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

Percentage Accurate: 85.1% → 89.2%

Time: 27.7s

Alternatives: 23

Speedup: 0.5×

• 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: 85.1% 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: 89.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-65} \lor \neg \left(t \leq 8 \cdot 10^{-156}\right):\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, \mathsf{fma}\left(t, \mathsf{fma}\left(x, \left(z \cdot 18\right) \cdot y, a \cdot -4\right), \mathsf{fma}\left(b, c, -4 \cdot \left(x \cdot i\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right), b \cdot c\right) + \left(j \cdot -27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -2.9e-65) (not (<= t 8e-156)))
   (fma
    (* j -27.0)
    k
    (fma t (fma x (* (* z 18.0) y) (* a -4.0)) (fma b c (* -4.0 (* x i)))))
   (+ (fma x (fma -4.0 i (* t (* z (* 18.0 y)))) (* b c)) (* (* j -27.0) k))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -2.9e-65) || !(t <= 8e-156)) {
		tmp = fma((j * -27.0), k, fma(t, fma(x, ((z * 18.0) * y), (a * -4.0)), fma(b, c, (-4.0 * (x * i)))));
	} else {
		tmp = fma(x, fma(-4.0, i, (t * (z * (18.0 * y)))), (b * c)) + ((j * -27.0) * k);
	}
	return tmp;
}

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -2.9e-65) || !(t <= 8e-156))
		tmp = fma(Float64(j * -27.0), k, fma(t, fma(x, Float64(Float64(z * 18.0) * y), Float64(a * -4.0)), fma(b, c, Float64(-4.0 * Float64(x * i)))));
	else
		tmp = Float64(fma(x, fma(-4.0, i, Float64(t * Float64(z * Float64(18.0 * y)))), Float64(b * c)) + Float64(Float64(j * -27.0) * k));
	end
	return tmp
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -2.9e-65], N[Not[LessEqual[t, 8e-156]], $MachinePrecision]], N[(N[(j * -27.0), $MachinePrecision] * k + N[(t * N[(x * N[(N[(z * 18.0), $MachinePrecision] * y), $MachinePrecision] + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b * c + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(-4.0 * i + N[(t * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] + N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8999999999999998e-65 or 8.00000000000000032e-156 < t

   1. Initial program 84.8%

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

   3. Simplified 89.0%

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

      1. +-commutative 89.0%

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

      2. *-commutative 89.0%

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

      3. fma-def 91.9%

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

      4. associate-*r* 91.9%

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

      5. associate-*r* 91.9%

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

   5. Applied egg-rr 91.9%

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

   if -2.8999999999999998e-65 < t < 8.00000000000000032e-156

   1. Initial program 76.9%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in a around 0 78.1%

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

   6. Simplified 89.6%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-65} \lor \neg \left(t \leq 8 \cdot 10^{-156}\right):\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, \mathsf{fma}\left(t, \mathsf{fma}\left(x, \left(z \cdot 18\right) \cdot y, a \cdot -4\right), \mathsf{fma}\left(b, c, -4 \cdot \left(x \cdot i\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right), b \cdot c\right) + \left(j \cdot -27\right) \cdot k\\ \end{array} \]

Alternative 2: 89.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := \left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_1 \leq 10^{+299}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right), b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (-
           (+ (* b c) (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))))
           (* i (* x 4.0)))
          (* k (* j 27.0)))))
   (if (<= t_1 1e+299)
     t_1
     (fma -27.0 (* j k) (fma x (fma -4.0 i (* t (* z (* 18.0 y)))) (* b c))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	double tmp;
	if (t_1 <= 1e+299) {
		tmp = t_1;
	} else {
		tmp = fma(-27.0, (j * k), fma(x, fma(-4.0, i, (t * (z * (18.0 * y)))), (b * c)));
	}
	return tmp;
}

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)))
	tmp = 0.0
	if (t_1 <= 1e+299)
		tmp = t_1;
	else
		tmp = fma(-27.0, Float64(j * k), fma(x, fma(-4.0, i, Float64(t * Float64(z * Float64(18.0 * y)))), Float64(b * c)));
	end
	return tmp
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+299], t$95$1, N[(-27.0 * N[(j * k), $MachinePrecision] + N[(x * N[(-4.0 * i + N[(t * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $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)) < 1.0000000000000001e299

   1. Initial program 95.7%

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

   if 1.0000000000000001e299 < (-.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 59.0%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in a around 0 63.4%

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

   6. Simplified 79.2%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right) \leq 10^{+299}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, \mathsf{fma}\left(x, \mathsf{fma}\left(-4, i, t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right), b \cdot c\right)\right)\\ \end{array} \]

Alternative 3: 86.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := \left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{if}\;t_1 \leq 10^{+299}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k - x \cdot \mathsf{fma}\left(i, 4, z \cdot \left(y \cdot \left(t \cdot -18\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (-
           (+ (* b c) (- (* t (* z (* y (* x 18.0)))) (* t (* a 4.0))))
           (* i (* x 4.0)))
          (* k (* j 27.0)))))
   (if (<= t_1 1e+299)
     t_1
     (- (* (* j -27.0) k) (* x (fma i 4.0 (* z (* y (* t -18.0)))))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (((b * c) + ((t * (z * (y * (x * 18.0)))) - (t * (a * 4.0)))) - (i * (x * 4.0))) - (k * (j * 27.0));
	double tmp;
	if (t_1 <= 1e+299) {
		tmp = t_1;
	} else {
		tmp = ((j * -27.0) * k) - (x * fma(i, 4.0, (z * (y * (t * -18.0)))));
	}
	return tmp;
}

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(b * c) + Float64(Float64(t * Float64(z * Float64(y * Float64(x * 18.0)))) - Float64(t * Float64(a * 4.0)))) - Float64(i * Float64(x * 4.0))) - Float64(k * Float64(j * 27.0)))
	tmp = 0.0
	if (t_1 <= 1e+299)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(j * -27.0) * k) - Float64(x * fma(i, 4.0, Float64(z * Float64(y * Float64(t * -18.0))))));
	end
	return tmp
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+299], t$95$1, N[(N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision] - N[(x * N[(i * 4.0 + N[(z * N[(y * N[(t * -18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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)) < 1.0000000000000001e299

