
    if ((b * c) <= (-1.1d+111)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if ((b * c) <= (-3.6d-112)) then
        tmp = t_2
    else if ((b * c) <= (-8d-239)) then
        tmp = (-4.0d0) * ((t * a) + (x * i))
    else if ((b * c) <= 1.8d-229) then
        tmp = t_2
    else if ((b * c) <= 3.3d-15) then
        tmp = t_1 + (x * (i * (-4.0d0)))
    else
        tmp = (b * c) + t_1
    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 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (t * a));
	double tmp;
	if ((b * c) <= -1.1e+111) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -3.6e-112) {
		tmp = t_2;
	} else if ((b * c) <= -8e-239) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else if ((b * c) <= 1.8e-229) {
		tmp = t_2;
	} else if ((b * c) <= 3.3e-15) {
		tmp = t_1 + (x * (i * -4.0));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (-4.0 * (t * a))
	tmp = 0
	if (b * c) <= -1.1e+111:
		tmp = (b * c) - (4.0 * (x * i))
	elif (b * c) <= -3.6e-112:
		tmp = t_2
	elif (b * c) <= -8e-239:
		tmp = -4.0 * ((t * a) + (x * i))
	elif (b * c) <= 1.8e-229:
		tmp = t_2
	elif (b * c) <= 3.3e-15:
		tmp = t_1 + (x * (i * -4.0))
	else:
		tmp = (b * c) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(-4.0 * Float64(t * a)))
	tmp = 0.0
	if (Float64(b * c) <= -1.1e+111)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= -3.6e-112)
		tmp = t_2;
	elseif (Float64(b * c) <= -8e-239)
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	elseif (Float64(b * c) <= 1.8e-229)
		tmp = t_2;
	elseif (Float64(b * c) <= 3.3e-15)
		tmp = Float64(t_1 + Float64(x * Float64(i * -4.0)));
	else
		tmp = Float64(Float64(b * c) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (-4.0 * (t * a));
	tmp = 0.0;
	if ((b * c) <= -1.1e+111)
		tmp = (b * c) - (4.0 * (x * i));
	elseif ((b * c) <= -3.6e-112)
		tmp = t_2;
	elseif ((b * c) <= -8e-239)
		tmp = -4.0 * ((t * a) + (x * i));
	elseif ((b * c) <= 1.8e-229)
		tmp = t_2;
	elseif ((b * c) <= 3.3e-15)
		tmp = t_1 + (x * (i * -4.0));
	else
		tmp = (b * c) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.1e+111], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.6e-112], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -8e-239], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.8e-229], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 3.3e-15], N[(t$95$1 + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -1.09999999999999999e111

   1. Initial program 88.9%

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

   2. Taylor expanded in y around 0 88.9%

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

   3. Taylor expanded in a around 0 83.6%

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

      1. associate-*r* 83.6%

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

      2. *-commutative 83.6%

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

      3. *-commutative 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in j around 0 75.0%

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

   if -1.09999999999999999e111 < (*.f64 b c) < -3.6000000000000001e-112 or -8.0000000000000006e-239 < (*.f64 b c) < 1.80000000000000001e-229

   1. Initial program 82.5%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in a around inf 61.9%

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

      1. *-commutative 61.9%

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

   6. Simplified 61.9%

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

   if -3.6000000000000001e-112 < (*.f64 b c) < -8.0000000000000006e-239

   1. Initial program 87.0%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in y around 0 62.7%

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

      1. associate-+r+ 62.7%

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

      2. +-commutative 62.7%

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

      3. distribute-lft-out 62.7%

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

      4. metadata-eval 62.7%

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

      5. cancel-sign-sub-inv 62.7%

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

      6. distribute-lft-out 62.7%

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

      7. fma-neg 62.7%

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

      8. distribute-lft-out 62.7%

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

      9. distribute-lft-neg-in 62.7%

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

      10. metadata-eval 62.7%

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

      11. +-commutative 62.7%

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

      12. *-commutative 62.7%

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

   6. Simplified 62.7%

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

   7. Taylor expanded in j around 0 62.7%

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

   8. Taylor expanded in b around 0 58.5%

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

   if 1.80000000000000001e-229 < (*.f64 b c) < 3.3e-15

   1. Initial program 86.6%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in i around inf 64.8%

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

      1. associate-*r* 64.8%

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

      2. *-commutative 64.8%

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

   6. Simplified 64.8%

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

   if 3.3e-15 < (*.f64 b c)

   1. Initial program 77.7%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in b around inf 57.0%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.1 \cdot 10^{+111}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -3.6 \cdot 10^{-112}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -8 \cdot 10^{-239}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.8 \cdot 10^{-229}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 3.3 \cdot 10^{-15}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 8: 87.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(18 \cdot y\right) \cdot \left(x \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -3.5e+167)
   (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))
   (-
    (+ (* b c) (* t (- (* (* 18.0 y) (* x z)) (* a 4.0))))
    (+ (* 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) {
	double tmp;
	if (x <= -3.5e+167) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else {
		tmp = ((b * c) + (t * (((18.0 * y) * (x * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	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) :: tmp
    if (x <= (-3.5d+167)) then
        tmp = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    else
        tmp = ((b * c) + (t * (((18.0d0 * y) * (x * z)) - (a * 4.0d0)))) - ((x * (4.0d0 * i)) + (j * (27.0d0 * k)))
    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 tmp;
	if (x <= -3.5e+167) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else {
		tmp = ((b * c) + (t * (((18.0 * y) * (x * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if x <= -3.5e+167:
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	else:
		tmp = ((b * c) + (t * (((18.0 * y) * (x * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -3.5e+167)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	else
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(Float64(18.0 * y) * Float64(x * z)) - Float64(a * 4.0)))) - Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (x <= -3.5e+167)
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	else
		tmp = ((b * c) + (t * (((18.0 * y) * (x * z)) - (a * 4.0)))) - ((x * (4.0 * i)) + (j * (27.0 * k)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -3.5e+167], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.49999999999999987e167

   1. Initial program 46.7%

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

      1. associate--l- 46.7%

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

      2. associate-+l- 46.7%

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

      3. associate--l- 46.7%

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

      4. *-commutative 46.7%

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

      5. associate-*r* 49.9%

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

      6. associate-*l* 53.4%

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

      7. associate-*r* 50.3%

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

      8. *-commutative 50.3%

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

      9. associate-*l* 46.7%

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

      10. associate--l- 46.7%

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

   3. Simplified 53.9%

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

   4. Taylor expanded in a around 0 57.3%

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

      1. +-commutative 57.3%

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

      2. *-commutative 57.3%

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

      3. associate-*r* 53.8%

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

      4. associate-*l* 53.7%

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

      5. associate-*r* 53.7%

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

      6. *-commutative 53.7%

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

      7. associate-*r* 57.4%

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

      8. fma-def 57.4%

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

      9. *-commutative 57.4%

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

      10. associate-*l* 64.2%

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

      11. *-commutative 64.2%

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

      12. associate-*l* 64.2%

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

      13. *-commutative 64.2%

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

      14. associate-*r* 64.2%

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

      15. *-commutative 64.2%

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

      16. *-commutative 64.2%

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

      17. associate-*r* 64.2%

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

      18. associate-*l* 64.2%

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

      19. *-commutative 64.2%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in x around inf 89.4%

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

      1. cancel-sign-sub-inv 89.4%

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

      2. metadata-eval 89.4%

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

      3. *-commutative 89.4%

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

      4. associate-*r* 89.4%

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

   9. Simplified 89.4%

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

   if -3.49999999999999987e167 < x

   1. Initial program 87.9%

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

      1. associate--l- 87.9%

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

      2. associate-+l- 87.9%

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

      3. associate--l- 87.9%

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

      4. *-commutative 87.9%

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

      5. associate-*r* 88.7%

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

      6. associate-*l* 86.9%

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

      7. associate-*r* 85.9%

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

      8. *-commutative 85.9%

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

      9. associate-*l* 87.0%

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

      10. associate--l- 87.0%

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

   3. Simplified 88.3%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(18 \cdot y\right) \cdot \left(x \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]

Alternative 9: 37.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -6.6 \cdot 10^{+102}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -0.02:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -4.8 \cdot 10^{-28}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -1.6 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -1.45 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{+196}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t a))))
   (if (<= (* b c) -6.6e+102)
     (* b c)
     (if (<= (* b c) -0.02)
       t_1
       (if (<= (* b c) -4.8e-28)
         (* k (* j -27.0))
         (if (<= (* b c) -1.6e-132)
           t_1
           (if (<= (* b c) -1.45e-235)
             (* x (* i -4.0))
             (if (<= (* b c) 4.2e+196) (* -27.0 (* j k)) (* b c)))))))))

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 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -6.6e+102) {
		tmp = b * c;
	} else if ((b * c) <= -0.02) {
		tmp = t_1;
	} else if ((b * c) <= -4.8e-28) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= -1.6e-132) {
		tmp = t_1;
	} else if ((b * c) <= -1.45e-235) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 4.2e+196) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	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) :: tmp
    t_1 = (-4.0d0) * (t * a)
    if ((b * c) <= (-6.6d+102)) then
        tmp = b * c
    else if ((b * c) <= (-0.02d0)) then
        tmp = t_1
    else if ((b * c) <= (-4.8d-28)) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= (-1.6d-132)) then
        tmp = t_1
    else if ((b * c) <= (-1.45d-235)) then
        tmp = x * (i * (-4.0d0))
    else if ((b * c) <= 4.2d+196) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = b * c
    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 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -6.6e+102) {
		tmp = b * c;
	} else if ((b * c) <= -0.02) {
		tmp = t_1;
	} else if ((b * c) <= -4.8e-28) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= -1.6e-132) {
		tmp = t_1;
	} else if ((b * c) <= -1.45e-235) {
		tmp = x * (i * -4.0);
	} else if ((b * c) <= 4.2e+196) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (t * a)
	tmp = 0
	if (b * c) <= -6.6e+102:
		tmp = b * c
	elif (b * c) <= -0.02:
		tmp = t_1
	elif (b * c) <= -4.8e-28:
		tmp = k * (j * -27.0)
	elif (b * c) <= -1.6e-132:
		tmp = t_1
	elif (b * c) <= -1.45e-235:
		tmp = x * (i * -4.0)
	elif (b * c) <= 4.2e+196:
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(t * a))
	tmp = 0.0
	if (Float64(b * c) <= -6.6e+102)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -0.02)
		tmp = t_1;
	elseif (Float64(b * c) <= -4.8e-28)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= -1.6e-132)
		tmp = t_1;
	elseif (Float64(b * c) <= -1.45e-235)
		tmp = Float64(x * Float64(i * -4.0));
	elseif (Float64(b * c) <= 4.2e+196)
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (t * a);
	tmp = 0.0;
	if ((b * c) <= -6.6e+102)
		tmp = b * c;
	elseif ((b * c) <= -0.02)
		tmp = t_1;
	elseif ((b * c) <= -4.8e-28)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= -1.6e-132)
		tmp = t_1;
	elseif ((b * c) <= -1.45e-235)
		tmp = x * (i * -4.0);
	elseif ((b * c) <= 4.2e+196)
		tmp = -27.0 * (j * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -6.6e+102], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -0.02], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -4.8e-28], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.6e-132], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1.45e-235], N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.2e+196], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -6.59999999999999997e102 or 4.20000000000000029e196 < (*.f64 b c)

   1. Initial program 78.0%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in y around 0 81.0%

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

      1. associate-+r+ 81.0%

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

      2. +-commutative 81.0%

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

      3. distribute-lft-out 81.0%

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

      4. metadata-eval 81.0%

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

      5. cancel-sign-sub-inv 81.0%

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

      6. distribute-lft-out 81.0%

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

      7. fma-neg 86.1%

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

      8. distribute-lft-out 86.1%

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

      9. distribute-lft-neg-in 86.1%

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

      10. metadata-eval 86.1%

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

      11. +-commutative 86.1%

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

      12. *-commutative 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in b around inf 66.4%

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

   if -6.59999999999999997e102 < (*.f64 b c) < -0.0200000000000000004 or -4.8000000000000004e-28 < (*.f64 b c) < -1.6000000000000001e-132

   1. Initial program 86.7%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around 0 71.1%

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

      1. associate-+r+ 71.1%

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

      2. +-commutative 71.1%

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

      3. distribute-lft-out 71.1%

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

      4. metadata-eval 71.1%

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

      5. cancel-sign-sub-inv 71.1%

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

      6. distribute-lft-out 71.1%

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

      7. fma-neg 71.1%

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

      8. distribute-lft-out 71.1%

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

      9. distribute-lft-neg-in 71.1%

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

      10. metadata-eval 71.1%

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

      11. +-commutative 71.1%

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

      12. *-commutative 71.1%

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

   6. Simplified 71.1%

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

   7. Taylor expanded in t around inf 48.1%

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

   if -0.0200000000000000004 < (*.f64 b c) < -4.8000000000000004e-28

   1. Initial program 79.8%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in j around inf 70.5%

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

      1. associate-*r* 70.6%

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

      2. *-commutative 70.6%

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

   6. Simplified 70.6%

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

   if -1.6000000000000001e-132 < (*.f64 b c) < -1.45000000000000004e-235

   1. Initial program 84.2%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in y around 0 64.7%

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

      1. associate-+r+ 64.7%

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

      2. +-commutative 64.7%

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

      3. distribute-lft-out 64.7%

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

      4. metadata-eval 64.7%

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

      5. cancel-sign-sub-inv 64.7%

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

      6. distribute-lft-out 64.7%

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

      7. fma-neg 64.7%

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

      8. distribute-lft-out 64.7%

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

      9. distribute-lft-neg-in 64.7%

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

      10. metadata-eval 64.7%

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

      11. +-commutative 64.7%

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

      12. *-commutative 64.7%

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

   6. Simplified 64.7%

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

   7. Taylor expanded in i around inf 44.2%

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

      1. associate-*r* 44.2%

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

      2. *-commutative 44.2%

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

   9. Simplified 44.2%

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

   if -1.45000000000000004e-235 < (*.f64 b c) < 4.20000000000000029e196

   1. Initial program 85.2%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in j around inf 37.3%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.6 \cdot 10^{+102}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -0.02:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -4.8 \cdot 10^{-28}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -1.6 \cdot 10^{-132}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -1.45 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{+196}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 10: 79.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ t_2 := t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ t_3 := t_2 + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+117}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (- (- (* b c) (+ (* 4.0 (* t a)) (* 4.0 (* x i)))) (* (* j 27.0) k)))
        (t_2 (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))))
        (t_3 (+ t_2 (* j (* k -27.0)))))
   (if (<= t -3.2e+117)
     t_3
     (if (<= t 2.4e+47)
       t_1
       (if (<= t 7.4e+117) t_2 (if (<= t 3.7e+208) t_1 t_3))))))

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 = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - ((j * 27.0) * k);
	double t_2 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double t_3 = t_2 + (j * (k * -27.0));
	double tmp;
	if (t <= -3.2e+117) {
		tmp = t_3;
	} else if (t <= 2.4e+47) {
		tmp = t_1;
	} else if (t <= 7.4e+117) {
		tmp = t_2;
	} else if (t <= 3.7e+208) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = ((b * c) - ((4.0d0 * (t * a)) + (4.0d0 * (x * i)))) - ((j * 27.0d0) * k)
    t_2 = t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0)))
    t_3 = t_2 + (j * (k * (-27.0d0)))
    if (t <= (-3.2d+117)) then
        tmp = t_3
    else if (t <= 2.4d+47) then
        tmp = t_1
    else if (t <= 7.4d+117) then
        tmp = t_2
    else if (t <= 3.7d+208) then
        tmp = t_1
    else
        tmp = t_3
    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 = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - ((j * 27.0) * k);
	double t_2 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	double t_3 = t_2 + (j * (k * -27.0));
	double tmp;
	if (t <= -3.2e+117) {
		tmp = t_3;
	} else if (t <= 2.4e+47) {
		tmp = t_1;
	} else if (t <= 7.4e+117) {
		tmp = t_2;
	} else if (t <= 3.7e+208) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - ((j * 27.0) * k)
	t_2 = t * ((18.0 * (x * (y * z))) + (a * -4.0))
	t_3 = t_2 + (j * (k * -27.0))
	tmp = 0
	if t <= -3.2e+117:
		tmp = t_3
	elif t <= 2.4e+47:
		tmp = t_1
	elif t <= 7.4e+117:
		tmp = t_2
	elif t <= 3.7e+208:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) - Float64(Float64(4.0 * Float64(t * a)) + Float64(4.0 * Float64(x * i)))) - Float64(Float64(j * 27.0) * k))
	t_2 = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0)))
	t_3 = Float64(t_2 + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (t <= -3.2e+117)
		tmp = t_3;
	elseif (t <= 2.4e+47)
		tmp = t_1;
	elseif (t <= 7.4e+117)
		tmp = t_2;
	elseif (t <= 3.7e+208)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) - ((4.0 * (t * a)) + (4.0 * (x * i)))) - ((j * 27.0) * k);
	t_2 = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	t_3 = t_2 + (j * (k * -27.0));
	tmp = 0.0;
	if (t <= -3.2e+117)
		tmp = t_3;
	elseif (t <= 2.4e+47)
		tmp = t_1;
	elseif (t <= 7.4e+117)
		tmp = t_2;
	elseif (t <= 3.7e+208)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] - N[(N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e+117], t$95$3, If[LessEqual[t, 2.4e+47], t$95$1, If[LessEqual[t, 7.4e+117], t$95$2, If[LessEqual[t, 3.7e+208], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.20000000000000005e117 or 3.69999999999999989e208 < t

   1. Initial program 78.7%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in t around inf 84.1%

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

   if -3.20000000000000005e117 < t < 2.40000000000000019e47 or 7.3999999999999997e117 < t < 3.69999999999999989e208

   1. Initial program 85.3%

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

   2. Taylor expanded in y around 0 85.5%

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

   if 2.40000000000000019e47 < t < 7.3999999999999997e117

   1. Initial program 81.0%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in b around 0 80.0%

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

   6. Simplified 80.2%

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

   7. Taylor expanded in t around inf 86.6%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+208}:\\ \;\;\;\;\left(b \cdot c - \left(4 \cdot \left(t \cdot a\right) + 4 \cdot \left(x \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 11: 74.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+45} \lor \neg \left(t \leq 6.3 \cdot 10^{-80}\right) \land \left(t \leq 5.6 \cdot 10^{+148} \lor \neg \left(t \leq 5 \cdot 10^{+172}\right)\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.3e+45)
         (and (not (<= t 6.3e-80)) (or (<= t 5.6e+148) (not (<= t 5e+172)))))
   (+ (* t (+ (* 18.0 (* x (* y z))) (* a -4.0))) (* j (* k -27.0)))
   (- (- (* b c) (* 4.0 (* x 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) {
	double tmp;
	if ((t <= -1.3e+45) || (!(t <= 6.3e-80) && ((t <= 5.6e+148) || !(t <= 5e+172)))) {
		tmp = (t * ((18.0 * (x * (y * z))) + (a * -4.0))) + (j * (k * -27.0));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	}
	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) :: tmp
    if ((t <= (-1.3d+45)) .or. (.not. (t <= 6.3d-80)) .and. (t <= 5.6d+148) .or. (.not. (t <= 5d+172))) then
        tmp = (t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0)))) + (j * (k * (-27.0d0)))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - ((j * 27.0d0) * k)
    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 tmp;
	if ((t <= -1.3e+45) || (!(t <= 6.3e-80) && ((t <= 5.6e+148) || !(t <= 5e+172)))) {
		tmp = (t * ((18.0 * (x * (y * z))) + (a * -4.0))) + (j * (k * -27.0));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.3e+45) or (not (t <= 6.3e-80) and ((t <= 5.6e+148) or not (t <= 5e+172))):
		tmp = (t * ((18.0 * (x * (y * z))) + (a * -4.0))) + (j * (k * -27.0))
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.3e+45) || (!(t <= 6.3e-80) && ((t <= 5.6e+148) || !(t <= 5e+172))))
		tmp = Float64(Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0))) + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1.3e+45) || (~((t <= 6.3e-80)) && ((t <= 5.6e+148) || ~((t <= 5e+172)))))
		tmp = (t * ((18.0 * (x * (y * z))) + (a * -4.0))) + (j * (k * -27.0));
	else
		tmp = ((b * c) - (4.0 * (x * i))) - ((j * 27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.3e+45], And[N[Not[LessEqual[t, 6.3e-80]], $MachinePrecision], Or[LessEqual[t, 5.6e+148], N[Not[LessEqual[t, 5e+172]], $MachinePrecision]]]], N[(N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.30000000000000004e45 or 6.29999999999999966e-80 < t < 5.59999999999999959e148 or 5.0000000000000001e172 < t

   1. Initial program 83.3%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in t around inf 79.6%

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

   if -1.30000000000000004e45 < t < 6.29999999999999966e-80 or 5.59999999999999959e148 < t < 5.0000000000000001e172

   1. Initial program 83.5%

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

   2. Taylor expanded in t around 0 82.4%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+45} \lor \neg \left(t \leq 6.3 \cdot 10^{-80}\right) \land \left(t \leq 5.6 \cdot 10^{+148} \lor \neg \left(t \leq 5 \cdot 10^{+172}\right)\right):\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]

Alternative 12: 56.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t_1 + -4 \cdot \left(t \cdot a\right)\\ t_3 := b \cdot c + t_1\\ t_4 := x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+167}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+53}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-16}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-210}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ t_1 (* -4.0 (* t a))))
        (t_3 (+ (* b c) t_1))
        (t_4 (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))))
   (if (<= x -3.3e+167)
     t_4
     (if (<= x -2.6e+53)
       t_3
       (if (<= x -1.5e-16)
         t_4
         (if (<= x -2.6e-307)
           t_2
           (if (<= x 9.5e-210) t_3 (if (<= x 4.5e-30) t_2 t_4))))))))

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 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (t * a));
	double t_3 = (b * c) + t_1;
	double t_4 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -3.3e+167) {
		tmp = t_4;
	} else if (x <= -2.6e+53) {
		tmp = t_3;
	} else if (x <= -1.5e-16) {
		tmp = t_4;
	} else if (x <= -2.6e-307) {
		tmp = t_2;
	} else if (x <= 9.5e-210) {
		tmp = t_3;
	} else if (x <= 4.5e-30) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + ((-4.0d0) * (t * a))
    t_3 = (b * c) + t_1
    t_4 = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    if (x <= (-3.3d+167)) then
        tmp = t_4
    else if (x <= (-2.6d+53)) then
        tmp = t_3
    else if (x <= (-1.5d-16)) then
        tmp = t_4
    else if (x <= (-2.6d-307)) then
        tmp = t_2
    else if (x <= 9.5d-210) then
        tmp = t_3
    else if (x <= 4.5d-30) then
        tmp = t_2
    else
        tmp = t_4
    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 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (t * a));
	double t_3 = (b * c) + t_1;
	double t_4 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -3.3e+167) {
		tmp = t_4;
	} else if (x <= -2.6e+53) {
		tmp = t_3;
	} else if (x <= -1.5e-16) {
		tmp = t_4;
	} else if (x <= -2.6e-307) {
		tmp = t_2;
	} else if (x <= 9.5e-210) {
		tmp = t_3;
	} else if (x <= 4.5e-30) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (-4.0 * (t * a))
	t_3 = (b * c) + t_1
	t_4 = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	tmp = 0
	if x <= -3.3e+167:
		tmp = t_4
	elif x <= -2.6e+53:
		tmp = t_3
	elif x <= -1.5e-16:
		tmp = t_4
	elif x <= -2.6e-307:
		tmp = t_2
	elif x <= 9.5e-210:
		tmp = t_3
	elif x <= 4.5e-30:
		tmp = t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(-4.0 * Float64(t * a)))
	t_3 = Float64(Float64(b * c) + t_1)
	t_4 = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)))
	tmp = 0.0
	if (x <= -3.3e+167)
		tmp = t_4;
	elseif (x <= -2.6e+53)
		tmp = t_3;
	elseif (x <= -1.5e-16)
		tmp = t_4;
	elseif (x <= -2.6e-307)
		tmp = t_2;
	elseif (x <= 9.5e-210)
		tmp = t_3;
	elseif (x <= 4.5e-30)
		tmp = t_2;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (-4.0 * (t * a));
	t_3 = (b * c) + t_1;
	t_4 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	tmp = 0.0;
	if (x <= -3.3e+167)
		tmp = t_4;
	elseif (x <= -2.6e+53)
		tmp = t_3;
	elseif (x <= -1.5e-16)
		tmp = t_4;
	elseif (x <= -2.6e-307)
		tmp = t_2;
	elseif (x <= 9.5e-210)
		tmp = t_3;
	elseif (x <= 4.5e-30)
		tmp = t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.3e+167], t$95$4, If[LessEqual[x, -2.6e+53], t$95$3, If[LessEqual[x, -1.5e-16], t$95$4, If[LessEqual[x, -2.6e-307], t$95$2, If[LessEqual[x, 9.5e-210], t$95$3, If[LessEqual[x, 4.5e-30], t$95$2, t$95$4]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.30000000000000018e167 or -2.59999999999999998e53 < x < -1.49999999999999997e-16 or 4.49999999999999967e-30 < x

   1. Initial program 70.2%

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

      1. associate--l- 70.2%

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

      2. associate-+l- 70.2%

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

      3. associate--l- 70.2%

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

      4. *-commutative 70.2%

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

      5. associate-*r* 71.9%

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

      6. associate-*l* 72.8%

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

      7. associate-*r* 71.8%

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

      8. *-commutative 71.8%

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

      9. associate-*l* 68.1%

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

      10. associate--l- 68.1%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in a around 0 71.3%

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

      1. +-commutative 71.3%

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

      2. *-commutative 71.3%

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

      3. associate-*r* 72.9%

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

      4. associate-*l* 72.9%

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

      5. associate-*r* 72.9%

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

      6. *-commutative 72.9%

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

      7. associate-*r* 71.4%

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

      8. fma-def 71.4%

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

      9. *-commutative 71.4%

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

      10. associate-*l* 78.6%

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

      11. *-commutative 78.6%

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

      12. associate-*l* 78.6%

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

      13. *-commutative 78.6%

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

      14. associate-*r* 78.6%

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

      15. *-commutative 78.6%

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

      16. *-commutative 78.6%

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

      17. associate-*r* 78.7%

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

      18. associate-*l* 78.7%

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

      19. *-commutative 78.7%

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

   6. Simplified 78.7%

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

   7. Taylor expanded in x around inf 73.4%

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

      1. cancel-sign-sub-inv 73.4%

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

      2. metadata-eval 73.4%

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

      3. *-commutative 73.4%

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

      4. associate-*r* 72.4%

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

   9. Simplified 72.4%

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

   if -3.30000000000000018e167 < x < -2.59999999999999998e53 or -2.59999999999999996e-307 < x < 9.4999999999999997e-210

   1. Initial program 89.9%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in b around inf 66.0%

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

   if -1.49999999999999997e-16 < x < -2.59999999999999996e-307 or 9.4999999999999997e-210 < x < 4.49999999999999967e-30

   1. Initial program 93.0%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in a around inf 64.9%

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

      1. *-commutative 64.9%

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

   6. Simplified 64.9%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+53}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-307}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-210}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-30}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]

Alternative 13: 56.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := t_1 + -4 \cdot \left(t \cdot a\right)\\ t_3 := b \cdot c + t_1\\ t_4 := x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+167}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+52}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-20}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-305}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-209}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ t_1 (* -4.0 (* t a))))
        (t_3 (+ (* b c) t_1))
        (t_4 (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))))
   (if (<= x -3.3e+167)
     t_4
     (if (<= x -5.4e+52)
       t_3
       (if (<= x -4.1e-20)
         t_4
         (if (<= x -2.8e-305)
           t_2
           (if (<= x 1.75e-209)
             t_3
             (if (<= x 2.7e-30)
               t_2
               (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))))))))

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 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (t * a));
	double t_3 = (b * c) + t_1;
	double t_4 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -3.3e+167) {
		tmp = t_4;
	} else if (x <= -5.4e+52) {
		tmp = t_3;
	} else if (x <= -4.1e-20) {
		tmp = t_4;
	} else if (x <= -2.8e-305) {
		tmp = t_2;
	} else if (x <= 1.75e-209) {
		tmp = t_3;
	} else if (x <= 2.7e-30) {
		tmp = t_2;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = t_1 + ((-4.0d0) * (t * a))
    t_3 = (b * c) + t_1
    t_4 = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    if (x <= (-3.3d+167)) then
        tmp = t_4
    else if (x <= (-5.4d+52)) then
        tmp = t_3
    else if (x <= (-4.1d-20)) then
        tmp = t_4
    else if (x <= (-2.8d-305)) then
        tmp = t_2
    else if (x <= 1.75d-209) then
        tmp = t_3
    else if (x <= 2.7d-30) then
        tmp = t_2
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    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 = j * (k * -27.0);
	double t_2 = t_1 + (-4.0 * (t * a));
	double t_3 = (b * c) + t_1;
	double t_4 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -3.3e+167) {
		tmp = t_4;
	} else if (x <= -5.4e+52) {
		tmp = t_3;
	} else if (x <= -4.1e-20) {
		tmp = t_4;
	} else if (x <= -2.8e-305) {
		tmp = t_2;
	} else if (x <= 1.75e-209) {
		tmp = t_3;
	} else if (x <= 2.7e-30) {
		tmp = t_2;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = t_1 + (-4.0 * (t * a))
	t_3 = (b * c) + t_1
	t_4 = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	tmp = 0
	if x <= -3.3e+167:
		tmp = t_4
	elif x <= -5.4e+52:
		tmp = t_3
	elif x <= -4.1e-20:
		tmp = t_4
	elif x <= -2.8e-305:
		tmp = t_2
	elif x <= 1.75e-209:
		tmp = t_3
	elif x <= 2.7e-30:
		tmp = t_2
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(t_1 + Float64(-4.0 * Float64(t * a)))
	t_3 = Float64(Float64(b * c) + t_1)
	t_4 = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)))
	tmp = 0.0
	if (x <= -3.3e+167)
		tmp = t_4;
	elseif (x <= -5.4e+52)
		tmp = t_3;
	elseif (x <= -4.1e-20)
		tmp = t_4;
	elseif (x <= -2.8e-305)
		tmp = t_2;
	elseif (x <= 1.75e-209)
		tmp = t_3;
	elseif (x <= 2.7e-30)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = t_1 + (-4.0 * (t * a));
	t_3 = (b * c) + t_1;
	t_4 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	tmp = 0.0;
	if (x <= -3.3e+167)
		tmp = t_4;
	elseif (x <= -5.4e+52)
		tmp = t_3;
	elseif (x <= -4.1e-20)
		tmp = t_4;
	elseif (x <= -2.8e-305)
		tmp = t_2;
	elseif (x <= 1.75e-209)
		tmp = t_3;
	elseif (x <= 2.7e-30)
		tmp = t_2;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.3e+167], t$95$4, If[LessEqual[x, -5.4e+52], t$95$3, If[LessEqual[x, -4.1e-20], t$95$4, If[LessEqual[x, -2.8e-305], t$95$2, If[LessEqual[x, 1.75e-209], t$95$3, If[LessEqual[x, 2.7e-30], t$95$2, N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.30000000000000018e167 or -5.4e52 < x < -4.1000000000000001e-20

   1. Initial program 62.0%

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

      1. associate--l- 62.0%

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

      2. associate-+l- 62.0%

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

      3. associate--l- 62.0%

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

      4. *-commutative 62.0%

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

      5. associate-*r* 61.9%

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

      6. associate-*l* 64.3%

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

      7. associate-*r* 62.2%

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

      8. *-commutative 62.2%

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

      9. associate-*l* 62.1%

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

      10. associate--l- 62.1%

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

   3. Simplified 66.8%

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

   4. Taylor expanded in a around 0 69.4%

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

      1. +-commutative 69.4%

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

      2. *-commutative 69.4%

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

      3. associate-*r* 67.0%

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

      4. associate-*l* 67.0%

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

      5. associate-*r* 67.0%

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

      6. *-commutative 67.0%

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

      7. associate-*r* 69.5%

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

      8. fma-def 69.5%

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

      9. *-commutative 69.5%

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

      10. associate-*l* 74.0%

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

      11. *-commutative 74.0%

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

      12. associate-*l* 74.0%

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

      13. *-commutative 74.0%

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

      14. associate-*r* 74.0%

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

      15. *-commutative 74.0%

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

      16. *-commutative 74.0%

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

      17. associate-*r* 71.8%

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

      18. associate-*l* 71.8%

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

      19. *-commutative 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in x around inf 83.1%

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

      1. cancel-sign-sub-inv 83.1%

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

      2. metadata-eval 83.1%

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

      3. *-commutative 83.1%

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

      4. associate-*r* 80.9%

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

   9. Simplified 80.9%

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

   if -3.30000000000000018e167 < x < -5.4e52 or -2.80000000000000014e-305 < x < 1.75000000000000001e-209

   1. Initial program 89.9%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in b around inf 66.0%

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

   if -4.1000000000000001e-20 < x < -2.80000000000000014e-305 or 1.75000000000000001e-209 < x < 2.69999999999999987e-30