   1. Initial program 95.7%

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

   if 1.0000000000000001e299 < (-.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 59.0%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in x around -inf 73.3%

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

      1. mul-1-neg 73.3%

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

      2. metadata-eval 73.3%

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

      3. cancel-sign-sub-inv 73.3%

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

      4. *-commutative 73.3%

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

      5. distribute-rgt-neg-in 73.3%

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

      6. cancel-sign-sub-inv 73.3%

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

      7. metadata-eval 73.3%

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

      8. +-commutative 73.3%

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

      9. *-commutative 73.3%

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

      10. fma-def 74.4%

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

      11. associate-*r* 74.4%

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

      12. associate-*r* 77.3%

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

      13. *-commutative 77.3%

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

   6. Simplified 77.3%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right) \leq 10^{+299}:\\ \;\;\;\;\left(\left(b \cdot c + \left(t \cdot \left(z \cdot \left(y \cdot \left(x \cdot 18\right)\right)\right) - t \cdot \left(a \cdot 4\right)\right)\right) - i \cdot \left(x \cdot 4\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k - x \cdot \mathsf{fma}\left(i, 4, z \cdot \left(y \cdot \left(t \cdot -18\right)\right)\right)\\ \end{array} \]

Alternative 4: 89.4% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(z * y), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] - N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * -27.0), $MachinePrecision] * k + N[(N[(t * 18.0), $MachinePrecision] * N[(x * N[(z * y), $MachinePrecision]), $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 93.2%

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

      1. associate-*l* 93.2%

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

      2. associate--l+ 93.2%

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

      3. distribute-rgt-out-- 93.2%

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

      4. associate-*l* 92.8%

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

      5. associate-*l* 92.8%

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

   3. Simplified 92.8%

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

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

   1. Initial program 0.0%

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

   3. Simplified 30.0%

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

   4. Taylor expanded in z around inf 40.5%

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

      1. +-commutative 40.5%

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

      2. *-commutative 40.5%

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

      3. fma-def 50.5%

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

      4. associate-*r* 50.5%

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

      5. *-commutative 50.5%

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

   6. Applied egg-rr 50.5%

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

4. Final simplification 87.9%

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

Alternative 5: 89.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(N[(N[(N[(b * c), $MachinePrecision] + N[(N[(t * N[(z * N[(y * N[(x * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(t * N[(N[(N[(x * 18.0), $MachinePrecision] * N[(z * y), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * c), $MachinePrecision] - N[(x * N[(i * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $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 93.2%

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

      1. associate-*l* 93.2%

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

      2. associate--l+ 93.2%

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

      3. distribute-rgt-out-- 93.2%

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

      4. associate-*l* 92.8%

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

      5. associate-*l* 92.8%

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

   3. Simplified 92.8%

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

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

   1. Initial program 0.0%

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

      1. associate-*l* 0.0%

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

      2. associate--l+ 0.0%

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

      3. distribute-rgt-out-- 13.3%

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

      4. associate-*l* 13.3%

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

      5. associate-*l* 13.3%

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

   3. Simplified 13.3%

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

   4. Taylor expanded in i around 0 33.3%

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

   5. Taylor expanded in j around 0 43.3%

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

4. Final simplification 87.0%

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

Alternative 6: 55.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := \left(j \cdot -27\right) \cdot k\\ t_2 := t_1 + 18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -8 \cdot 10^{+30}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -3.3 \cdot 10^{-168}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 5.2 \cdot 10^{-282}:\\ \;\;\;\;t_1 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.85 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j -27.0) k)) (t_2 (+ t_1 (* 18.0 (* t (* x (* z y)))))))
   (if (<= (* b c) -8e+30)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= (* b c) -3.3e-168)
       t_2
       (if (<= (* b c) 5.2e-282)
         (+ t_1 (* x (* -4.0 i)))
         (if (<= (* b c) 1.85e+40) t_2 (- (* b c) (* 27.0 (* j k)))))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double t_2 = t_1 + (18.0 * (t * (x * (z * y))));
	double tmp;
	if ((b * c) <= -8e+30) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -3.3e-168) {
		tmp = t_2;
	} else if ((b * c) <= 5.2e-282) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if ((b * c) <= 1.85e+40) {
		tmp = t_2;
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * (-27.0d0)) * k
    t_2 = t_1 + (18.0d0 * (t * (x * (z * y))))
    if ((b * c) <= (-8d+30)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if ((b * c) <= (-3.3d-168)) then
        tmp = t_2
    else if ((b * c) <= 5.2d-282) then
        tmp = t_1 + (x * ((-4.0d0) * i))
    else if ((b * c) <= 1.85d+40) then
        tmp = t_2
    else
        tmp = (b * c) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double t_2 = t_1 + (18.0 * (t * (x * (z * y))));
	double tmp;
	if ((b * c) <= -8e+30) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -3.3e-168) {
		tmp = t_2;
	} else if ((b * c) <= 5.2e-282) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if ((b * c) <= 1.85e+40) {
		tmp = t_2;
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * -27.0) * k
	t_2 = t_1 + (18.0 * (t * (x * (z * y))))
	tmp = 0
	if (b * c) <= -8e+30:
		tmp = (b * c) - (4.0 * (x * i))
	elif (b * c) <= -3.3e-168:
		tmp = t_2
	elif (b * c) <= 5.2e-282:
		tmp = t_1 + (x * (-4.0 * i))
	elif (b * c) <= 1.85e+40:
		tmp = t_2
	else:
		tmp = (b * c) - (27.0 * (j * k))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * -27.0) * k)
	t_2 = Float64(t_1 + Float64(18.0 * Float64(t * Float64(x * Float64(z * y)))))
	tmp = 0.0
	if (Float64(b * c) <= -8e+30)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= -3.3e-168)
		tmp = t_2;
	elseif (Float64(b * c) <= 5.2e-282)
		tmp = Float64(t_1 + Float64(x * Float64(-4.0 * i)));
	elseif (Float64(b * c) <= 1.85e+40)
		tmp = t_2;
	else
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * -27.0) * k;
	t_2 = t_1 + (18.0 * (t * (x * (z * y))));
	tmp = 0.0;
	if ((b * c) <= -8e+30)
		tmp = (b * c) - (4.0 * (x * i));
	elseif ((b * c) <= -3.3e-168)
		tmp = t_2;
	elseif ((b * c) <= 5.2e-282)
		tmp = t_1 + (x * (-4.0 * i));
	elseif ((b * c) <= 1.85e+40)
		tmp = t_2;
	else
		tmp = (b * c) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(18.0 * N[(t * N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -8e+30], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3.3e-168], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 5.2e-282], N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.85e+40], t$95$2, N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -8.0000000000000002e30

   1. Initial program 75.4%

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

      1. associate-*l* 75.5%

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

      2. associate--l+ 75.5%

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

      3. distribute-rgt-out-- 75.5%

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

      4. associate-*l* 74.2%

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

      5. associate-*l* 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in t around 0 71.3%

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

   5. Taylor expanded in j around 0 66.9%

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

   if -8.0000000000000002e30 < (*.f64 b c) < -3.3000000000000001e-168 or 5.20000000000000025e-282 < (*.f64 b c) < 1.85e40

   1. Initial program 83.5%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in z around inf 65.6%

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

   if -3.3000000000000001e-168 < (*.f64 b c) < 5.20000000000000025e-282

   1. Initial program 87.7%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in i around inf 58.9%

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

      1. associate-*r* 58.9%

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

      2. *-commutative 58.9%

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

   6. Simplified 58.9%

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

   if 1.85e40 < (*.f64 b c)

   1. Initial program 84.2%

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

      1. associate-*l* 84.1%

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

      2. associate--l+ 84.1%

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

      3. distribute-rgt-out-- 86.1%

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

      4. associate-*l* 86.1%

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

      5. associate-*l* 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in i around 0 77.7%

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

   5. Taylor expanded in t around 0 57.8%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -8 \cdot 10^{+30}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -3.3 \cdot 10^{-168}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + 18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 5.2 \cdot 10^{-282}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.85 \cdot 10^{+40}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + 18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 7: 55.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := \left(j \cdot -27\right) \cdot k\\ \mathbf{if}\;b \cdot c \leq -5.9 \cdot 10^{+32}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1.85 \cdot 10^{-167}:\\ \;\;\;\;t_1 + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2.75 \cdot 10^{-283}:\\ \;\;\;\;t_1 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.05 \cdot 10^{+40}:\\ \;\;\;\;t_1 + 18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j -27.0) k)))
   (if (<= (* b c) -5.9e+32)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= (* b c) -1.85e-167)
       (+ t_1 (* 18.0 (* t (* y (* x z)))))
       (if (<= (* b c) 2.75e-283)
         (+ t_1 (* x (* -4.0 i)))
         (if (<= (* b c) 1.05e+40)
           (+ t_1 (* 18.0 (* t (* x (* z y)))))
           (- (* b c) (* 27.0 (* j k)))))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double tmp;
	if ((b * c) <= -5.9e+32) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -1.85e-167) {
		tmp = t_1 + (18.0 * (t * (y * (x * z))));
	} else if ((b * c) <= 2.75e-283) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if ((b * c) <= 1.05e+40) {
		tmp = t_1 + (18.0 * (t * (x * (z * y))));
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (-27.0d0)) * k
    if ((b * c) <= (-5.9d+32)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if ((b * c) <= (-1.85d-167)) then
        tmp = t_1 + (18.0d0 * (t * (y * (x * z))))
    else if ((b * c) <= 2.75d-283) then
        tmp = t_1 + (x * ((-4.0d0) * i))
    else if ((b * c) <= 1.05d+40) then
        tmp = t_1 + (18.0d0 * (t * (x * (z * y))))
    else
        tmp = (b * c) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double tmp;
	if ((b * c) <= -5.9e+32) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -1.85e-167) {
		tmp = t_1 + (18.0 * (t * (y * (x * z))));
	} else if ((b * c) <= 2.75e-283) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if ((b * c) <= 1.05e+40) {
		tmp = t_1 + (18.0 * (t * (x * (z * y))));
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * -27.0) * k
	tmp = 0
	if (b * c) <= -5.9e+32:
		tmp = (b * c) - (4.0 * (x * i))
	elif (b * c) <= -1.85e-167:
		tmp = t_1 + (18.0 * (t * (y * (x * z))))
	elif (b * c) <= 2.75e-283:
		tmp = t_1 + (x * (-4.0 * i))
	elif (b * c) <= 1.05e+40:
		tmp = t_1 + (18.0 * (t * (x * (z * y))))
	else:
		tmp = (b * c) - (27.0 * (j * k))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * -27.0) * k)
	tmp = 0.0
	if (Float64(b * c) <= -5.9e+32)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= -1.85e-167)
		tmp = Float64(t_1 + Float64(18.0 * Float64(t * Float64(y * Float64(x * z)))));
	elseif (Float64(b * c) <= 2.75e-283)
		tmp = Float64(t_1 + Float64(x * Float64(-4.0 * i)));
	elseif (Float64(b * c) <= 1.05e+40)
		tmp = Float64(t_1 + Float64(18.0 * Float64(t * Float64(x * Float64(z * y)))));
	else
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * -27.0) * k;
	tmp = 0.0;
	if ((b * c) <= -5.9e+32)
		tmp = (b * c) - (4.0 * (x * i));
	elseif ((b * c) <= -1.85e-167)
		tmp = t_1 + (18.0 * (t * (y * (x * z))));
	elseif ((b * c) <= 2.75e-283)
		tmp = t_1 + (x * (-4.0 * i));
	elseif ((b * c) <= 1.05e+40)
		tmp = t_1 + (18.0 * (t * (x * (z * y))));
	else
		tmp = (b * c) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5.9e+32], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.85e-167], N[(t$95$1 + N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.75e-283], N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.05e+40], N[(t$95$1 + N[(18.0 * N[(t * N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -5.89999999999999965e32