   1. Initial program 93.0%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in a around inf 64.9%

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

      1. *-commutative 64.9%

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

   6. Simplified 64.9%

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

   if 2.69999999999999987e-30 < x

   1. Initial program 75.8%

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

      1. associate--l- 75.8%

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

      2. associate-+l- 75.8%

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

      3. associate--l- 75.8%

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

      4. *-commutative 75.8%

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

      5. associate-*r* 78.8%

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

      6. associate-*l* 78.8%

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

      7. associate-*r* 78.4%

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

      8. *-commutative 78.4%

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

      9. associate-*l* 72.4%

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

      10. associate--l- 72.4%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in x around inf 66.6%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+52}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-305}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-209}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-30}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 14: 56.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_3 := b \cdot c + t_1\\ \mathbf{if}\;k \leq -1.7 \cdot 10^{-71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq -4.2 \cdot 10^{-194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -9.6 \cdot 10^{-226}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 4.7 \cdot 10^{+201}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + -4 \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k -27.0)))
        (t_2 (+ (* b c) (* -4.0 (+ (* t a) (* x i)))))
        (t_3 (+ (* b c) t_1)))
   (if (<= k -1.7e-71)
     t_3
     (if (<= k -4.2e-194)
       t_2
       (if (<= k -9.6e-226)
         t_3
         (if (<= k 5.6e-275)
           (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))
           (if (<= k 1.5e+84)
             t_2
             (if (<= k 4.7e+201)
               (* t (+ (* 18.0 (* x (* y z))) (* a -4.0)))
               (+ t_1 (* -4.0 (* t a)))))))))))

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 = j * (k * -27.0);
	double t_2 = (b * c) + (-4.0 * ((t * a) + (x * i)));
	double t_3 = (b * c) + t_1;
	double tmp;
	if (k <= -1.7e-71) {
		tmp = t_3;
	} else if (k <= -4.2e-194) {
		tmp = t_2;
	} else if (k <= -9.6e-226) {
		tmp = t_3;
	} else if (k <= 5.6e-275) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (k <= 1.5e+84) {
		tmp = t_2;
	} else if (k <= 4.7e+201) {
		tmp = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	} else {
		tmp = t_1 + (-4.0 * (t * a));
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = j * (k * (-27.0d0))
    t_2 = (b * c) + ((-4.0d0) * ((t * a) + (x * i)))
    t_3 = (b * c) + t_1
    if (k <= (-1.7d-71)) then
        tmp = t_3
    else if (k <= (-4.2d-194)) then
        tmp = t_2
    else if (k <= (-9.6d-226)) then
        tmp = t_3
    else if (k <= 5.6d-275) then
        tmp = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    else if (k <= 1.5d+84) then
        tmp = t_2
    else if (k <= 4.7d+201) then
        tmp = t * ((18.0d0 * (x * (y * z))) + (a * (-4.0d0)))
    else
        tmp = t_1 + ((-4.0d0) * (t * a))
    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 = j * (k * -27.0);
	double t_2 = (b * c) + (-4.0 * ((t * a) + (x * i)));
	double t_3 = (b * c) + t_1;
	double tmp;
	if (k <= -1.7e-71) {
		tmp = t_3;
	} else if (k <= -4.2e-194) {
		tmp = t_2;
	} else if (k <= -9.6e-226) {
		tmp = t_3;
	} else if (k <= 5.6e-275) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (k <= 1.5e+84) {
		tmp = t_2;
	} else if (k <= 4.7e+201) {
		tmp = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	} else {
		tmp = t_1 + (-4.0 * (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * -27.0)
	t_2 = (b * c) + (-4.0 * ((t * a) + (x * i)))
	t_3 = (b * c) + t_1
	tmp = 0
	if k <= -1.7e-71:
		tmp = t_3
	elif k <= -4.2e-194:
		tmp = t_2
	elif k <= -9.6e-226:
		tmp = t_3
	elif k <= 5.6e-275:
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	elif k <= 1.5e+84:
		tmp = t_2
	elif k <= 4.7e+201:
		tmp = t * ((18.0 * (x * (y * z))) + (a * -4.0))
	else:
		tmp = t_1 + (-4.0 * (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * -27.0))
	t_2 = Float64(Float64(b * c) + Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i))))
	t_3 = Float64(Float64(b * c) + t_1)
	tmp = 0.0
	if (k <= -1.7e-71)
		tmp = t_3;
	elseif (k <= -4.2e-194)
		tmp = t_2;
	elseif (k <= -9.6e-226)
		tmp = t_3;
	elseif (k <= 5.6e-275)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	elseif (k <= 1.5e+84)
		tmp = t_2;
	elseif (k <= 4.7e+201)
		tmp = Float64(t * Float64(Float64(18.0 * Float64(x * Float64(y * z))) + Float64(a * -4.0)));
	else
		tmp = Float64(t_1 + Float64(-4.0 * Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * -27.0);
	t_2 = (b * c) + (-4.0 * ((t * a) + (x * i)));
	t_3 = (b * c) + t_1;
	tmp = 0.0;
	if (k <= -1.7e-71)
		tmp = t_3;
	elseif (k <= -4.2e-194)
		tmp = t_2;
	elseif (k <= -9.6e-226)
		tmp = t_3;
	elseif (k <= 5.6e-275)
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	elseif (k <= 1.5e+84)
		tmp = t_2;
	elseif (k <= 4.7e+201)
		tmp = t * ((18.0 * (x * (y * z))) + (a * -4.0));
	else
		tmp = t_1 + (-4.0 * (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[k, -1.7e-71], t$95$3, If[LessEqual[k, -4.2e-194], t$95$2, If[LessEqual[k, -9.6e-226], t$95$3, If[LessEqual[k, 5.6e-275], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.5e+84], t$95$2, If[LessEqual[k, 4.7e+201], N[(t * N[(N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if k < -1.70000000000000002e-71 or -4.2e-194 < k < -9.5999999999999998e-226

   1. Initial program 82.4%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in b around inf 57.2%

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

   if -1.70000000000000002e-71 < k < -4.2e-194 or 5.59999999999999989e-275 < k < 1.49999999999999998e84

   1. Initial program 88.6%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in y around 0 73.5%

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

      1. associate-+r+ 73.5%

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

      2. +-commutative 73.5%

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

      3. distribute-lft-out 73.5%

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

      4. metadata-eval 73.5%

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

      5. cancel-sign-sub-inv 73.5%

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

      6. distribute-lft-out 73.5%

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

      7. fma-neg 74.6%

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

      8. distribute-lft-out 74.6%

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

      9. distribute-lft-neg-in 74.6%

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

      10. metadata-eval 74.6%

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

      11. +-commutative 74.6%

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

      12. *-commutative 74.6%

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

   6. Simplified 74.6%

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

   7. Taylor expanded in j around 0 62.9%

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

   if -9.5999999999999998e-226 < k < 5.59999999999999989e-275

   1. Initial program 69.3%

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

      1. associate--l- 69.3%

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

      2. associate-+l- 69.3%

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

      3. associate--l- 69.3%

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

      4. *-commutative 69.3%

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

      5. associate-*r* 79.1%

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

      6. associate-*l* 79.1%

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

      7. associate-*r* 75.3%

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

      8. *-commutative 75.3%

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

      9. associate-*l* 68.7%

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

      10. associate--l- 68.7%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in a around 0 58.7%

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

      1. +-commutative 58.7%

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

      2. *-commutative 58.7%

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

      3. associate-*r* 68.6%

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

      4. associate-*l* 68.5%

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

      5. associate-*r* 68.5%

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

      6. *-commutative 68.5%

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

      7. associate-*r* 58.7%

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

      8. fma-def 58.7%

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

      9. *-commutative 58.7%

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

      10. associate-*l* 65.0%

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

      11. *-commutative 65.0%

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

      12. associate-*l* 65.0%

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

      13. *-commutative 65.0%

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

      14. associate-*r* 65.0%

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

      15. *-commutative 65.0%

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

      16. *-commutative 65.0%

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

      17. associate-*r* 68.4%

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

      18. associate-*l* 68.4%

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

      19. *-commutative 68.4%

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

   6. Simplified 68.4%

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

   7. Taylor expanded in x around inf 58.5%

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

      1. cancel-sign-sub-inv 58.5%

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

      2. metadata-eval 58.5%

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

      3. *-commutative 58.5%

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

      4. associate-*r* 62.0%

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

   9. Simplified 62.0%

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

   if 1.49999999999999998e84 < k < 4.6999999999999998e201

   1. Initial program 89.5%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in b around 0 84.3%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in t around inf 59.0%

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

   if 4.6999999999999998e201 < k

   1. Initial program 78.8%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in a around inf 74.6%

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

      1. *-commutative 74.6%

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

   6. Simplified 74.6%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -1.7 \cdot 10^{-71}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq -4.2 \cdot 10^{-194}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;k \leq -9.6 \cdot 10^{-226}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 5.6 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;k \leq 1.5 \cdot 10^{+84}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;k \leq 4.7 \cdot 10^{+201}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right) + -4 \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 15: 37.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;b \cdot c \leq -7.2 \cdot 10^{+102}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -0.059:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -2.6 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq -6.8 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 1.66 \cdot 10^{+196}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t a))) (t_2 (* -27.0 (* j k))))
   (if (<= (* b c) -7.2e+102)
     (* b c)
     (if (<= (* b c) -0.059)
       t_1
       (if (<= (* b c) -2.6e-29)
         t_2
         (if (<= (* b c) -6.8e-240)
           t_1
           (if (<= (* b c) 1.66e+196) t_2 (* b c))))))))

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 = -4.0 * (t * a);
	double t_2 = -27.0 * (j * k);
	double tmp;
	if ((b * c) <= -7.2e+102) {
		tmp = b * c;
	} else if ((b * c) <= -0.059) {
		tmp = t_1;
	} else if ((b * c) <= -2.6e-29) {
		tmp = t_2;
	} else if ((b * c) <= -6.8e-240) {
		tmp = t_1;
	} else if ((b * c) <= 1.66e+196) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	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 = (-4.0d0) * (t * a)
    t_2 = (-27.0d0) * (j * k)
    if ((b * c) <= (-7.2d+102)) then
        tmp = b * c
    else if ((b * c) <= (-0.059d0)) then
        tmp = t_1
    else if ((b * c) <= (-2.6d-29)) then
        tmp = t_2
    else if ((b * c) <= (-6.8d-240)) then
        tmp = t_1
    else if ((b * c) <= 1.66d+196) then
        tmp = t_2
    else
        tmp = b * c
    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 = -4.0 * (t * a);
	double t_2 = -27.0 * (j * k);
	double tmp;
	if ((b * c) <= -7.2e+102) {
		tmp = b * c;
	} else if ((b * c) <= -0.059) {
		tmp = t_1;
	} else if ((b * c) <= -2.6e-29) {
		tmp = t_2;
	} else if ((b * c) <= -6.8e-240) {
		tmp = t_1;
	} else if ((b * c) <= 1.66e+196) {
		tmp = t_2;
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (t * a)
	t_2 = -27.0 * (j * k)
	tmp = 0
	if (b * c) <= -7.2e+102:
		tmp = b * c
	elif (b * c) <= -0.059:
		tmp = t_1
	elif (b * c) <= -2.6e-29:
		tmp = t_2
	elif (b * c) <= -6.8e-240:
		tmp = t_1
	elif (b * c) <= 1.66e+196:
		tmp = t_2
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(t * a))
	t_2 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (Float64(b * c) <= -7.2e+102)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -0.059)
		tmp = t_1;
	elseif (Float64(b * c) <= -2.6e-29)
		tmp = t_2;
	elseif (Float64(b * c) <= -6.8e-240)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.66e+196)
		tmp = t_2;
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (t * a);
	t_2 = -27.0 * (j * k);
	tmp = 0.0;
	if ((b * c) <= -7.2e+102)
		tmp = b * c;
	elseif ((b * c) <= -0.059)
		tmp = t_1;
	elseif ((b * c) <= -2.6e-29)
		tmp = t_2;
	elseif ((b * c) <= -6.8e-240)
		tmp = t_1;
	elseif ((b * c) <= 1.66e+196)
		tmp = t_2;
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -7.2e+102], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -0.059], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -2.6e-29], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], -6.8e-240], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.66e+196], t$95$2, N[(b * c), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -7.2000000000000003e102 or 1.65999999999999994e196 < (*.f64 b c)

   1. Initial program 78.0%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in y around 0 81.0%

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

      1. associate-+r+ 81.0%

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

      2. +-commutative 81.0%

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

      3. distribute-lft-out 81.0%

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

      4. metadata-eval 81.0%

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

      5. cancel-sign-sub-inv 81.0%

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

      6. distribute-lft-out 81.0%

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

      7. fma-neg 86.1%

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

      8. distribute-lft-out 86.1%

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

      9. distribute-lft-neg-in 86.1%

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

      10. metadata-eval 86.1%

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

      11. +-commutative 86.1%

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

      12. *-commutative 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in b around inf 66.4%

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

   if -7.2000000000000003e102 < (*.f64 b c) < -0.058999999999999997 or -2.6000000000000002e-29 < (*.f64 b c) < -6.79999999999999979e-240

   1. Initial program 86.0%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in y around 0 67.3%

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

      1. associate-+r+ 67.3%

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

      2. +-commutative 67.3%

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

      3. distribute-lft-out 67.3%

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

      4. metadata-eval 67.3%

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

      5. cancel-sign-sub-inv 67.3%

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

      6. distribute-lft-out 67.3%

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

      7. fma-neg 67.3%

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

      8. distribute-lft-out 67.3%

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

      9. distribute-lft-neg-in 67.3%

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

      10. metadata-eval 67.3%

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

      11. +-commutative 67.3%

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

      12. *-commutative 67.3%

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

   6. Simplified 67.3%

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

   7. Taylor expanded in t around inf 35.9%

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

   if -0.058999999999999997 < (*.f64 b c) < -2.6000000000000002e-29 or -6.79999999999999979e-240 < (*.f64 b c) < 1.65999999999999994e196

   1. Initial program 84.7%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in j around inf 39.8%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7.2 \cdot 10^{+102}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -0.059:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -2.6 \cdot 10^{-29}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;b \cdot c \leq -6.8 \cdot 10^{-240}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.66 \cdot 10^{+196}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 16: 37.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -1.15 \cdot 10^{+103}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -0.0145:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq -1.9 \cdot 10^{-28}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -7.8 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot c \leq 1.9 \cdot 10^{+196}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* t a))))
   (if (<= (* b c) -1.15e+103)
     (* b c)
     (if (<= (* b c) -0.0145)
       t_1
       (if (<= (* b c) -1.9e-28)
         (* k (* j -27.0))
         (if (<= (* b c) -7.8e-240)
           t_1
           (if (<= (* b c) 1.9e+196) (* -27.0 (* j k)) (* b c))))))))

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 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -1.15e+103) {
		tmp = b * c;
	} else if ((b * c) <= -0.0145) {
		tmp = t_1;
	} else if ((b * c) <= -1.9e-28) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= -7.8e-240) {
		tmp = t_1;
	} else if ((b * c) <= 1.9e+196) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	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) :: tmp
    t_1 = (-4.0d0) * (t * a)
    if ((b * c) <= (-1.15d+103)) then
        tmp = b * c
    else if ((b * c) <= (-0.0145d0)) then
        tmp = t_1
    else if ((b * c) <= (-1.9d-28)) then
        tmp = k * (j * (-27.0d0))
    else if ((b * c) <= (-7.8d-240)) then
        tmp = t_1
    else if ((b * c) <= 1.9d+196) then
        tmp = (-27.0d0) * (j * k)
    else
        tmp = b * c
    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 = -4.0 * (t * a);
	double tmp;
	if ((b * c) <= -1.15e+103) {
		tmp = b * c;
	} else if ((b * c) <= -0.0145) {
		tmp = t_1;
	} else if ((b * c) <= -1.9e-28) {
		tmp = k * (j * -27.0);
	} else if ((b * c) <= -7.8e-240) {
		tmp = t_1;
	} else if ((b * c) <= 1.9e+196) {
		tmp = -27.0 * (j * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * (t * a)
	tmp = 0
	if (b * c) <= -1.15e+103:
		tmp = b * c
	elif (b * c) <= -0.0145:
		tmp = t_1
	elif (b * c) <= -1.9e-28:
		tmp = k * (j * -27.0)
	elif (b * c) <= -7.8e-240:
		tmp = t_1
	elif (b * c) <= 1.9e+196:
		tmp = -27.0 * (j * k)
	else:
		tmp = b * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(t * a))
	tmp = 0.0
	if (Float64(b * c) <= -1.15e+103)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= -0.0145)
		tmp = t_1;
	elseif (Float64(b * c) <= -1.9e-28)
		tmp = Float64(k * Float64(j * -27.0));
	elseif (Float64(b * c) <= -7.8e-240)
		tmp = t_1;
	elseif (Float64(b * c) <= 1.9e+196)
		tmp = Float64(-27.0 * Float64(j * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * (t * a);
	tmp = 0.0;
	if ((b * c) <= -1.15e+103)
		tmp = b * c;
	elseif ((b * c) <= -0.0145)
		tmp = t_1;
	elseif ((b * c) <= -1.9e-28)
		tmp = k * (j * -27.0);
	elseif ((b * c) <= -7.8e-240)
		tmp = t_1;
	elseif ((b * c) <= 1.9e+196)
		tmp = -27.0 * (j * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1.15e+103], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -0.0145], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], -1.9e-28], N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -7.8e-240], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1.9e+196], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -1.15000000000000004e103 or 1.9000000000000001e196 < (*.f64 b c)