   1. Initial program 75.4%

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

      1. associate-*l* 75.5%

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

      2. associate--l+ 75.5%

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

      3. distribute-rgt-out-- 75.5%

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

      4. associate-*l* 74.2%

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

      5. associate-*l* 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in t around 0 71.3%

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

   5. Taylor expanded in j around 0 66.9%

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

   if -5.89999999999999965e32 < (*.f64 b c) < -1.8500000000000001e-167

   1. Initial program 83.0%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in z around inf 62.7%

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

      1. expm1-log1p-u 47.6%

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

      2. expm1-udef 46.8%

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

      3. *-commutative 46.8%

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

   6. Applied egg-rr 46.8%

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

      1. expm1-def 47.6%

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

      2. expm1-log1p 62.7%

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

      3. associate-*r* 62.6%

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

   8. Simplified 62.6%

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

   if -1.8500000000000001e-167 < (*.f64 b c) < 2.74999999999999976e-283

   1. Initial program 87.7%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in i around inf 58.9%

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

      1. associate-*r* 58.9%

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

      2. *-commutative 58.9%

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

   6. Simplified 58.9%

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

   if 2.74999999999999976e-283 < (*.f64 b c) < 1.05000000000000005e40

   1. Initial program 84.0%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in z around inf 68.1%

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

   if 1.05000000000000005e40 < (*.f64 b c)

   1. Initial program 84.2%

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

      1. associate-*l* 84.1%

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

      2. associate--l+ 84.1%

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

      3. distribute-rgt-out-- 86.1%

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

      4. associate-*l* 86.1%

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

      5. associate-*l* 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in i around 0 77.7%

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

   5. Taylor expanded in t around 0 57.8%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.9 \cdot 10^{+32}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1.85 \cdot 10^{-167}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 2.75 \cdot 10^{-283}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.05 \cdot 10^{+40}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + 18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 8: 55.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := \left(j \cdot -27\right) \cdot k\\ t_2 := t_1 + 18 \cdot \left(x \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{if}\;b \cdot c \leq -4.2 \cdot 10^{+32}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -2.7 \cdot 10^{-166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot c \leq 4.3 \cdot 10^{-308}:\\ \;\;\;\;t_1 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2.85 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j -27.0) k)) (t_2 (+ t_1 (* 18.0 (* x (* t (* z y)))))))
   (if (<= (* b c) -4.2e+32)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= (* b c) -2.7e-166)
       t_2
       (if (<= (* b c) 4.3e-308)
         (+ t_1 (* x (* -4.0 i)))
         (if (<= (* b c) 2.85e+107) t_2 (+ (* b c) t_1)))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double t_2 = t_1 + (18.0 * (x * (t * (z * y))));
	double tmp;
	if ((b * c) <= -4.2e+32) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -2.7e-166) {
		tmp = t_2;
	} else if ((b * c) <= 4.3e-308) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if ((b * c) <= 2.85e+107) {
		tmp = t_2;
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * (-27.0d0)) * k
    t_2 = t_1 + (18.0d0 * (x * (t * (z * y))))
    if ((b * c) <= (-4.2d+32)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if ((b * c) <= (-2.7d-166)) then
        tmp = t_2
    else if ((b * c) <= 4.3d-308) then
        tmp = t_1 + (x * ((-4.0d0) * i))
    else if ((b * c) <= 2.85d+107) then
        tmp = t_2
    else
        tmp = (b * c) + t_1
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double t_2 = t_1 + (18.0 * (x * (t * (z * y))));
	double tmp;
	if ((b * c) <= -4.2e+32) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -2.7e-166) {
		tmp = t_2;
	} else if ((b * c) <= 4.3e-308) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if ((b * c) <= 2.85e+107) {
		tmp = t_2;
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * -27.0) * k
	t_2 = t_1 + (18.0 * (x * (t * (z * y))))
	tmp = 0
	if (b * c) <= -4.2e+32:
		tmp = (b * c) - (4.0 * (x * i))
	elif (b * c) <= -2.7e-166:
		tmp = t_2
	elif (b * c) <= 4.3e-308:
		tmp = t_1 + (x * (-4.0 * i))
	elif (b * c) <= 2.85e+107:
		tmp = t_2
	else:
		tmp = (b * c) + t_1
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * -27.0) * k)
	t_2 = Float64(t_1 + Float64(18.0 * Float64(x * Float64(t * Float64(z * y)))))
	tmp = 0.0
	if (Float64(b * c) <= -4.2e+32)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= -2.7e-166)
		tmp = t_2;
	elseif (Float64(b * c) <= 4.3e-308)
		tmp = Float64(t_1 + Float64(x * Float64(-4.0 * i)));
	elseif (Float64(b * c) <= 2.85e+107)
		tmp = t_2;
	else
		tmp = Float64(Float64(b * c) + t_1);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * -27.0) * k;
	t_2 = t_1 + (18.0 * (x * (t * (z * y))));
	tmp = 0.0;
	if ((b * c) <= -4.2e+32)
		tmp = (b * c) - (4.0 * (x * i));
	elseif ((b * c) <= -2.7e-166)
		tmp = t_2;
	elseif ((b * c) <= 4.3e-308)
		tmp = t_1 + (x * (-4.0 * i));
	elseif ((b * c) <= 2.85e+107)
		tmp = t_2;
	else
		tmp = (b * c) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(18.0 * N[(x * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -4.2e+32], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2.7e-166], t$95$2, If[LessEqual[N[(b * c), $MachinePrecision], 4.3e-308], N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.85e+107], t$95$2, N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -4.2000000000000001e32

   1. Initial program 75.4%

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

      1. associate-*l* 75.5%

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

      2. associate--l+ 75.5%

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

      3. distribute-rgt-out-- 75.5%

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

      4. associate-*l* 74.2%

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

      5. associate-*l* 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in t around 0 71.3%

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

   5. Taylor expanded in j around 0 66.9%

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

   if -4.2000000000000001e32 < (*.f64 b c) < -2.70000000000000006e-166 or 4.3000000000000002e-308 < (*.f64 b c) < 2.84999999999999986e107

   1. Initial program 83.0%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in z around inf 60.4%

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

      1. expm1-log1p-u 44.2%

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

      2. expm1-udef 43.9%

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

      3. *-commutative 43.9%

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

   6. Applied egg-rr 43.9%

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

      1. expm1-def 44.2%

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

      2. expm1-log1p 60.4%

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

      3. *-commutative 60.4%

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

      4. associate-*l* 63.9%

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

      5. *-commutative 63.9%

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

      6. *-commutative 63.9%

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

   8. Simplified 63.9%

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

   if -2.70000000000000006e-166 < (*.f64 b c) < 4.3000000000000002e-308

   1. Initial program 88.8%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in i around inf 59.4%

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

      1. associate-*r* 59.4%

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

      2. *-commutative 59.4%

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

   6. Simplified 59.4%

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

   if 2.84999999999999986e107 < (*.f64 b c)

   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 91.1%

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

   4. Taylor expanded in b around inf 67.7%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4.2 \cdot 10^{+32}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -2.7 \cdot 10^{-166}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + 18 \cdot \left(x \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 4.3 \cdot 10^{-308}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2.85 \cdot 10^{+107}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + 18 \cdot \left(x \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(j \cdot -27\right) \cdot k\\ \end{array} \]

Alternative 9: 55.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := \left(j \cdot -27\right) \cdot k\\ \mathbf{if}\;b \cdot c \leq -5.2 \cdot 10^{+32}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1.7 \cdot 10^{-166}:\\ \;\;\;\;t_1 + 18 \cdot \left(x \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.26 \cdot 10^{-307}:\\ \;\;\;\;t_1 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.75 \cdot 10^{+107}:\\ \;\;\;\;t_1 + 18 \cdot \left(x \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j -27.0) k)))
   (if (<= (* b c) -5.2e+32)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= (* b c) -1.7e-166)
       (+ t_1 (* 18.0 (* x (* y (* t z)))))
       (if (<= (* b c) 1.26e-307)
         (+ t_1 (* x (* -4.0 i)))
         (if (<= (* b c) 1.75e+107)
           (+ t_1 (* 18.0 (* x (* t (* z y)))))
           (+ (* b c) t_1)))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double tmp;
	if ((b * c) <= -5.2e+32) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -1.7e-166) {
		tmp = t_1 + (18.0 * (x * (y * (t * z))));
	} else if ((b * c) <= 1.26e-307) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if ((b * c) <= 1.75e+107) {
		tmp = t_1 + (18.0 * (x * (t * (z * y))));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (-27.0d0)) * k
    if ((b * c) <= (-5.2d+32)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if ((b * c) <= (-1.7d-166)) then
        tmp = t_1 + (18.0d0 * (x * (y * (t * z))))
    else if ((b * c) <= 1.26d-307) then
        tmp = t_1 + (x * ((-4.0d0) * i))
    else if ((b * c) <= 1.75d+107) then
        tmp = t_1 + (18.0d0 * (x * (t * (z * y))))
    else
        tmp = (b * c) + t_1
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double tmp;
	if ((b * c) <= -5.2e+32) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -1.7e-166) {
		tmp = t_1 + (18.0 * (x * (y * (t * z))));
	} else if ((b * c) <= 1.26e-307) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if ((b * c) <= 1.75e+107) {
		tmp = t_1 + (18.0 * (x * (t * (z * y))));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * -27.0) * k
	tmp = 0
	if (b * c) <= -5.2e+32:
		tmp = (b * c) - (4.0 * (x * i))
	elif (b * c) <= -1.7e-166:
		tmp = t_1 + (18.0 * (x * (y * (t * z))))
	elif (b * c) <= 1.26e-307:
		tmp = t_1 + (x * (-4.0 * i))
	elif (b * c) <= 1.75e+107:
		tmp = t_1 + (18.0 * (x * (t * (z * y))))
	else:
		tmp = (b * c) + t_1
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * -27.0) * k)
	tmp = 0.0
	if (Float64(b * c) <= -5.2e+32)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= -1.7e-166)
		tmp = Float64(t_1 + Float64(18.0 * Float64(x * Float64(y * Float64(t * z)))));
	elseif (Float64(b * c) <= 1.26e-307)
		tmp = Float64(t_1 + Float64(x * Float64(-4.0 * i)));
	elseif (Float64(b * c) <= 1.75e+107)
		tmp = Float64(t_1 + Float64(18.0 * Float64(x * Float64(t * Float64(z * y)))));
	else
		tmp = Float64(Float64(b * c) + t_1);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * -27.0) * k;
	tmp = 0.0;
	if ((b * c) <= -5.2e+32)
		tmp = (b * c) - (4.0 * (x * i));
	elseif ((b * c) <= -1.7e-166)
		tmp = t_1 + (18.0 * (x * (y * (t * z))));
	elseif ((b * c) <= 1.26e-307)
		tmp = t_1 + (x * (-4.0 * i));
	elseif ((b * c) <= 1.75e+107)
		tmp = t_1 + (18.0 * (x * (t * (z * y))));
	else
		tmp = (b * c) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5.2e+32], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.7e-166], N[(t$95$1 + N[(18.0 * N[(x * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.26e-307], N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.75e+107], N[(t$95$1 + N[(18.0 * N[(x * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -5.2000000000000004e32

   1. Initial program 75.4%

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

      1. associate-*l* 75.5%

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

      2. associate--l+ 75.5%

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

      3. distribute-rgt-out-- 75.5%

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

      4. associate-*l* 74.2%

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

      5. associate-*l* 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in t around 0 71.3%