   1. Initial program 78.0%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in y around 0 81.0%

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

      1. associate-+r+ 81.0%

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

      2. +-commutative 81.0%

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

      3. distribute-lft-out 81.0%

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

      4. metadata-eval 81.0%

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

      5. cancel-sign-sub-inv 81.0%

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

      6. distribute-lft-out 81.0%

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

      7. fma-neg 86.1%

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

      8. distribute-lft-out 86.1%

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

      9. distribute-lft-neg-in 86.1%

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

      10. metadata-eval 86.1%

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

      11. +-commutative 86.1%

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

      12. *-commutative 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in b around inf 66.4%

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

   if -1.15000000000000004e103 < (*.f64 b c) < -0.0145000000000000007 or -1.90000000000000005e-28 < (*.f64 b c) < -7.80000000000000029e-240

   1. Initial program 86.0%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in y around 0 67.3%

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

      1. associate-+r+ 67.3%

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

      2. +-commutative 67.3%

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

      3. distribute-lft-out 67.3%

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

      4. metadata-eval 67.3%

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

      5. cancel-sign-sub-inv 67.3%

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

      6. distribute-lft-out 67.3%

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

      7. fma-neg 67.3%

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

      8. distribute-lft-out 67.3%

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

      9. distribute-lft-neg-in 67.3%

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

      10. metadata-eval 67.3%

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

      11. +-commutative 67.3%

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

      12. *-commutative 67.3%

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

   6. Simplified 67.3%

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

   7. Taylor expanded in t around inf 35.9%

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

   if -0.0145000000000000007 < (*.f64 b c) < -1.90000000000000005e-28

   1. Initial program 79.8%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in j around inf 70.5%

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

      1. associate-*r* 70.6%

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

      2. *-commutative 70.6%

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

   6. Simplified 70.6%

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

   if -7.80000000000000029e-240 < (*.f64 b c) < 1.9000000000000001e196

   1. Initial program 85.1%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in j around inf 37.6%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.15 \cdot 10^{+103}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq -0.0145:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq -1.9 \cdot 10^{-28}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;b \cdot c \leq -7.8 \cdot 10^{-240}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;b \cdot c \leq 1.9 \cdot 10^{+196}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 17: 40.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_2 := 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{if}\;j \leq -9.5 \cdot 10^{+140}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.42 \cdot 10^{-139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4.9 \cdot 10^{-204}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (+ (* t a) (* x i)))) (t_2 (* 18.0 (* t (* z (* x y))))))
   (if (<= j -9.5e+140)
     (* -27.0 (* j k))
     (if (<= j -4.2e+93)
       t_2
       (if (<= j -1e-54)
         t_1
         (if (<= j -1.42e-139)
           t_2
           (if (<= j 1.2e-253)
             t_1
             (if (<= j 4.9e-204)
               (* 18.0 (* t (* x (* y z))))
               (if (<= j 2e-41) t_1 (* j (* k -27.0)))))))))))

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 = -4.0 * ((t * a) + (x * i));
	double t_2 = 18.0 * (t * (z * (x * y)));
	double tmp;
	if (j <= -9.5e+140) {
		tmp = -27.0 * (j * k);
	} else if (j <= -4.2e+93) {
		tmp = t_2;
	} else if (j <= -1e-54) {
		tmp = t_1;
	} else if (j <= -1.42e-139) {
		tmp = t_2;
	} else if (j <= 1.2e-253) {
		tmp = t_1;
	} else if (j <= 4.9e-204) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (j <= 2e-41) {
		tmp = t_1;
	} else {
		tmp = j * (k * -27.0);
	}
	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 = (-4.0d0) * ((t * a) + (x * i))
    t_2 = 18.0d0 * (t * (z * (x * y)))
    if (j <= (-9.5d+140)) then
        tmp = (-27.0d0) * (j * k)
    else if (j <= (-4.2d+93)) then
        tmp = t_2
    else if (j <= (-1d-54)) then
        tmp = t_1
    else if (j <= (-1.42d-139)) then
        tmp = t_2
    else if (j <= 1.2d-253) then
        tmp = t_1
    else if (j <= 4.9d-204) then
        tmp = 18.0d0 * (t * (x * (y * z)))
    else if (j <= 2d-41) then
        tmp = t_1
    else
        tmp = j * (k * (-27.0d0))
    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 = -4.0 * ((t * a) + (x * i));
	double t_2 = 18.0 * (t * (z * (x * y)));
	double tmp;
	if (j <= -9.5e+140) {
		tmp = -27.0 * (j * k);
	} else if (j <= -4.2e+93) {
		tmp = t_2;
	} else if (j <= -1e-54) {
		tmp = t_1;
	} else if (j <= -1.42e-139) {
		tmp = t_2;
	} else if (j <= 1.2e-253) {
		tmp = t_1;
	} else if (j <= 4.9e-204) {
		tmp = 18.0 * (t * (x * (y * z)));
	} else if (j <= 2e-41) {
		tmp = t_1;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * ((t * a) + (x * i))
	t_2 = 18.0 * (t * (z * (x * y)))
	tmp = 0
	if j <= -9.5e+140:
		tmp = -27.0 * (j * k)
	elif j <= -4.2e+93:
		tmp = t_2
	elif j <= -1e-54:
		tmp = t_1
	elif j <= -1.42e-139:
		tmp = t_2
	elif j <= 1.2e-253:
		tmp = t_1
	elif j <= 4.9e-204:
		tmp = 18.0 * (t * (x * (y * z)))
	elif j <= 2e-41:
		tmp = t_1
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)))
	t_2 = Float64(18.0 * Float64(t * Float64(z * Float64(x * y))))
	tmp = 0.0
	if (j <= -9.5e+140)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (j <= -4.2e+93)
		tmp = t_2;
	elseif (j <= -1e-54)
		tmp = t_1;
	elseif (j <= -1.42e-139)
		tmp = t_2;
	elseif (j <= 1.2e-253)
		tmp = t_1;
	elseif (j <= 4.9e-204)
		tmp = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))));
	elseif (j <= 2e-41)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * ((t * a) + (x * i));
	t_2 = 18.0 * (t * (z * (x * y)));
	tmp = 0.0;
	if (j <= -9.5e+140)
		tmp = -27.0 * (j * k);
	elseif (j <= -4.2e+93)
		tmp = t_2;
	elseif (j <= -1e-54)
		tmp = t_1;
	elseif (j <= -1.42e-139)
		tmp = t_2;
	elseif (j <= 1.2e-253)
		tmp = t_1;
	elseif (j <= 4.9e-204)
		tmp = 18.0 * (t * (x * (y * z)));
	elseif (j <= 2e-41)
		tmp = t_1;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.5e+140], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.2e+93], t$95$2, If[LessEqual[j, -1e-54], t$95$1, If[LessEqual[j, -1.42e-139], t$95$2, If[LessEqual[j, 1.2e-253], t$95$1, If[LessEqual[j, 4.9e-204], N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2e-41], t$95$1, N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -9.4999999999999994e140

   1. Initial program 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in j around inf 62.3%

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

   if -9.4999999999999994e140 < j < -4.1999999999999996e93 or -1e-54 < j < -1.41999999999999997e-139

   1. Initial program 90.5%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in b around 0 66.1%

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

   6. Simplified 66.1%

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

   7. Taylor expanded in y around inf 43.2%

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

      1. associate-*r* 50.6%

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

   9. Simplified 50.6%

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

   if -4.1999999999999996e93 < j < -1e-54 or -1.41999999999999997e-139 < j < 1.20000000000000005e-253 or 4.90000000000000009e-204 < j < 2.00000000000000001e-41

   1. Initial program 85.8%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in y around 0 80.3%

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

      1. associate-+r+ 80.3%

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

      2. +-commutative 80.3%

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

      3. distribute-lft-out 80.3%

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

      4. metadata-eval 80.3%

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

      5. cancel-sign-sub-inv 80.3%

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

      6. distribute-lft-out 80.3%

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

      7. fma-neg 81.4%

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

      8. distribute-lft-out 81.4%

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

      9. distribute-lft-neg-in 81.4%

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

      10. metadata-eval 81.4%

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

      11. +-commutative 81.4%

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

      12. *-commutative 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in j around 0 65.8%

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

   8. Taylor expanded in b around 0 48.5%

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

   if 1.20000000000000005e-253 < j < 4.90000000000000009e-204

   1. Initial program 90.4%

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

      1. associate--l- 90.4%

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

      2. associate-+l- 90.4%

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

      3. associate--l- 90.4%

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

      4. *-commutative 90.4%

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

      5. associate-*r* 100.0%

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

      6. associate-*l* 100.0%

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

      7. associate-*r* 100.0%

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

      8. *-commutative 100.0%

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

      9. associate-*l* 90.4%

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

      10. associate--l- 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in a around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. *-commutative 80.4%

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

      3. associate-*r* 90.0%

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

      4. associate-*l* 90.0%

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

      5. associate-*r* 89.9%

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

      6. *-commutative 89.9%

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

      7. associate-*r* 80.4%

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

      8. fma-def 80.4%

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

      9. *-commutative 80.4%

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

      10. associate-*l* 89.9%

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

      11. *-commutative 89.9%

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

      12. associate-*l* 89.9%

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

      13. *-commutative 89.9%

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

      14. associate-*r* 90.0%

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

      15. *-commutative 90.0%

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

      16. *-commutative 90.0%

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

      17. associate-*r* 89.9%

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

      18. associate-*l* 90.0%

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

      19. *-commutative 90.0%

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

   6. Simplified 90.0%

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

   7. Taylor expanded in t around inf 41.8%

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

   if 2.00000000000000001e-41 < j

   1. Initial program 77.7%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in y around 0 73.2%

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

      1. associate-+r+ 73.2%

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

      2. +-commutative 73.2%

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

      3. distribute-lft-out 73.2%

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

      4. metadata-eval 73.2%

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

      5. cancel-sign-sub-inv 73.2%

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

      6. distribute-lft-out 73.2%

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

      7. fma-neg 74.3%

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

      8. distribute-lft-out 74.3%

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

      9. distribute-lft-neg-in 74.3%

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

      10. metadata-eval 74.3%

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

      11. +-commutative 74.3%

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

      12. *-commutative 74.3%

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

   6. Simplified 74.3%

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

   7. Taylor expanded in j around inf 35.8%

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

      1. *-commutative 35.8%

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

      2. associate-*r* 35.8%

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

      3. *-commutative 35.8%

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

   9. Simplified 35.8%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{+140}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{+93}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;j \leq -1 \cdot 10^{-54}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;j \leq -1.42 \cdot 10^{-139}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-253}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;j \leq 4.9 \cdot 10^{-204}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-41}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 18: 40.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ t_2 := 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{if}\;j \leq -1.85 \cdot 10^{+140}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -4.3 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3.1 \cdot 10^{-139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.06 \cdot 10^{-203}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (+ (* t a) (* x i)))) (t_2 (* 18.0 (* t (* z (* x y))))))
   (if (<= j -1.85e+140)
     (* -27.0 (* j k))
     (if (<= j -4.3e+93)
       t_2
       (if (<= j -9e-49)
         t_1
         (if (<= j -3.1e-139)
           t_2
           (if (<= j 1.5e-253)
             t_1
             (if (<= j 1.06e-203)
               (* 18.0 (* x (* z (* y t))))
               (if (<= j 2.15e-41) t_1 (* j (* k -27.0)))))))))))

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 = -4.0 * ((t * a) + (x * i));
	double t_2 = 18.0 * (t * (z * (x * y)));
	double tmp;
	if (j <= -1.85e+140) {
		tmp = -27.0 * (j * k);
	} else if (j <= -4.3e+93) {
		tmp = t_2;
	} else if (j <= -9e-49) {
		tmp = t_1;
	} else if (j <= -3.1e-139) {
		tmp = t_2;
	} else if (j <= 1.5e-253) {
		tmp = t_1;
	} else if (j <= 1.06e-203) {
		tmp = 18.0 * (x * (z * (y * t)));
	} else if (j <= 2.15e-41) {
		tmp = t_1;
	} else {
		tmp = j * (k * -27.0);
	}
	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 = (-4.0d0) * ((t * a) + (x * i))
    t_2 = 18.0d0 * (t * (z * (x * y)))
    if (j <= (-1.85d+140)) then
        tmp = (-27.0d0) * (j * k)
    else if (j <= (-4.3d+93)) then
        tmp = t_2
    else if (j <= (-9d-49)) then
        tmp = t_1
    else if (j <= (-3.1d-139)) then
        tmp = t_2
    else if (j <= 1.5d-253) then
        tmp = t_1
    else if (j <= 1.06d-203) then
        tmp = 18.0d0 * (x * (z * (y * t)))
    else if (j <= 2.15d-41) then
        tmp = t_1
    else
        tmp = j * (k * (-27.0d0))
    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 = -4.0 * ((t * a) + (x * i));
	double t_2 = 18.0 * (t * (z * (x * y)));
	double tmp;
	if (j <= -1.85e+140) {
		tmp = -27.0 * (j * k);
	} else if (j <= -4.3e+93) {
		tmp = t_2;
	} else if (j <= -9e-49) {
		tmp = t_1;
	} else if (j <= -3.1e-139) {
		tmp = t_2;
	} else if (j <= 1.5e-253) {
		tmp = t_1;
	} else if (j <= 1.06e-203) {
		tmp = 18.0 * (x * (z * (y * t)));
	} else if (j <= 2.15e-41) {
		tmp = t_1;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -4.0 * ((t * a) + (x * i))
	t_2 = 18.0 * (t * (z * (x * y)))
	tmp = 0
	if j <= -1.85e+140:
		tmp = -27.0 * (j * k)
	elif j <= -4.3e+93:
		tmp = t_2
	elif j <= -9e-49:
		tmp = t_1
	elif j <= -3.1e-139:
		tmp = t_2
	elif j <= 1.5e-253:
		tmp = t_1
	elif j <= 1.06e-203:
		tmp = 18.0 * (x * (z * (y * t)))
	elif j <= 2.15e-41:
		tmp = t_1
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)))
	t_2 = Float64(18.0 * Float64(t * Float64(z * Float64(x * y))))
	tmp = 0.0
	if (j <= -1.85e+140)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (j <= -4.3e+93)
		tmp = t_2;
	elseif (j <= -9e-49)
		tmp = t_1;
	elseif (j <= -3.1e-139)
		tmp = t_2;
	elseif (j <= 1.5e-253)
		tmp = t_1;
	elseif (j <= 1.06e-203)
		tmp = Float64(18.0 * Float64(x * Float64(z * Float64(y * t))));
	elseif (j <= 2.15e-41)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -4.0 * ((t * a) + (x * i));
	t_2 = 18.0 * (t * (z * (x * y)));
	tmp = 0.0;
	if (j <= -1.85e+140)
		tmp = -27.0 * (j * k);
	elseif (j <= -4.3e+93)
		tmp = t_2;
	elseif (j <= -9e-49)
		tmp = t_1;
	elseif (j <= -3.1e-139)
		tmp = t_2;
	elseif (j <= 1.5e-253)
		tmp = t_1;
	elseif (j <= 1.06e-203)
		tmp = 18.0 * (x * (z * (y * t)));
	elseif (j <= 2.15e-41)
		tmp = t_1;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.85e+140], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.3e+93], t$95$2, If[LessEqual[j, -9e-49], t$95$1, If[LessEqual[j, -3.1e-139], t$95$2, If[LessEqual[j, 1.5e-253], t$95$1, If[LessEqual[j, 1.06e-203], N[(18.0 * N[(x * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.15e-41], t$95$1, N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.85000000000000001e140

   1. Initial program 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in j around inf 62.3%

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

   if -1.85000000000000001e140 < j < -4.3e93 or -9.0000000000000004e-49 < j < -3.0999999999999999e-139

   1. Initial program 88.1%

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

   3. Simplified 79.6%

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

   4. Taylor expanded in b around 0 65.1%

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

   6. Simplified 65.1%

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

   7. Taylor expanded in y around inf 40.7%

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

      1. associate-*r* 47.7%

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) \]