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

   5. Taylor expanded in j around 0 66.9%

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

   if -5.2000000000000004e32 < (*.f64 b c) < -1.6999999999999999e-166

   1. Initial program 83.0%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in z around inf 62.7%

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

      1. expm1-log1p-u 47.6%

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

      2. expm1-udef 46.8%

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

      3. *-commutative 46.8%

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

   6. Applied egg-rr 46.8%

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

      1. expm1-def 47.6%

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

      2. expm1-log1p 62.7%

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

      3. *-commutative 62.7%

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

      4. associate-*l* 62.8%

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

      5. *-commutative 62.8%

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

      6. *-commutative 62.8%

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

   8. Simplified 62.8%

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

      1. expm1-log1p-u 48.1%

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

      2. expm1-udef 47.6%

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

      3. associate-*r* 49.8%

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

   10. Applied egg-rr 49.8%

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

       1. expm1-def 50.2%

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

       2. expm1-log1p 65.0%

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

       3. *-commutative 65.0%

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

       4. associate-*r* 65.1%

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

   12. Simplified 65.1%

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

   if -1.6999999999999999e-166 < (*.f64 b c) < 1.2599999999999999e-307

   1. Initial program 88.8%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in i around inf 59.4%

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

      1. associate-*r* 59.4%

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

      2. *-commutative 59.4%

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

   6. Simplified 59.4%

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

   if 1.2599999999999999e-307 < (*.f64 b c) < 1.7499999999999999e107

   1. Initial program 83.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in z around inf 59.1%

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

      1. expm1-log1p-u 42.2%

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

      2. expm1-udef 42.2%

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

      3. *-commutative 42.2%

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

   6. Applied egg-rr 42.2%

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

      1. expm1-def 42.2%

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

      2. expm1-log1p 59.1%

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

      3. *-commutative 59.1%

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

      4. associate-*l* 64.6%

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

      5. *-commutative 64.6%

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

      6. *-commutative 64.6%

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

   8. Simplified 64.6%

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

   if 1.7499999999999999e107 < (*.f64 b c)

   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 91.1%

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

   4. Taylor expanded in b around inf 67.7%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5.2 \cdot 10^{+32}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1.7 \cdot 10^{-166}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + 18 \cdot \left(x \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 1.26 \cdot 10^{-307}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.75 \cdot 10^{+107}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + 18 \cdot \left(x \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(j \cdot -27\right) \cdot k\\ \end{array} \]

Alternative 10: 55.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := \left(j \cdot -27\right) \cdot k\\ \mathbf{if}\;b \cdot c \leq -6.2 \cdot 10^{+32}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -3 \cdot 10^{-166}:\\ \;\;\;\;t_1 + 18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{-308}:\\ \;\;\;\;t_1 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{+106}:\\ \;\;\;\;t_1 + 18 \cdot \left(x \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j -27.0) k)))
   (if (<= (* b c) -6.2e+32)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= (* b c) -3e-166)
       (+ t_1 (* 18.0 (* (* x z) (* t y))))
       (if (<= (* b c) 3.2e-308)
         (+ t_1 (* x (* -4.0 i)))
         (if (<= (* b c) 4.2e+106)
           (+ t_1 (* 18.0 (* x (* t (* z y)))))
           (+ (* b c) t_1)))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double tmp;
	if ((b * c) <= -6.2e+32) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -3e-166) {
		tmp = t_1 + (18.0 * ((x * z) * (t * y)));
	} else if ((b * c) <= 3.2e-308) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if ((b * c) <= 4.2e+106) {
		tmp = t_1 + (18.0 * (x * (t * (z * y))));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (-27.0d0)) * k
    if ((b * c) <= (-6.2d+32)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if ((b * c) <= (-3d-166)) then
        tmp = t_1 + (18.0d0 * ((x * z) * (t * y)))
    else if ((b * c) <= 3.2d-308) then
        tmp = t_1 + (x * ((-4.0d0) * i))
    else if ((b * c) <= 4.2d+106) then
        tmp = t_1 + (18.0d0 * (x * (t * (z * y))))
    else
        tmp = (b * c) + t_1
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double tmp;
	if ((b * c) <= -6.2e+32) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -3e-166) {
		tmp = t_1 + (18.0 * ((x * z) * (t * y)));
	} else if ((b * c) <= 3.2e-308) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if ((b * c) <= 4.2e+106) {
		tmp = t_1 + (18.0 * (x * (t * (z * y))));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * -27.0) * k
	tmp = 0
	if (b * c) <= -6.2e+32:
		tmp = (b * c) - (4.0 * (x * i))
	elif (b * c) <= -3e-166:
		tmp = t_1 + (18.0 * ((x * z) * (t * y)))
	elif (b * c) <= 3.2e-308:
		tmp = t_1 + (x * (-4.0 * i))
	elif (b * c) <= 4.2e+106:
		tmp = t_1 + (18.0 * (x * (t * (z * y))))
	else:
		tmp = (b * c) + t_1
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * -27.0) * k)
	tmp = 0.0
	if (Float64(b * c) <= -6.2e+32)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= -3e-166)
		tmp = Float64(t_1 + Float64(18.0 * Float64(Float64(x * z) * Float64(t * y))));
	elseif (Float64(b * c) <= 3.2e-308)
		tmp = Float64(t_1 + Float64(x * Float64(-4.0 * i)));
	elseif (Float64(b * c) <= 4.2e+106)
		tmp = Float64(t_1 + Float64(18.0 * Float64(x * Float64(t * Float64(z * y)))));
	else
		tmp = Float64(Float64(b * c) + t_1);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * -27.0) * k;
	tmp = 0.0;
	if ((b * c) <= -6.2e+32)
		tmp = (b * c) - (4.0 * (x * i));
	elseif ((b * c) <= -3e-166)
		tmp = t_1 + (18.0 * ((x * z) * (t * y)));
	elseif ((b * c) <= 3.2e-308)
		tmp = t_1 + (x * (-4.0 * i));
	elseif ((b * c) <= 4.2e+106)
		tmp = t_1 + (18.0 * (x * (t * (z * y))));
	else
		tmp = (b * c) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -6.2e+32], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -3e-166], N[(t$95$1 + N[(18.0 * N[(N[(x * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.2e-308], N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.2e+106], N[(t$95$1 + N[(18.0 * N[(x * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -6.19999999999999986e32

   1. Initial program 75.4%

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

      1. associate-*l* 75.5%

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

      2. associate--l+ 75.5%

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

      3. distribute-rgt-out-- 75.5%

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

      4. associate-*l* 74.2%

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

      5. associate-*l* 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in t around 0 71.3%

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

   5. Taylor expanded in j around 0 66.9%

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

   if -6.19999999999999986e32 < (*.f64 b c) < -3.0000000000000003e-166

   1. Initial program 83.0%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in z around inf 62.7%

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

      1. expm1-log1p-u 47.6%

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

      2. expm1-udef 46.8%

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

      3. *-commutative 46.8%

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

   6. Applied egg-rr 46.8%

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

      1. expm1-def 47.6%

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

      2. expm1-log1p 62.7%

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

      3. associate-*r* 62.6%

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

   8. Simplified 62.6%

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

   9. Taylor expanded in t around 0 62.7%

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

       1. *-commutative 62.7%

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

       2. associate-*r* 62.6%

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

       3. associate-*l* 67.3%

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

       4. *-commutative 67.3%

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

       5. associate-*l* 64.9%

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

   11. Simplified 64.9%

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

   if -3.0000000000000003e-166 < (*.f64 b c) < 3.2000000000000001e-308

   1. Initial program 88.8%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in i around inf 59.4%

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

      1. associate-*r* 59.4%

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

      2. *-commutative 59.4%

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

   6. Simplified 59.4%

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

   if 3.2000000000000001e-308 < (*.f64 b c) < 4.2000000000000001e106

   1. Initial program 83.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in z around inf 59.1%

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

      1. expm1-log1p-u 42.2%

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

      2. expm1-udef 42.2%

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

      3. *-commutative 42.2%

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

   6. Applied egg-rr 42.2%

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

      1. expm1-def 42.2%

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

      2. expm1-log1p 59.1%

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

      3. *-commutative 59.1%

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

      4. associate-*l* 64.6%

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

      5. *-commutative 64.6%

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

      6. *-commutative 64.6%

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

   8. Simplified 64.6%

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

   if 4.2000000000000001e106 < (*.f64 b c)

   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 91.1%

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

   4. Taylor expanded in b around inf 67.7%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6.2 \cdot 10^{+32}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -3 \cdot 10^{-166}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + 18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 3.2 \cdot 10^{-308}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 4.2 \cdot 10^{+106}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + 18 \cdot \left(x \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(j \cdot -27\right) \cdot k\\ \end{array} \]

Alternative 11: 55.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := \left(j \cdot -27\right) \cdot k\\ \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+32}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1.6 \cdot 10^{-167}:\\ \;\;\;\;t_1 + 18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 8.5 \cdot 10^{-306}:\\ \;\;\;\;t_1 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.06 \cdot 10^{+107}:\\ \;\;\;\;t_1 + x \cdot \left(t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j -27.0) k)))
   (if (<= (* b c) -1e+32)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= (* b c) -1.6e-167)
       (+ t_1 (* 18.0 (* (* x z) (* t y))))
       (if (<= (* b c) 8.5e-306)
         (+ t_1 (* x (* -4.0 i)))
         (if (<= (* b c) 1.06e+107)
           (+ t_1 (* x (* t (* z (* 18.0 y)))))
           (+ (* b c) t_1)))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double tmp;
	if ((b * c) <= -1e+32) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -1.6e-167) {
		tmp = t_1 + (18.0 * ((x * z) * (t * y)));
	} else if ((b * c) <= 8.5e-306) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if ((b * c) <= 1.06e+107) {
		tmp = t_1 + (x * (t * (z * (18.0 * y))));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (-27.0d0)) * k
    if ((b * c) <= (-1d+32)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if ((b * c) <= (-1.6d-167)) then
        tmp = t_1 + (18.0d0 * ((x * z) * (t * y)))
    else if ((b * c) <= 8.5d-306) then
        tmp = t_1 + (x * ((-4.0d0) * i))
    else if ((b * c) <= 1.06d+107) then
        tmp = t_1 + (x * (t * (z * (18.0d0 * y))))
    else
        tmp = (b * c) + t_1
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double tmp;
	if ((b * c) <= -1e+32) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= -1.6e-167) {
		tmp = t_1 + (18.0 * ((x * z) * (t * y)));
	} else if ((b * c) <= 8.5e-306) {
		tmp = t_1 + (x * (-4.0 * i));
	} else if ((b * c) <= 1.06e+107) {
		tmp = t_1 + (x * (t * (z * (18.0 * y))));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * -27.0) * k
	tmp = 0
	if (b * c) <= -1e+32:
		tmp = (b * c) - (4.0 * (x * i))
	elif (b * c) <= -1.6e-167:
		tmp = t_1 + (18.0 * ((x * z) * (t * y)))
	elif (b * c) <= 8.5e-306:
		tmp = t_1 + (x * (-4.0 * i))
	elif (b * c) <= 1.06e+107:
		tmp = t_1 + (x * (t * (z * (18.0 * y))))
	else:
		tmp = (b * c) + t_1
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * -27.0) * k)
	tmp = 0.0
	if (Float64(b * c) <= -1e+32)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= -1.6e-167)
		tmp = Float64(t_1 + Float64(18.0 * Float64(Float64(x * z) * Float64(t * y))));
	elseif (Float64(b * c) <= 8.5e-306)
		tmp = Float64(t_1 + Float64(x * Float64(-4.0 * i)));
	elseif (Float64(b * c) <= 1.06e+107)
		tmp = Float64(t_1 + Float64(x * Float64(t * Float64(z * Float64(18.0 * y)))));
	else
		tmp = Float64(Float64(b * c) + t_1);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * -27.0) * k;
	tmp = 0.0;
	if ((b * c) <= -1e+32)
		tmp = (b * c) - (4.0 * (x * i));
	elseif ((b * c) <= -1.6e-167)
		tmp = t_1 + (18.0 * ((x * z) * (t * y)));
	elseif ((b * c) <= 8.5e-306)
		tmp = t_1 + (x * (-4.0 * i));
	elseif ((b * c) <= 1.06e+107)
		tmp = t_1 + (x * (t * (z * (18.0 * y))));
	else
		tmp = (b * c) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -1e+32], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -1.6e-167], N[(t$95$1 + N[(18.0 * N[(N[(x * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 8.5e-306], N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1.06e+107], N[(t$95$1 + N[(x * N[(t * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -1.00000000000000005e32