   9. Simplified 47.7%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(\left(x \cdot y\right) \cdot z\right)\right)} \]

   if -4.3e93 < j < -9.0000000000000004e-49 or -3.0999999999999999e-139 < j < 1.5000000000000001e-253 or 1.0599999999999999e-203 < j < 2.1499999999999999e-41

   1. Initial program 86.6%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in y around 0 79.9%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   5. Step-by-step derivation

      1. associate-+r+ 79.9%

         \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) + b \cdot c\right)} + j \cdot \left(k \cdot -27\right) \]

      2. +-commutative 79.9%

         \[\leadsto \color{blue}{\left(b \cdot c + \left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      3. distribute-lft-out 79.9%

         \[\leadsto \left(b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      4. metadata-eval 79.9%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(-4\right)} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      5. cancel-sign-sub-inv 79.9%

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t + i \cdot x\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-lft-out 79.9%

         \[\leadsto \left(b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      7. fma-neg 81.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      8. distribute-lft-out 81.0%

         \[\leadsto \mathsf{fma}\left(b, c, -\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      9. distribute-lft-neg-in 81.0%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(-4\right) \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      10. metadata-eval 81.0%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      11. +-commutative 81.0%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\left(i \cdot x + a \cdot t\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      12. *-commutative 81.0%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + \color{blue}{t \cdot a}\right)\right) + j \cdot \left(k \cdot -27\right) \]

   6. Simplified 81.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + t \cdot a\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Taylor expanded in j around 0 66.1%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right) + b \cdot c} \]

   8. Taylor expanded in b around 0 48.4%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)} \]

   if 1.5000000000000001e-253 < j < 1.0599999999999999e-203

   1. Initial program 90.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l- 90.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 90.4%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

      3. associate--l- 90.4%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-commutative 90.4%

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)} \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. associate-*r* 100.0%

         \[\leadsto \color{blue}{z \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 100.0%

         \[\leadsto z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot t\right)\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot 18\right)\right) \cdot \left(y \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(x \cdot 18\right) \cdot z\right)} \cdot \left(y \cdot t\right) - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. associate-*l* 90.4%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. associate--l- 90.4%

          \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

   3. Simplified 90.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(18 \cdot y\right) \cdot \left(x \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in a around 0 80.4%

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   5. Step-by-step derivation

      1. +-commutative 80.4%

         \[\leadsto \color{blue}{\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 80.4%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot 18}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*r* 90.0%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \cdot 18\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 90.0%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(t \cdot x\right) \cdot \left(\left(y \cdot z\right) \cdot 18\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 89.9%

         \[\leadsto \left(b \cdot c + \left(t \cdot x\right) \cdot \color{blue}{\left(y \cdot \left(z \cdot 18\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 89.9%

         \[\leadsto \left(b \cdot c + \left(t \cdot x\right) \cdot \left(y \cdot \color{blue}{\left(18 \cdot z\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 80.4%

         \[\leadsto \left(b \cdot c + \color{blue}{t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. fma-def 80.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 80.4%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right) \cdot t}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. associate-*l* 89.9%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{x \cdot \left(\left(y \cdot \left(18 \cdot z\right)\right) \cdot t\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      11. *-commutative 89.9%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(\left(18 \cdot z\right) \cdot y\right)} \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      12. associate-*l* 89.9%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(18 \cdot \left(z \cdot y\right)\right)} \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      13. *-commutative 89.9%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right) \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      14. associate-*r* 90.0%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      15. *-commutative 90.0%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(18 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      16. *-commutative 90.0%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 18\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      17. associate-*r* 89.9%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(\left(t \cdot y\right) \cdot z\right)} \cdot 18\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      18. associate-*l* 90.0%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot \left(z \cdot 18\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      19. *-commutative 90.0%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\left(t \cdot y\right) \cdot \color{blue}{\left(18 \cdot z\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Simplified 90.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in t around inf 41.8%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 41.8%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot t\right)} \]

      2. associate-*l* 51.4%

         \[\leadsto 18 \cdot \color{blue}{\left(x \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)} \]

      3. *-commutative 51.4%

         \[\leadsto 18 \cdot \left(x \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right) \]

      4. associate-*r* 51.3%

         \[\leadsto 18 \cdot \left(x \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot z\right)}\right) \]

      5. *-commutative 51.3%

         \[\leadsto 18 \cdot \left(x \cdot \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)}\right) \]

   9. Simplified 51.3%

      \[\leadsto \color{blue}{18 \cdot \left(x \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)} \]

   if 2.1499999999999999e-41 < j

   1. Initial program 77.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in y around 0 73.2%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   5. Step-by-step derivation

      1. associate-+r+ 73.2%

         \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) + b \cdot c\right)} + j \cdot \left(k \cdot -27\right) \]

      2. +-commutative 73.2%

         \[\leadsto \color{blue}{\left(b \cdot c + \left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      3. distribute-lft-out 73.2%

         \[\leadsto \left(b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      4. metadata-eval 73.2%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(-4\right)} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      5. cancel-sign-sub-inv 73.2%

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t + i \cdot x\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-lft-out 73.2%

         \[\leadsto \left(b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      7. fma-neg 74.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      8. distribute-lft-out 74.3%

         \[\leadsto \mathsf{fma}\left(b, c, -\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      9. distribute-lft-neg-in 74.3%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(-4\right) \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      10. metadata-eval 74.3%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      11. +-commutative 74.3%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\left(i \cdot x + a \cdot t\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      12. *-commutative 74.3%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + \color{blue}{t \cdot a}\right)\right) + j \cdot \left(k \cdot -27\right) \]

   6. Simplified 74.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + t \cdot a\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Taylor expanded in j around inf 35.8%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.8%

         \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} \]

      2. associate-*r* 35.8%

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

      3. *-commutative 35.8%

         \[\leadsto j \cdot \color{blue}{\left(-27 \cdot k\right)} \]

   9. Simplified 35.8%

      \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.85 \cdot 10^{+140}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -4.3 \cdot 10^{+93}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-49}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;j \leq -3.1 \cdot 10^{-139}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-253}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;j \leq 1.06 \cdot 10^{-203}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-41}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 19: 43.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := 18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ t_3 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -8.5 \cdot 10^{+139}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-254}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-222}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* -4.0 (* t a))))
        (t_2 (* 18.0 (* t (* z (* x y)))))
        (t_3 (* -27.0 (* j k))))
   (if (<= j -8.5e+139)
     t_3
     (if (<= j -4.8e+93)
       t_2
       (if (<= j -3.7e-67)
         t_1
         (if (<= j -3.3e-139)
           t_2
           (if (<= j 3.5e-254)
             (* -4.0 (+ (* t a) (* x i)))
             (if (<= j 6.5e-222)
               (* 18.0 (* x (* z (* y t))))
               (if (<= j 5e-19) t_1 t_3)))))))))

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 = (b * c) + (-4.0 * (t * a));
	double t_2 = 18.0 * (t * (z * (x * y)));
	double t_3 = -27.0 * (j * k);
	double tmp;
	if (j <= -8.5e+139) {
		tmp = t_3;
	} else if (j <= -4.8e+93) {
		tmp = t_2;
	} else if (j <= -3.7e-67) {
		tmp = t_1;
	} else if (j <= -3.3e-139) {
		tmp = t_2;
	} else if (j <= 3.5e-254) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else if (j <= 6.5e-222) {
		tmp = 18.0 * (x * (z * (y * t)));
	} else if (j <= 5e-19) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (b * c) + ((-4.0d0) * (t * a))
    t_2 = 18.0d0 * (t * (z * (x * y)))
    t_3 = (-27.0d0) * (j * k)
    if (j <= (-8.5d+139)) then
        tmp = t_3
    else if (j <= (-4.8d+93)) then
        tmp = t_2
    else if (j <= (-3.7d-67)) then
        tmp = t_1
    else if (j <= (-3.3d-139)) then
        tmp = t_2
    else if (j <= 3.5d-254) then
        tmp = (-4.0d0) * ((t * a) + (x * i))
    else if (j <= 6.5d-222) then
        tmp = 18.0d0 * (x * (z * (y * t)))
    else if (j <= 5d-19) then
        tmp = t_1
    else
        tmp = t_3
    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 = (b * c) + (-4.0 * (t * a));
	double t_2 = 18.0 * (t * (z * (x * y)));
	double t_3 = -27.0 * (j * k);
	double tmp;
	if (j <= -8.5e+139) {
		tmp = t_3;
	} else if (j <= -4.8e+93) {
		tmp = t_2;
	} else if (j <= -3.7e-67) {
		tmp = t_1;
	} else if (j <= -3.3e-139) {
		tmp = t_2;
	} else if (j <= 3.5e-254) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else if (j <= 6.5e-222) {
		tmp = 18.0 * (x * (z * (y * t)));
	} else if (j <= 5e-19) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (-4.0 * (t * a))
	t_2 = 18.0 * (t * (z * (x * y)))
	t_3 = -27.0 * (j * k)
	tmp = 0
	if j <= -8.5e+139:
		tmp = t_3
	elif j <= -4.8e+93:
		tmp = t_2
	elif j <= -3.7e-67:
		tmp = t_1
	elif j <= -3.3e-139:
		tmp = t_2
	elif j <= 3.5e-254:
		tmp = -4.0 * ((t * a) + (x * i))
	elif j <= 6.5e-222:
		tmp = 18.0 * (x * (z * (y * t)))
	elif j <= 5e-19:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)))
	t_2 = Float64(18.0 * Float64(t * Float64(z * Float64(x * y))))
	t_3 = Float64(-27.0 * Float64(j * k))
	tmp = 0.0
	if (j <= -8.5e+139)
		tmp = t_3;
	elseif (j <= -4.8e+93)
		tmp = t_2;
	elseif (j <= -3.7e-67)
		tmp = t_1;
	elseif (j <= -3.3e-139)
		tmp = t_2;
	elseif (j <= 3.5e-254)
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	elseif (j <= 6.5e-222)
		tmp = Float64(18.0 * Float64(x * Float64(z * Float64(y * t))));
	elseif (j <= 5e-19)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (-4.0 * (t * a));
	t_2 = 18.0 * (t * (z * (x * y)));
	t_3 = -27.0 * (j * k);
	tmp = 0.0;
	if (j <= -8.5e+139)
		tmp = t_3;
	elseif (j <= -4.8e+93)
		tmp = t_2;
	elseif (j <= -3.7e-67)
		tmp = t_1;
	elseif (j <= -3.3e-139)
		tmp = t_2;
	elseif (j <= 3.5e-254)
		tmp = -4.0 * ((t * a) + (x * i));
	elseif (j <= 6.5e-222)
		tmp = 18.0 * (x * (z * (y * t)));
	elseif (j <= 5e-19)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.5e+139], t$95$3, If[LessEqual[j, -4.8e+93], t$95$2, If[LessEqual[j, -3.7e-67], t$95$1, If[LessEqual[j, -3.3e-139], t$95$2, If[LessEqual[j, 3.5e-254], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.5e-222], N[(18.0 * N[(x * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5e-19], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -8.5e139 or 5.0000000000000004e-19 < j

   1. Initial program 78.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 82.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in j around inf 45.1%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -8.5e139 < j < -4.80000000000000021e93 or -3.6999999999999999e-67 < j < -3.3e-139

   1. Initial program 89.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in b around 0 64.8%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(-4 \cdot \left(i \cdot x\right) + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} \]

   6. Simplified 64.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right), \mathsf{fma}\left(x, -4 \cdot i, k \cdot \left(-27 \cdot j\right)\right)\right)} \]

   7. Taylor expanded in y around inf 42.1%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 50.6%

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) \]

   9. Simplified 50.6%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(\left(x \cdot y\right) \cdot z\right)\right)} \]

   if -4.80000000000000021e93 < j < -3.6999999999999999e-67 or 6.5000000000000005e-222 < j < 5.0000000000000004e-19

   1. Initial program 87.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in y around 0 85.2%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   5. Step-by-step derivation

      1. associate-+r+ 85.2%

         \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) + b \cdot c\right)} + j \cdot \left(k \cdot -27\right) \]

      2. +-commutative 85.2%

         \[\leadsto \color{blue}{\left(b \cdot c + \left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      3. distribute-lft-out 85.2%

         \[\leadsto \left(b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      4. metadata-eval 85.2%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(-4\right)} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      5. cancel-sign-sub-inv 85.2%

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t + i \cdot x\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-lft-out 85.2%

         \[\leadsto \left(b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      7. fma-neg 86.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      8. distribute-lft-out 86.7%

         \[\leadsto \mathsf{fma}\left(b, c, -\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      9. distribute-lft-neg-in 86.7%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(-4\right) \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      10. metadata-eval 86.7%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      11. +-commutative 86.7%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\left(i \cdot x + a \cdot t\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      12. *-commutative 86.7%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + \color{blue}{t \cdot a}\right)\right) + j \cdot \left(k \cdot -27\right) \]

   6. Simplified 86.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + t \cdot a\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Taylor expanded in j around 0 68.4%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right) + b \cdot c} \]

   8. Taylor expanded in a around inf 55.0%

      \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} + b \cdot c \]
   9. Step-by-step derivation

      1. *-commutative 55.0%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot a\right)} + b \cdot c \]

   10. Simplified 55.0%

       \[\leadsto -4 \cdot \color{blue}{\left(t \cdot a\right)} + b \cdot c \]

   if -3.3e-139 < j < 3.50000000000000007e-254

   1. Initial program 89.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 92.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in y around 0 75.4%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   5. Step-by-step derivation

      1. associate-+r+ 75.4%

         \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) + b \cdot c\right)} + j \cdot \left(k \cdot -27\right) \]

      2. +-commutative 75.4%

         \[\leadsto \color{blue}{\left(b \cdot c + \left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      3. distribute-lft-out 75.4%

         \[\leadsto \left(b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      4. metadata-eval 75.4%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(-4\right)} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      5. cancel-sign-sub-inv 75.4%

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t + i \cdot x\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-lft-out 75.4%

         \[\leadsto \left(b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      7. fma-neg 75.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      8. distribute-lft-out 75.4%

         \[\leadsto \mathsf{fma}\left(b, c, -\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      9. distribute-lft-neg-in 75.4%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(-4\right) \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      10. metadata-eval 75.4%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      11. +-commutative 75.4%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\left(i \cdot x + a \cdot t\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      12. *-commutative 75.4%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + \color{blue}{t \cdot a}\right)\right) + j \cdot \left(k \cdot -27\right) \]

   6. Simplified 75.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + t \cdot a\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Taylor expanded in j around 0 63.6%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right) + b \cdot c} \]

   8. Taylor expanded in b around 0 55.9%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)} \]

   if 3.50000000000000007e-254 < j < 6.5000000000000005e-222

   1. Initial program 75.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l- 75.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 75.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

      3. associate--l- 75.9%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-commutative 75.9%

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)} \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. associate-*r* 100.0%

         \[\leadsto \color{blue}{z \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 100.0%

         \[\leadsto z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot t\right)\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot 18\right)\right) \cdot \left(y \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(x \cdot 18\right) \cdot z\right)} \cdot \left(y \cdot t\right) - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. associate-*l* 75.9%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. associate--l- 75.9%

          \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

   3. Simplified 75.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(18 \cdot y\right) \cdot \left(x \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in a around 0 75.9%

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   5. Step-by-step derivation

      1. +-commutative 75.9%

         \[\leadsto \color{blue}{\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 75.9%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot 18}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*r* 100.0%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \cdot 18\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 100.0%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(t \cdot x\right) \cdot \left(\left(y \cdot z\right) \cdot 18\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 99.6%

         \[\leadsto \left(b \cdot c + \left(t \cdot x\right) \cdot \color{blue}{\left(y \cdot \left(z \cdot 18\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 99.6%

         \[\leadsto \left(b \cdot c + \left(t \cdot x\right) \cdot \left(y \cdot \color{blue}{\left(18 \cdot z\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 75.9%

         \[\leadsto \left(b \cdot c + \color{blue}{t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. fma-def 75.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 75.9%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right) \cdot t}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. associate-*l* 99.6%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{x \cdot \left(\left(y \cdot \left(18 \cdot z\right)\right) \cdot t\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      11. *-commutative 99.6%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(\left(18 \cdot z\right) \cdot y\right)} \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      12. associate-*l* 99.6%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(18 \cdot \left(z \cdot y\right)\right)} \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      13. *-commutative 99.6%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right) \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      14. associate-*r* 100.0%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      15. *-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(18 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      16. *-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 18\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      17. associate-*r* 99.6%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(\left(t \cdot y\right) \cdot z\right)} \cdot 18\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      18. associate-*l* 100.0%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot \left(z \cdot 18\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      19. *-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\left(t \cdot y\right) \cdot \color{blue}{\left(18 \cdot z\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in t around inf 51.4%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. *-commutative 51.4%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(x \cdot \left(y \cdot z\right)\right) \cdot t\right)} \]

      2. associate-*l* 75.5%

         \[\leadsto 18 \cdot \color{blue}{\left(x \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)} \]

      3. *-commutative 75.5%

         \[\leadsto 18 \cdot \left(x \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right) \]

      4. associate-*r* 75.2%

         \[\leadsto 18 \cdot \left(x \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot z\right)}\right) \]

      5. *-commutative 75.2%

         \[\leadsto 18 \cdot \left(x \cdot \color{blue}{\left(z \cdot \left(t \cdot y\right)\right)}\right) \]

   9. Simplified 75.2%

      \[\leadsto \color{blue}{18 \cdot \left(x \cdot \left(z \cdot \left(t \cdot y\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.5 \cdot 10^{+139}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{+93}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-67}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-139}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-254}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-222}:\\ \;\;\;\;18 \cdot \left(x \cdot \left(z \cdot \left(y \cdot t\right)\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-19}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 20: 69.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ t_2 := x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+167}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (- (* b c) (* 4.0 (* t a))) (* (* j 27.0) k)))
        (t_2 (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))))
   (if (<= x -3.3e+167)
     t_2
     (if (<= x -2.25e+52)
       t_1
       (if (<= x -1.9e-6)
         t_2
         (if (<= x 8.8e-30)
           t_1
           (* x (- (* 18.0 (* t (* y z))) (* 4.0 i)))))))))

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 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	double t_2 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -3.3e+167) {
		tmp = t_2;
	} else if (x <= -2.25e+52) {
		tmp = t_1;
	} else if (x <= -1.9e-6) {
		tmp = t_2;
	} else if (x <= 8.8e-30) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	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 = ((b * c) - (4.0d0 * (t * a))) - ((j * 27.0d0) * k)
    t_2 = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    if (x <= (-3.3d+167)) then
        tmp = t_2
    else if (x <= (-2.25d+52)) then
        tmp = t_1
    else if (x <= (-1.9d-6)) then
        tmp = t_2
    else if (x <= 8.8d-30) then
        tmp = t_1
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    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 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	double t_2 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	double tmp;
	if (x <= -3.3e+167) {
		tmp = t_2;
	} else if (x <= -2.25e+52) {
		tmp = t_1;
	} else if (x <= -1.9e-6) {
		tmp = t_2;
	} else if (x <= 8.8e-30) {
		tmp = t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k)
	t_2 = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	tmp = 0
	if x <= -3.3e+167:
		tmp = t_2
	elif x <= -2.25e+52:
		tmp = t_1
	elif x <= -1.9e-6:
		tmp = t_2
	elif x <= 8.8e-30:
		tmp = t_1
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(Float64(j * 27.0) * k))
	t_2 = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)))
	tmp = 0.0
	if (x <= -3.3e+167)
		tmp = t_2;
	elseif (x <= -2.25e+52)
		tmp = t_1;
	elseif (x <= -1.9e-6)
		tmp = t_2;
	elseif (x <= 8.8e-30)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((b * c) - (4.0 * (t * a))) - ((j * 27.0) * k);
	t_2 = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	tmp = 0.0;
	if (x <= -3.3e+167)
		tmp = t_2;
	elseif (x <= -2.25e+52)
		tmp = t_1;
	elseif (x <= -1.9e-6)
		tmp = t_2;
	elseif (x <= 8.8e-30)
		tmp = t_1;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.3e+167], t$95$2, If[LessEqual[x, -2.25e+52], t$95$1, If[LessEqual[x, -1.9e-6], t$95$2, If[LessEqual[x, 8.8e-30], t$95$1, N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.30000000000000018e167 or -2.25e52 < x < -1.9e-6

   1. Initial program 62.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l- 62.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 62.0%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

      3. associate--l- 62.0%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-commutative 62.0%

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)} \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. associate-*r* 61.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 64.3%

         \[\leadsto z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot t\right)\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. associate-*r* 62.2%

         \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot 18\right)\right) \cdot \left(y \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-commutative 62.2%

         \[\leadsto \color{blue}{\left(\left(x \cdot 18\right) \cdot z\right)} \cdot \left(y \cdot t\right) - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. associate-*l* 62.1%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. associate--l- 62.1%

          \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

   3. Simplified 66.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(18 \cdot y\right) \cdot \left(x \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in a around 0 69.4%

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   5. Step-by-step derivation

      1. +-commutative 69.4%

         \[\leadsto \color{blue}{\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 69.4%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot 18}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*r* 67.0%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \cdot 18\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 67.0%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(t \cdot x\right) \cdot \left(\left(y \cdot z\right) \cdot 18\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 67.0%

         \[\leadsto \left(b \cdot c + \left(t \cdot x\right) \cdot \color{blue}{\left(y \cdot \left(z \cdot 18\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 67.0%

         \[\leadsto \left(b \cdot c + \left(t \cdot x\right) \cdot \left(y \cdot \color{blue}{\left(18 \cdot z\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 69.5%

         \[\leadsto \left(b \cdot c + \color{blue}{t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. fma-def 69.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 69.5%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right) \cdot t}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. associate-*l* 74.0%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{x \cdot \left(\left(y \cdot \left(18 \cdot z\right)\right) \cdot t\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      11. *-commutative 74.0%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(\left(18 \cdot z\right) \cdot y\right)} \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      12. associate-*l* 74.0%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(18 \cdot \left(z \cdot y\right)\right)} \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      13. *-commutative 74.0%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right) \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      14. associate-*r* 74.0%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      15. *-commutative 74.0%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(18 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      16. *-commutative 74.0%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 18\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      17. associate-*r* 71.8%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(\left(t \cdot y\right) \cdot z\right)} \cdot 18\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      18. associate-*l* 71.8%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot \left(z \cdot 18\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      19. *-commutative 71.8%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\left(t \cdot y\right) \cdot \color{blue}{\left(18 \cdot z\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Simplified 71.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in x around inf 83.1%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   8. Step-by-step derivation

      1. cancel-sign-sub-inv 83.1%

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(-4\right) \cdot i\right)} \]

      2. metadata-eval 83.1%

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \]

      3. *-commutative 83.1%

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{i \cdot -4}\right) \]

      4. associate-*r* 80.9%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot z\right)} + i \cdot -4\right) \]

   9. Simplified 80.9%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(\left(t \cdot y\right) \cdot z\right) + i \cdot -4\right)} \]

   if -3.30000000000000018e167 < x < -2.25e52 or -1.9e-6 < x < 8.79999999999999933e-30

   1. Initial program 92.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 79.0%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if 8.79999999999999933e-30 < x

   1. Initial program 75.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l- 75.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 75.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

      3. associate--l- 75.8%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-commutative 75.8%

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)} \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. associate-*r* 78.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 78.8%

         \[\leadsto z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot t\right)\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. associate-*r* 78.4%

         \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot 18\right)\right) \cdot \left(y \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-commutative 78.4%

         \[\leadsto \color{blue}{\left(\left(x \cdot 18\right) \cdot z\right)} \cdot \left(y \cdot t\right) - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. associate-*l* 72.4%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. associate--l- 72.4%

          \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(18 \cdot y\right) \cdot \left(x \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 66.6%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{+52}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-30}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 21: 40.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ t_2 := -4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{if}\;j \leq -2 \cdot 10^{+139}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* t (* x (* y z))))) (t_2 (* -4.0 (+ (* t a) (* x i)))))
   (if (<= j -2e+139)
     (* -27.0 (* j k))
     (if (<= j -1.2e-53)
       t_2
       (if (<= j -3.7e-140)
         t_1
         (if (<= j 1.6e-253)
           t_2
           (if (<= j 4.4e-204)
             t_1
             (if (<= j 2.2e-41) t_2 (* j (* k -27.0))))))))))

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 = 18.0 * (t * (x * (y * z)));
	double t_2 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if (j <= -2e+139) {
		tmp = -27.0 * (j * k);
	} else if (j <= -1.2e-53) {
		tmp = t_2;
	} else if (j <= -3.7e-140) {
		tmp = t_1;
	} else if (j <= 1.6e-253) {
		tmp = t_2;
	} else if (j <= 4.4e-204) {
		tmp = t_1;
	} else if (j <= 2.2e-41) {
		tmp = t_2;
	} else {
		tmp = j * (k * -27.0);
	}
	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 = 18.0d0 * (t * (x * (y * z)))
    t_2 = (-4.0d0) * ((t * a) + (x * i))
    if (j <= (-2d+139)) then
        tmp = (-27.0d0) * (j * k)
    else if (j <= (-1.2d-53)) then
        tmp = t_2
    else if (j <= (-3.7d-140)) then
        tmp = t_1
    else if (j <= 1.6d-253) then
        tmp = t_2
    else if (j <= 4.4d-204) then
        tmp = t_1
    else if (j <= 2.2d-41) then
        tmp = t_2
    else
        tmp = j * (k * (-27.0d0))
    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 = 18.0 * (t * (x * (y * z)));
	double t_2 = -4.0 * ((t * a) + (x * i));
	double tmp;
	if (j <= -2e+139) {
		tmp = -27.0 * (j * k);
	} else if (j <= -1.2e-53) {
		tmp = t_2;
	} else if (j <= -3.7e-140) {
		tmp = t_1;
	} else if (j <= 1.6e-253) {
		tmp = t_2;
	} else if (j <= 4.4e-204) {
		tmp = t_1;
	} else if (j <= 2.2e-41) {
		tmp = t_2;
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = 18.0 * (t * (x * (y * z)))
	t_2 = -4.0 * ((t * a) + (x * i))
	tmp = 0
	if j <= -2e+139:
		tmp = -27.0 * (j * k)
	elif j <= -1.2e-53:
		tmp = t_2
	elif j <= -3.7e-140:
		tmp = t_1
	elif j <= 1.6e-253:
		tmp = t_2
	elif j <= 4.4e-204:
		tmp = t_1
	elif j <= 2.2e-41:
		tmp = t_2
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(x * Float64(y * z))))
	t_2 = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)))
	tmp = 0.0
	if (j <= -2e+139)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (j <= -1.2e-53)
		tmp = t_2;
	elseif (j <= -3.7e-140)
		tmp = t_1;
	elseif (j <= 1.6e-253)
		tmp = t_2;
	elseif (j <= 4.4e-204)
		tmp = t_1;
	elseif (j <= 2.2e-41)
		tmp = t_2;
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = 18.0 * (t * (x * (y * z)));
	t_2 = -4.0 * ((t * a) + (x * i));
	tmp = 0.0;
	if (j <= -2e+139)
		tmp = -27.0 * (j * k);
	elseif (j <= -1.2e-53)
		tmp = t_2;
	elseif (j <= -3.7e-140)
		tmp = t_1;
	elseif (j <= 1.6e-253)
		tmp = t_2;
	elseif (j <= 4.4e-204)
		tmp = t_1;
	elseif (j <= 2.2e-41)
		tmp = t_2;
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2e+139], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.2e-53], t$95$2, If[LessEqual[j, -3.7e-140], t$95$1, If[LessEqual[j, 1.6e-253], t$95$2, If[LessEqual[j, 4.4e-204], t$95$1, If[LessEqual[j, 2.2e-41], t$95$2, N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.00000000000000007e139

   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 83.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in j around inf 60.7%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -2.00000000000000007e139 < j < -1.20000000000000004e-53 or -3.69999999999999977e-140 < j < 1.5999999999999999e-253 or 4.3999999999999997e-204 < j < 2.2e-41

   1. Initial program 86.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in y around 0 78.9%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   5. Step-by-step derivation

      1. associate-+r+ 78.9%

         \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) + b \cdot c\right)} + j \cdot \left(k \cdot -27\right) \]

      2. +-commutative 78.9%

         \[\leadsto \color{blue}{\left(b \cdot c + \left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      3. distribute-lft-out 78.9%

         \[\leadsto \left(b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      4. metadata-eval 78.9%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(-4\right)} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      5. cancel-sign-sub-inv 78.9%

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t + i \cdot x\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-lft-out 78.9%

         \[\leadsto \left(b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      7. fma-neg 79.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      8. distribute-lft-out 79.9%

         \[\leadsto \mathsf{fma}\left(b, c, -\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      9. distribute-lft-neg-in 79.9%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(-4\right) \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      10. metadata-eval 79.9%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      11. +-commutative 79.9%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\left(i \cdot x + a \cdot t\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      12. *-commutative 79.9%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + \color{blue}{t \cdot a}\right)\right) + j \cdot \left(k \cdot -27\right) \]

   6. Simplified 79.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + t \cdot a\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Taylor expanded in j around 0 65.1%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right) + b \cdot c} \]

   8. Taylor expanded in b around 0 46.7%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)} \]

   if -1.20000000000000004e-53 < j < -3.69999999999999977e-140 or 1.5999999999999999e-253 < j < 4.3999999999999997e-204

   1. Initial program 87.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l- 87.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 87.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

      3. associate--l- 87.9%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-commutative 87.9%

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)} \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. associate-*r* 90.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 90.8%

         \[\leadsto z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot t\right)\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. associate-*r* 90.8%

         \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot 18\right)\right) \cdot \left(y \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-commutative 90.8%

         \[\leadsto \color{blue}{\left(\left(x \cdot 18\right) \cdot z\right)} \cdot \left(y \cdot t\right) - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. associate-*l* 87.8%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. associate--l- 87.8%

          \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(18 \cdot y\right) \cdot \left(x \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in a around 0 69.9%

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   5. Step-by-step derivation

      1. +-commutative 69.9%

         \[\leadsto \color{blue}{\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 69.9%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot 18}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*r* 72.8%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \cdot 18\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 72.8%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(t \cdot x\right) \cdot \left(\left(y \cdot z\right) \cdot 18\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 72.7%

         \[\leadsto \left(b \cdot c + \left(t \cdot x\right) \cdot \color{blue}{\left(y \cdot \left(z \cdot 18\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 72.7%

         \[\leadsto \left(b \cdot c + \left(t \cdot x\right) \cdot \left(y \cdot \color{blue}{\left(18 \cdot z\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 69.9%

         \[\leadsto \left(b \cdot c + \color{blue}{t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. fma-def 69.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 69.9%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right) \cdot t}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. associate-*l* 72.8%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{x \cdot \left(\left(y \cdot \left(18 \cdot z\right)\right) \cdot t\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      11. *-commutative 72.8%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(\left(18 \cdot z\right) \cdot y\right)} \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      12. associate-*l* 72.8%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(18 \cdot \left(z \cdot y\right)\right)} \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      13. *-commutative 72.8%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right) \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      14. associate-*r* 72.8%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      15. *-commutative 72.8%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(18 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      16. *-commutative 72.8%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 18\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      17. associate-*r* 72.8%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(\left(t \cdot y\right) \cdot z\right)} \cdot 18\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      18. associate-*l* 72.8%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot \left(z \cdot 18\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      19. *-commutative 72.8%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\left(t \cdot y\right) \cdot \color{blue}{\left(18 \cdot z\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Simplified 72.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in t around inf 42.2%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]

   if 2.2e-41 < j

   1. Initial program 77.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in y around 0 73.2%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   5. Step-by-step derivation

      1. associate-+r+ 73.2%

         \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) + b \cdot c\right)} + j \cdot \left(k \cdot -27\right) \]

      2. +-commutative 73.2%

         \[\leadsto \color{blue}{\left(b \cdot c + \left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      3. distribute-lft-out 73.2%

         \[\leadsto \left(b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      4. metadata-eval 73.2%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(-4\right)} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      5. cancel-sign-sub-inv 73.2%

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t + i \cdot x\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-lft-out 73.2%

         \[\leadsto \left(b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      7. fma-neg 74.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      8. distribute-lft-out 74.3%

         \[\leadsto \mathsf{fma}\left(b, c, -\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      9. distribute-lft-neg-in 74.3%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(-4\right) \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      10. metadata-eval 74.3%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      11. +-commutative 74.3%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\left(i \cdot x + a \cdot t\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      12. *-commutative 74.3%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + \color{blue}{t \cdot a}\right)\right) + j \cdot \left(k \cdot -27\right) \]

   6. Simplified 74.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + t \cdot a\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Taylor expanded in j around inf 35.8%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.8%

         \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} \]

      2. associate-*r* 35.8%

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

      3. *-commutative 35.8%

         \[\leadsto j \cdot \color{blue}{\left(-27 \cdot k\right)} \]

   9. Simplified 35.8%

      \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2 \cdot 10^{+139}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-53}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-140}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-253}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-204}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{-41}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 22: 71.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-36}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-30}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= x -3.3e+167)
     (* x (+ (* 18.0 (* z (* y t))) (* i -4.0)))
     (if (<= x -5.6e-36)
       (- (- (* b c) (* 4.0 (* x i))) t_1)
       (if (<= x 8.5e-30)
         (- (- (* b c) (* 4.0 (* t a))) t_1)
         (* x (- (* 18.0 (* t (* y z))) (* 4.0 i))))))))

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 = (j * 27.0) * k;
	double tmp;
	if (x <= -3.3e+167) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (x <= -5.6e-36) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (x <= 8.5e-30) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	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) :: tmp
    t_1 = (j * 27.0d0) * k
    if (x <= (-3.3d+167)) then
        tmp = x * ((18.0d0 * (z * (y * t))) + (i * (-4.0d0)))
    else if (x <= (-5.6d-36)) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    else if (x <= 8.5d-30) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - t_1
    else
        tmp = x * ((18.0d0 * (t * (y * z))) - (4.0d0 * i))
    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 = (j * 27.0) * k;
	double tmp;
	if (x <= -3.3e+167) {
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	} else if (x <= -5.6e-36) {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	} else if (x <= 8.5e-30) {
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	} else {
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if x <= -3.3e+167:
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0))
	elif x <= -5.6e-36:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	elif x <= 8.5e-30:
		tmp = ((b * c) - (4.0 * (t * a))) - t_1
	else:
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (x <= -3.3e+167)
		tmp = Float64(x * Float64(Float64(18.0 * Float64(z * Float64(y * t))) + Float64(i * -4.0)));
	elseif (x <= -5.6e-36)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	elseif (x <= 8.5e-30)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - t_1);
	else
		tmp = Float64(x * Float64(Float64(18.0 * Float64(t * Float64(y * z))) - Float64(4.0 * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (x <= -3.3e+167)
		tmp = x * ((18.0 * (z * (y * t))) + (i * -4.0));
	elseif (x <= -5.6e-36)
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	elseif (x <= 8.5e-30)
		tmp = ((b * c) - (4.0 * (t * a))) - t_1;
	else
		tmp = x * ((18.0 * (t * (y * z))) - (4.0 * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[x, -3.3e+167], N[(x * N[(N[(18.0 * N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.6e-36], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 8.5e-30], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(x * N[(N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.30000000000000018e167

   1. Initial program 46.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l- 46.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 46.7%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

      3. associate--l- 46.7%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-commutative 46.7%

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)} \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. associate-*r* 49.9%

         \[\leadsto \color{blue}{z \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 53.4%

         \[\leadsto z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot t\right)\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. associate-*r* 50.3%

         \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot 18\right)\right) \cdot \left(y \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-commutative 50.3%

         \[\leadsto \color{blue}{\left(\left(x \cdot 18\right) \cdot z\right)} \cdot \left(y \cdot t\right) - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. associate-*l* 46.7%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. associate--l- 46.7%

          \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

   3. Simplified 53.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(18 \cdot y\right) \cdot \left(x \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in a around 0 57.3%

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   5. Step-by-step derivation

      1. +-commutative 57.3%

         \[\leadsto \color{blue}{\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 57.3%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot 18}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*r* 53.8%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \cdot 18\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 53.7%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(t \cdot x\right) \cdot \left(\left(y \cdot z\right) \cdot 18\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 53.7%

         \[\leadsto \left(b \cdot c + \left(t \cdot x\right) \cdot \color{blue}{\left(y \cdot \left(z \cdot 18\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 53.7%

         \[\leadsto \left(b \cdot c + \left(t \cdot x\right) \cdot \left(y \cdot \color{blue}{\left(18 \cdot z\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 57.4%

         \[\leadsto \left(b \cdot c + \color{blue}{t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. fma-def 57.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 57.4%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right) \cdot t}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. associate-*l* 64.2%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{x \cdot \left(\left(y \cdot \left(18 \cdot z\right)\right) \cdot t\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      11. *-commutative 64.2%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(\left(18 \cdot z\right) \cdot y\right)} \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      12. associate-*l* 64.2%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(18 \cdot \left(z \cdot y\right)\right)} \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      13. *-commutative 64.2%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right) \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      14. associate-*r* 64.2%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      15. *-commutative 64.2%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(18 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      16. *-commutative 64.2%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 18\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      17. associate-*r* 64.2%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(\left(t \cdot y\right) \cdot z\right)} \cdot 18\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      18. associate-*l* 64.2%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot \left(z \cdot 18\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      19. *-commutative 64.2%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\left(t \cdot y\right) \cdot \color{blue}{\left(18 \cdot z\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Simplified 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in x around inf 89.4%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   8. Step-by-step derivation

      1. cancel-sign-sub-inv 89.4%

         \[\leadsto x \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(-4\right) \cdot i\right)} \]

      2. metadata-eval 89.4%

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{-4} \cdot i\right) \]

      3. *-commutative 89.4%

         \[\leadsto x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \color{blue}{i \cdot -4}\right) \]

      4. associate-*r* 89.4%

         \[\leadsto x \cdot \left(18 \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot z\right)} + i \cdot -4\right) \]

   9. Simplified 89.4%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(\left(t \cdot y\right) \cdot z\right) + i \cdot -4\right)} \]

   if -3.30000000000000018e167 < x < -5.6000000000000002e-36

   1. Initial program 89.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in t around 0 72.9%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(i \cdot x\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if -5.6000000000000002e-36 < x < 8.49999999999999931e-30

   1. Initial program 93.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in x around 0 80.7%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   if 8.49999999999999931e-30 < x

   1. Initial program 75.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l- 75.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 75.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

      3. associate--l- 75.8%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-commutative 75.8%

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)} \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. associate-*r* 78.8%

         \[\leadsto \color{blue}{z \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 78.8%

         \[\leadsto z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot t\right)\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. associate-*r* 78.4%

         \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot 18\right)\right) \cdot \left(y \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-commutative 78.4%

         \[\leadsto \color{blue}{\left(\left(x \cdot 18\right) \cdot z\right)} \cdot \left(y \cdot t\right) - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. associate-*l* 72.4%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. associate--l- 72.4%

          \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(18 \cdot y\right) \cdot \left(x \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in x around inf 66.6%

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(z \cdot \left(y \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-36}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-30}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)\\ \end{array} \]

Alternative 23: 52.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+59}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-306}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* j (* k -27.0)))))
   (if (<= a -3.3e+59)
     (+ (* b c) (* -4.0 (* t a)))
     (if (<= a -7.8e-263)
       t_1
       (if (<= a -2.5e-306)
         (* 18.0 (* (* y z) (* x t)))
         (if (<= a 2.7e+85) t_1 (* -4.0 (+ (* t a) (* x i)))))))))

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 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (a <= -3.3e+59) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (a <= -7.8e-263) {
		tmp = t_1;
	} else if (a <= -2.5e-306) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else if (a <= 2.7e+85) {
		tmp = t_1;
	} else {
		tmp = -4.0 * ((t * a) + (x * i));
	}
	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) :: tmp
    t_1 = (b * c) + (j * (k * (-27.0d0)))
    if (a <= (-3.3d+59)) then
        tmp = (b * c) + ((-4.0d0) * (t * a))
    else if (a <= (-7.8d-263)) then
        tmp = t_1
    else if (a <= (-2.5d-306)) then
        tmp = 18.0d0 * ((y * z) * (x * t))
    else if (a <= 2.7d+85) then
        tmp = t_1
    else
        tmp = (-4.0d0) * ((t * a) + (x * i))
    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 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (a <= -3.3e+59) {
		tmp = (b * c) + (-4.0 * (t * a));
	} else if (a <= -7.8e-263) {
		tmp = t_1;
	} else if (a <= -2.5e-306) {
		tmp = 18.0 * ((y * z) * (x * t));
	} else if (a <= 2.7e+85) {
		tmp = t_1;
	} else {
		tmp = -4.0 * ((t * a) + (x * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if a <= -3.3e+59:
		tmp = (b * c) + (-4.0 * (t * a))
	elif a <= -7.8e-263:
		tmp = t_1
	elif a <= -2.5e-306:
		tmp = 18.0 * ((y * z) * (x * t))
	elif a <= 2.7e+85:
		tmp = t_1
	else:
		tmp = -4.0 * ((t * a) + (x * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (a <= -3.3e+59)
		tmp = Float64(Float64(b * c) + Float64(-4.0 * Float64(t * a)));
	elseif (a <= -7.8e-263)
		tmp = t_1;
	elseif (a <= -2.5e-306)
		tmp = Float64(18.0 * Float64(Float64(y * z) * Float64(x * t)));
	elseif (a <= 2.7e+85)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (k * -27.0));
	tmp = 0.0;
	if (a <= -3.3e+59)
		tmp = (b * c) + (-4.0 * (t * a));
	elseif (a <= -7.8e-263)
		tmp = t_1;
	elseif (a <= -2.5e-306)
		tmp = 18.0 * ((y * z) * (x * t));
	elseif (a <= 2.7e+85)
		tmp = t_1;
	else
		tmp = -4.0 * ((t * a) + (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.3e+59], N[(N[(b * c), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.8e-263], t$95$1, If[LessEqual[a, -2.5e-306], N[(18.0 * N[(N[(y * z), $MachinePrecision] * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+85], t$95$1, N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.2999999999999999e59

   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 90.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in y around 0 77.1%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   5. Step-by-step derivation

      1. associate-+r+ 77.1%

         \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) + b \cdot c\right)} + j \cdot \left(k \cdot -27\right) \]

      2. +-commutative 77.1%

         \[\leadsto \color{blue}{\left(b \cdot c + \left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      3. distribute-lft-out 77.1%

         \[\leadsto \left(b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      4. metadata-eval 77.1%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(-4\right)} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      5. cancel-sign-sub-inv 77.1%

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t + i \cdot x\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-lft-out 77.1%

         \[\leadsto \left(b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      7. fma-neg 77.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      8. distribute-lft-out 77.2%

         \[\leadsto \mathsf{fma}\left(b, c, -\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      9. distribute-lft-neg-in 77.2%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(-4\right) \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      10. metadata-eval 77.2%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      11. +-commutative 77.2%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\left(i \cdot x + a \cdot t\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      12. *-commutative 77.2%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + \color{blue}{t \cdot a}\right)\right) + j \cdot \left(k \cdot -27\right) \]

   6. Simplified 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + t \cdot a\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Taylor expanded in j around 0 58.7%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right) + b \cdot c} \]

   8. Taylor expanded in a around inf 51.6%

      \[\leadsto -4 \cdot \color{blue}{\left(a \cdot t\right)} + b \cdot c \]
   9. Step-by-step derivation

      1. *-commutative 51.6%

         \[\leadsto -4 \cdot \color{blue}{\left(t \cdot a\right)} + b \cdot c \]

   10. Simplified 51.6%

       \[\leadsto -4 \cdot \color{blue}{\left(t \cdot a\right)} + b \cdot c \]

   if -3.2999999999999999e59 < a < -7.79999999999999939e-263 or -2.49999999999999999e-306 < a < 2.69999999999999983e85

   1. Initial program 83.4%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 82.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in b around inf 56.3%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]

   if -7.79999999999999939e-263 < a < -2.49999999999999999e-306

   1. Initial program 82.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Step-by-step derivation

      1. associate--l- 82.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

      2. associate-+l- 82.2%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]

      3. associate--l- 82.2%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)} \]

      4. *-commutative 82.2%

         \[\leadsto \color{blue}{\left(z \cdot \left(\left(x \cdot 18\right) \cdot y\right)\right)} \cdot t - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      5. associate-*r* 90.6%

         \[\leadsto \color{blue}{z \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      6. associate-*l* 82.1%

         \[\leadsto z \cdot \color{blue}{\left(\left(x \cdot 18\right) \cdot \left(y \cdot t\right)\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      7. associate-*r* 73.7%

         \[\leadsto \color{blue}{\left(z \cdot \left(x \cdot 18\right)\right) \cdot \left(y \cdot t\right)} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      8. *-commutative 73.7%

         \[\leadsto \color{blue}{\left(\left(x \cdot 18\right) \cdot z\right)} \cdot \left(y \cdot t\right) - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      9. associate-*l* 82.1%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t} - \left(\left(\left(a \cdot 4\right) \cdot t - b \cdot c\right) + \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right) \]

      10. associate--l- 82.1%

          \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot z\right) \cdot y\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(18 \cdot y\right) \cdot \left(x \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)} \]

   4. Taylor expanded in a around 0 82.2%

      \[\leadsto \color{blue}{\left(18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
   5. Step-by-step derivation

      1. +-commutative 82.2%

         \[\leadsto \color{blue}{\left(b \cdot c + 18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      2. *-commutative 82.2%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \cdot 18}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      3. associate-*r* 90.8%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \cdot 18\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      4. associate-*l* 90.6%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(t \cdot x\right) \cdot \left(\left(y \cdot z\right) \cdot 18\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      5. associate-*r* 90.6%

         \[\leadsto \left(b \cdot c + \left(t \cdot x\right) \cdot \color{blue}{\left(y \cdot \left(z \cdot 18\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      6. *-commutative 90.6%

         \[\leadsto \left(b \cdot c + \left(t \cdot x\right) \cdot \left(y \cdot \color{blue}{\left(18 \cdot z\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      7. associate-*r* 82.2%

         \[\leadsto \left(b \cdot c + \color{blue}{t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      8. fma-def 82.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, t \cdot \left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      9. *-commutative 82.2%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(x \cdot \left(y \cdot \left(18 \cdot z\right)\right)\right) \cdot t}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      10. associate-*l* 73.6%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{x \cdot \left(\left(y \cdot \left(18 \cdot z\right)\right) \cdot t\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      11. *-commutative 73.6%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(\left(18 \cdot z\right) \cdot y\right)} \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      12. associate-*l* 73.6%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(18 \cdot \left(z \cdot y\right)\right)} \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      13. *-commutative 73.6%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\left(18 \cdot \color{blue}{\left(y \cdot z\right)}\right) \cdot t\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      14. associate-*r* 73.6%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(18 \cdot \left(\left(y \cdot z\right) \cdot t\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      15. *-commutative 73.6%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(18 \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      16. *-commutative 73.6%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(\left(t \cdot \left(y \cdot z\right)\right) \cdot 18\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      17. associate-*r* 73.6%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\color{blue}{\left(\left(t \cdot y\right) \cdot z\right)} \cdot 18\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      18. associate-*l* 73.6%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot \left(z \cdot 18\right)\right)}\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

      19. *-commutative 73.6%

          \[\leadsto \mathsf{fma}\left(b, c, x \cdot \left(\left(t \cdot y\right) \cdot \color{blue}{\left(18 \cdot z\right)}\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   6. Simplified 73.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, x \cdot \left(\left(t \cdot y\right) \cdot \left(18 \cdot z\right)\right)\right)} - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   7. Taylor expanded in t around inf 55.7%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 64.3%

         \[\leadsto 18 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \]

   9. Simplified 64.3%

      \[\leadsto \color{blue}{18 \cdot \left(\left(t \cdot x\right) \cdot \left(y \cdot z\right)\right)} \]

   if 2.69999999999999983e85 < a

   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 89.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in y around 0 79.9%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   5. Step-by-step derivation

      1. associate-+r+ 79.9%

         \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) + b \cdot c\right)} + j \cdot \left(k \cdot -27\right) \]

      2. +-commutative 79.9%

         \[\leadsto \color{blue}{\left(b \cdot c + \left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      3. distribute-lft-out 79.9%

         \[\leadsto \left(b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      4. metadata-eval 79.9%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(-4\right)} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      5. cancel-sign-sub-inv 79.9%

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t + i \cdot x\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-lft-out 79.9%

         \[\leadsto \left(b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      7. fma-neg 86.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      8. distribute-lft-out 86.0%

         \[\leadsto \mathsf{fma}\left(b, c, -\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      9. distribute-lft-neg-in 86.0%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(-4\right) \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      10. metadata-eval 86.0%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      11. +-commutative 86.0%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\left(i \cdot x + a \cdot t\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      12. *-commutative 86.0%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + \color{blue}{t \cdot a}\right)\right) + j \cdot \left(k \cdot -27\right) \]

   6. Simplified 86.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + t \cdot a\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Taylor expanded in j around 0 72.0%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right) + b \cdot c} \]

   8. Taylor expanded in b around 0 68.3%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+59}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-263}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-306}:\\ \;\;\;\;18 \cdot \left(\left(y \cdot z\right) \cdot \left(x \cdot t\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+85}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \end{array} \]

Alternative 24: 47.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;k \leq -3 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 5.3 \cdot 10^{-180}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 1.3 \cdot 10^{+190}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (+ (* b c) (* j (* k -27.0)))))
   (if (<= k -3e-224)
     t_1
     (if (<= k 5.3e-180)
       (* -4.0 (+ (* t a) (* x i)))
       (if (<= k 3.6e+86)
         (- (* b c) (* 4.0 (* x i)))
         (if (<= k 1.3e+190) (* 18.0 (* t (* z (* x y)))) t_1))))))

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 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (k <= -3e-224) {
		tmp = t_1;
	} else if (k <= 5.3e-180) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else if (k <= 3.6e+86) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (k <= 1.3e+190) {
		tmp = 18.0 * (t * (z * (x * y)));
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = (b * c) + (j * (k * (-27.0d0)))
    if (k <= (-3d-224)) then
        tmp = t_1
    else if (k <= 5.3d-180) then
        tmp = (-4.0d0) * ((t * a) + (x * i))
    else if (k <= 3.6d+86) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (k <= 1.3d+190) then
        tmp = 18.0d0 * (t * (z * (x * y)))
    else
        tmp = t_1
    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 = (b * c) + (j * (k * -27.0));
	double tmp;
	if (k <= -3e-224) {
		tmp = t_1;
	} else if (k <= 5.3e-180) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else if (k <= 3.6e+86) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (k <= 1.3e+190) {
		tmp = 18.0 * (t * (z * (x * y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (b * c) + (j * (k * -27.0))
	tmp = 0
	if k <= -3e-224:
		tmp = t_1
	elif k <= 5.3e-180:
		tmp = -4.0 * ((t * a) + (x * i))
	elif k <= 3.6e+86:
		tmp = (b * c) - (4.0 * (x * i))
	elif k <= 1.3e+190:
		tmp = 18.0 * (t * (z * (x * y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(b * c) + Float64(j * Float64(k * -27.0)))
	tmp = 0.0
	if (k <= -3e-224)
		tmp = t_1;
	elseif (k <= 5.3e-180)
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	elseif (k <= 3.6e+86)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (k <= 1.3e+190)
		tmp = Float64(18.0 * Float64(t * Float64(z * Float64(x * y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (b * c) + (j * (k * -27.0));
	tmp = 0.0;
	if (k <= -3e-224)
		tmp = t_1;
	elseif (k <= 5.3e-180)
		tmp = -4.0 * ((t * a) + (x * i));
	elseif (k <= 3.6e+86)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (k <= 1.3e+190)
		tmp = 18.0 * (t * (z * (x * y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[k, -3e-224], t$95$1, If[LessEqual[k, 5.3e-180], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 3.6e+86], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.3e+190], N[(18.0 * N[(t * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if k < -2.99999999999999982e-224 or 1.30000000000000005e190 < k

   1. Initial program 83.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in b around inf 57.3%

      \[\leadsto \color{blue}{b \cdot c} + j \cdot \left(k \cdot -27\right) \]

   if -2.99999999999999982e-224 < k < 5.2999999999999996e-180

   1. Initial program 78.0%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in y around 0 73.2%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   5. Step-by-step derivation

      1. associate-+r+ 73.2%

         \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) + b \cdot c\right)} + j \cdot \left(k \cdot -27\right) \]

      2. +-commutative 73.2%

         \[\leadsto \color{blue}{\left(b \cdot c + \left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      3. distribute-lft-out 73.2%

         \[\leadsto \left(b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      4. metadata-eval 73.2%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(-4\right)} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      5. cancel-sign-sub-inv 73.2%

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t + i \cdot x\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-lft-out 73.2%

         \[\leadsto \left(b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      7. fma-neg 73.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      8. distribute-lft-out 73.2%

         \[\leadsto \mathsf{fma}\left(b, c, -\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      9. distribute-lft-neg-in 73.2%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(-4\right) \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      10. metadata-eval 73.2%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      11. +-commutative 73.2%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\left(i \cdot x + a \cdot t\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      12. *-commutative 73.2%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + \color{blue}{t \cdot a}\right)\right) + j \cdot \left(k \cdot -27\right) \]

   6. Simplified 73.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + t \cdot a\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Taylor expanded in j around 0 73.2%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right) + b \cdot c} \]

   8. Taylor expanded in b around 0 52.7%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)} \]

   if 5.2999999999999996e-180 < k < 3.60000000000000005e86

   1. Initial program 85.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Taylor expanded in y around 0 71.9%

      \[\leadsto \color{blue}{\left(b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} - \left(j \cdot 27\right) \cdot k \]

   3. Taylor expanded in a around 0 61.5%

      \[\leadsto \left(b \cdot c - \color{blue}{4 \cdot \left(i \cdot x\right)}\right) - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. associate-*r* 61.5%

         \[\leadsto \left(b \cdot c - \color{blue}{\left(4 \cdot i\right) \cdot x}\right) - \left(j \cdot 27\right) \cdot k \]

      2. *-commutative 61.5%

         \[\leadsto \left(b \cdot c - \color{blue}{\left(i \cdot 4\right)} \cdot x\right) - \left(j \cdot 27\right) \cdot k \]

      3. *-commutative 61.5%

         \[\leadsto \left(b \cdot c - \color{blue}{x \cdot \left(i \cdot 4\right)}\right) - \left(j \cdot 27\right) \cdot k \]

   5. Simplified 61.5%

      \[\leadsto \left(b \cdot c - \color{blue}{x \cdot \left(i \cdot 4\right)}\right) - \left(j \cdot 27\right) \cdot k \]

   6. Taylor expanded in j around 0 48.5%

      \[\leadsto \color{blue}{b \cdot c - 4 \cdot \left(i \cdot x\right)} \]

   if 3.60000000000000005e86 < k < 1.30000000000000005e190

   1. Initial program 88.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in b around 0 83.4%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right) + \left(-4 \cdot \left(i \cdot x\right) + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right)} \]

   6. Simplified 83.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(-4, a, x \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right), \mathsf{fma}\left(x, -4 \cdot i, k \cdot \left(-27 \cdot j\right)\right)\right)} \]

   7. Taylor expanded in y around inf 45.4%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 50.7%

         \[\leadsto 18 \cdot \left(t \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot z\right)}\right) \]

   9. Simplified 50.7%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(\left(x \cdot y\right) \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;k \leq -3 \cdot 10^{-224}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;k \leq 5.3 \cdot 10^{-180}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{elif}\;k \leq 3.6 \cdot 10^{+86}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 1.3 \cdot 10^{+190}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 25: 38.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7 \cdot 10^{+138} \lor \neg \left(b \cdot c \leq 1.3 \cdot 10^{+196}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -7e+138) (not (<= (* b c) 1.3e+196)))
   (* b c)
   (* -27.0 (* j k))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -7e+138) || !((b * c) <= 1.3e+196)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	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) :: tmp
    if (((b * c) <= (-7d+138)) .or. (.not. ((b * c) <= 1.3d+196))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * k)
    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 tmp;
	if (((b * c) <= -7e+138) || !((b * c) <= 1.3e+196)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -7e+138) or not ((b * c) <= 1.3e+196):
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -7e+138) || !(Float64(b * c) <= 1.3e+196))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -7e+138) || ~(((b * c) <= 1.3e+196)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -7e+138], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1.3e+196]], $MachinePrecision]], N[(b * c), $MachinePrecision], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -6.9999999999999996e138 or 1.30000000000000006e196 < (*.f64 b c)

   1. Initial program 78.5%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 84.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in y around 0 80.0%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   5. Step-by-step derivation

      1. associate-+r+ 80.0%

         \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) + b \cdot c\right)} + j \cdot \left(k \cdot -27\right) \]

      2. +-commutative 80.0%

         \[\leadsto \color{blue}{\left(b \cdot c + \left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      3. distribute-lft-out 80.0%

         \[\leadsto \left(b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      4. metadata-eval 80.0%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(-4\right)} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      5. cancel-sign-sub-inv 80.0%

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t + i \cdot x\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-lft-out 80.0%

         \[\leadsto \left(b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      7. fma-neg 85.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      8. distribute-lft-out 85.9%

         \[\leadsto \mathsf{fma}\left(b, c, -\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      9. distribute-lft-neg-in 85.9%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(-4\right) \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      10. metadata-eval 85.9%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      11. +-commutative 85.9%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\left(i \cdot x + a \cdot t\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      12. *-commutative 85.9%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + \color{blue}{t \cdot a}\right)\right) + j \cdot \left(k \cdot -27\right) \]

   6. Simplified 85.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + t \cdot a\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Taylor expanded in b around inf 74.5%

      \[\leadsto \color{blue}{b \cdot c} \]

   if -6.9999999999999996e138 < (*.f64 b c) < 1.30000000000000006e196

   1. Initial program 84.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in j around inf 32.7%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7 \cdot 10^{+138} \lor \neg \left(b \cdot c \leq 1.3 \cdot 10^{+196}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 26: 42.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4.8 \cdot 10^{+138}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-41}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= j -4.8e+138)
   (* -27.0 (* j k))
   (if (<= j 2.15e-41) (* -4.0 (+ (* t a) (* x i))) (* j (* k -27.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (j <= -4.8e+138) {
		tmp = -27.0 * (j * k);
	} else if (j <= 2.15e-41) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else {
		tmp = j * (k * -27.0);
	}
	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) :: tmp
    if (j <= (-4.8d+138)) then
        tmp = (-27.0d0) * (j * k)
    else if (j <= 2.15d-41) then
        tmp = (-4.0d0) * ((t * a) + (x * i))
    else
        tmp = j * (k * (-27.0d0))
    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 tmp;
	if (j <= -4.8e+138) {
		tmp = -27.0 * (j * k);
	} else if (j <= 2.15e-41) {
		tmp = -4.0 * ((t * a) + (x * i));
	} else {
		tmp = j * (k * -27.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if j <= -4.8e+138:
		tmp = -27.0 * (j * k)
	elif j <= 2.15e-41:
		tmp = -4.0 * ((t * a) + (x * i))
	else:
		tmp = j * (k * -27.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (j <= -4.8e+138)
		tmp = Float64(-27.0 * Float64(j * k));
	elseif (j <= 2.15e-41)
		tmp = Float64(-4.0 * Float64(Float64(t * a) + Float64(x * i)));
	else
		tmp = Float64(j * Float64(k * -27.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (j <= -4.8e+138)
		tmp = -27.0 * (j * k);
	elseif (j <= 2.15e-41)
		tmp = -4.0 * ((t * a) + (x * i));
	else
		tmp = j * (k * -27.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[j, -4.8e+138], N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.15e-41], N[(-4.0 * N[(N[(t * a), $MachinePrecision] + N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -4.8000000000000002e138

   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 83.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in j around inf 60.7%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]

   if -4.8000000000000002e138 < j < 2.1499999999999999e-41

   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 87.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in y around 0 73.9%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   5. Step-by-step derivation

      1. associate-+r+ 73.9%

         \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) + b \cdot c\right)} + j \cdot \left(k \cdot -27\right) \]

      2. +-commutative 73.9%

         \[\leadsto \color{blue}{\left(b \cdot c + \left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      3. distribute-lft-out 73.9%

         \[\leadsto \left(b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      4. metadata-eval 73.9%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(-4\right)} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      5. cancel-sign-sub-inv 73.9%

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t + i \cdot x\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-lft-out 73.9%

         \[\leadsto \left(b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      7. fma-neg 75.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      8. distribute-lft-out 75.4%

         \[\leadsto \mathsf{fma}\left(b, c, -\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      9. distribute-lft-neg-in 75.4%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(-4\right) \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      10. metadata-eval 75.4%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      11. +-commutative 75.4%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\left(i \cdot x + a \cdot t\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      12. *-commutative 75.4%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + \color{blue}{t \cdot a}\right)\right) + j \cdot \left(k \cdot -27\right) \]

   6. Simplified 75.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + t \cdot a\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Taylor expanded in j around 0 60.5%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right) + b \cdot c} \]

   8. Taylor expanded in b around 0 43.0%

      \[\leadsto \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)} \]

   if 2.1499999999999999e-41 < j

   1. Initial program 77.7%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

   4. Taylor expanded in y around 0 73.2%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)\right)} + j \cdot \left(k \cdot -27\right) \]
   5. Step-by-step derivation

      1. associate-+r+ 73.2%

         \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) + b \cdot c\right)} + j \cdot \left(k \cdot -27\right) \]

      2. +-commutative 73.2%

         \[\leadsto \color{blue}{\left(b \cdot c + \left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      3. distribute-lft-out 73.2%

         \[\leadsto \left(b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      4. metadata-eval 73.2%

         \[\leadsto \left(b \cdot c + \color{blue}{\left(-4\right)} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      5. cancel-sign-sub-inv 73.2%

         \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t + i \cdot x\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      6. distribute-lft-out 73.2%

         \[\leadsto \left(b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      7. fma-neg 74.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

      8. distribute-lft-out 74.3%

         \[\leadsto \mathsf{fma}\left(b, c, -\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      9. distribute-lft-neg-in 74.3%

         \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(-4\right) \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      10. metadata-eval 74.3%

          \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

      11. +-commutative 74.3%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\left(i \cdot x + a \cdot t\right)}\right) + j \cdot \left(k \cdot -27\right) \]

      12. *-commutative 74.3%

          \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + \color{blue}{t \cdot a}\right)\right) + j \cdot \left(k \cdot -27\right) \]

   6. Simplified 74.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + t \cdot a\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   7. Taylor expanded in j around inf 35.8%

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.8%

         \[\leadsto \color{blue}{\left(j \cdot k\right) \cdot -27} \]

      2. associate-*r* 35.8%

         \[\leadsto \color{blue}{j \cdot \left(k \cdot -27\right)} \]

      3. *-commutative 35.8%

         \[\leadsto j \cdot \color{blue}{\left(-27 \cdot k\right)} \]

   9. Simplified 35.8%

      \[\leadsto \color{blue}{j \cdot \left(-27 \cdot k\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.8 \cdot 10^{+138}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;j \leq 2.15 \cdot 10^{-41}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 27: 24.4% accurate, 10.3× speedup

Math

\[\begin{array}{l} \\ b \cdot c \end{array} \]

FPCore

(FPCore (x y z t a b c i j k) :precision binary64 (* b c))

C

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

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

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

def code(x, y, z, t, a, b, c, i, j, k):
	return b * c

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(b * c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = b * c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(b * c), $MachinePrecision]

Derivation

1. Initial program 83.4%

   \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

3. Simplified 85.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(t, \mathsf{fma}\left(x, 18 \cdot \left(y \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, x \cdot \left(i \cdot -4\right)\right)\right) + j \cdot \left(k \cdot -27\right)} \]

4. Taylor expanded in y around 0 75.3%

   \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(-4 \cdot \left(i \cdot x\right) + b \cdot c\right)\right)} + j \cdot \left(k \cdot -27\right) \]
5. Step-by-step derivation

   1. associate-+r+ 75.3%

      \[\leadsto \color{blue}{\left(\left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right) + b \cdot c\right)} + j \cdot \left(k \cdot -27\right) \]

   2. +-commutative 75.3%

      \[\leadsto \color{blue}{\left(b \cdot c + \left(-4 \cdot \left(a \cdot t\right) + -4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   3. distribute-lft-out 75.3%

      \[\leadsto \left(b \cdot c + \color{blue}{-4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

   4. metadata-eval 75.3%

      \[\leadsto \left(b \cdot c + \color{blue}{\left(-4\right)} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

   5. cancel-sign-sub-inv 75.3%

      \[\leadsto \color{blue}{\left(b \cdot c - 4 \cdot \left(a \cdot t + i \cdot x\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   6. distribute-lft-out 75.3%

      \[\leadsto \left(b \cdot c - \color{blue}{\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)}\right) + j \cdot \left(k \cdot -27\right) \]

   7. fma-neg 76.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -\left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right)} + j \cdot \left(k \cdot -27\right) \]

   8. distribute-lft-out 76.5%

      \[\leadsto \mathsf{fma}\left(b, c, -\color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

   9. distribute-lft-neg-in 76.5%

      \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{\left(-4\right) \cdot \left(a \cdot t + i \cdot x\right)}\right) + j \cdot \left(k \cdot -27\right) \]

   10. metadata-eval 76.5%

       \[\leadsto \mathsf{fma}\left(b, c, \color{blue}{-4} \cdot \left(a \cdot t + i \cdot x\right)\right) + j \cdot \left(k \cdot -27\right) \]

   11. +-commutative 76.5%

       \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \color{blue}{\left(i \cdot x + a \cdot t\right)}\right) + j \cdot \left(k \cdot -27\right) \]

   12. *-commutative 76.5%

       \[\leadsto \mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + \color{blue}{t \cdot a}\right)\right) + j \cdot \left(k \cdot -27\right) \]

6. Simplified 76.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(b, c, -4 \cdot \left(i \cdot x + t \cdot a\right)\right)} + j \cdot \left(k \cdot -27\right) \]

7. Taylor expanded in b around inf 20.9%

   \[\leadsto \color{blue}{b \cdot c} \]

8. Final simplification 20.9%

   \[\leadsto b \cdot c \]

Developer target: 89.2% 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 2023301 
(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)))