   1. Initial program 75.4%

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

      1. associate-*l* 75.5%

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

      2. associate--l+ 75.5%

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

      3. distribute-rgt-out-- 75.5%

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

      4. associate-*l* 74.2%

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

      5. associate-*l* 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in t around 0 71.3%

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

   5. Taylor expanded in j around 0 66.9%

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

   if -1.00000000000000005e32 < (*.f64 b c) < -1.6000000000000001e-167

   1. Initial program 83.0%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in z around inf 62.7%

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

      1. expm1-log1p-u 47.6%

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

      2. expm1-udef 46.8%

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

      3. *-commutative 46.8%

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

   6. Applied egg-rr 46.8%

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

      1. expm1-def 47.6%

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

      2. expm1-log1p 62.7%

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

      3. associate-*r* 62.6%

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

   8. Simplified 62.6%

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

   9. Taylor expanded in t around 0 62.7%

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

       1. *-commutative 62.7%

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

       2. associate-*r* 62.6%

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

       3. associate-*l* 67.3%

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

       4. *-commutative 67.3%

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

       5. associate-*l* 64.9%

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

   11. Simplified 64.9%

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

   if -1.6000000000000001e-167 < (*.f64 b c) < 8.5000000000000002e-306

   1. Initial program 88.8%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in i around inf 59.4%

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

      1. associate-*r* 59.4%

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

      2. *-commutative 59.4%

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

   6. Simplified 59.4%

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

   if 8.5000000000000002e-306 < (*.f64 b c) < 1.06e107

   1. Initial program 83.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in z around inf 59.1%

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

      1. *-commutative 59.1%

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

      2. associate-*r* 64.6%

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

      3. associate-*l* 64.6%

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

      4. *-commutative 64.6%

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

      5. *-commutative 64.6%

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

      6. associate-*l* 64.6%

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

      7. associate-*r* 64.6%

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

      8. *-commutative 64.6%

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

      9. associate-*l* 63.2%

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

   6. Simplified 63.2%

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

   if 1.06e107 < (*.f64 b c)

   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 91.1%

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

   4. Taylor expanded in b around inf 67.7%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+32}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq -1.6 \cdot 10^{-167}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + 18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;b \cdot c \leq 8.5 \cdot 10^{-306}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 1.06 \cdot 10^{+107}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + x \cdot \left(t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(j \cdot -27\right) \cdot k\\ \end{array} \]

Alternative 12: 65.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := \left(j \cdot -27\right) \cdot k\\ t_2 := t_1 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+252}:\\ \;\;\;\;t_1 + \left(t \cdot 18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+214}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+191}:\\ \;\;\;\;t_1 + 18 \cdot \left(x \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+56}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+232}:\\ \;\;\;\;t_1 + x \cdot \left(t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+287}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 + 18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j -27.0) k)) (t_2 (+ t_1 (* x (* -4.0 i)))))
   (if (<= x -1.45e+252)
     (+ t_1 (* (* t 18.0) (* z (* x y))))
     (if (<= x -1.4e+214)
       (- (* b c) (* 4.0 (* x i)))
       (if (<= x -2.9e+191)
         (+ t_1 (* 18.0 (* x (* t (* z y)))))
         (if (<= x -8.5e+80)
           t_2
           (if (<= x 1.1e+56)
             (- (- (* b c) (* 4.0 (* t a))) (* k (* j 27.0)))
             (if (<= x 1.7e+232)
               (+ t_1 (* x (* t (* z (* 18.0 y)))))
               (if (<= x 4.9e+287)
                 t_2
                 (+ t_1 (* 18.0 (* t (* x (* z y))))))))))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double t_2 = t_1 + (x * (-4.0 * i));
	double tmp;
	if (x <= -1.45e+252) {
		tmp = t_1 + ((t * 18.0) * (z * (x * y)));
	} else if (x <= -1.4e+214) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (x <= -2.9e+191) {
		tmp = t_1 + (18.0 * (x * (t * (z * y))));
	} else if (x <= -8.5e+80) {
		tmp = t_2;
	} else if (x <= 1.1e+56) {
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	} else if (x <= 1.7e+232) {
		tmp = t_1 + (x * (t * (z * (18.0 * y))));
	} else if (x <= 4.9e+287) {
		tmp = t_2;
	} else {
		tmp = t_1 + (18.0 * (t * (x * (z * y))));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * (-27.0d0)) * k
    t_2 = t_1 + (x * ((-4.0d0) * i))
    if (x <= (-1.45d+252)) then
        tmp = t_1 + ((t * 18.0d0) * (z * (x * y)))
    else if (x <= (-1.4d+214)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if (x <= (-2.9d+191)) then
        tmp = t_1 + (18.0d0 * (x * (t * (z * y))))
    else if (x <= (-8.5d+80)) then
        tmp = t_2
    else if (x <= 1.1d+56) then
        tmp = ((b * c) - (4.0d0 * (t * a))) - (k * (j * 27.0d0))
    else if (x <= 1.7d+232) then
        tmp = t_1 + (x * (t * (z * (18.0d0 * y))))
    else if (x <= 4.9d+287) then
        tmp = t_2
    else
        tmp = t_1 + (18.0d0 * (t * (x * (z * y))))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double t_2 = t_1 + (x * (-4.0 * i));
	double tmp;
	if (x <= -1.45e+252) {
		tmp = t_1 + ((t * 18.0) * (z * (x * y)));
	} else if (x <= -1.4e+214) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if (x <= -2.9e+191) {
		tmp = t_1 + (18.0 * (x * (t * (z * y))));
	} else if (x <= -8.5e+80) {
		tmp = t_2;
	} else if (x <= 1.1e+56) {
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	} else if (x <= 1.7e+232) {
		tmp = t_1 + (x * (t * (z * (18.0 * y))));
	} else if (x <= 4.9e+287) {
		tmp = t_2;
	} else {
		tmp = t_1 + (18.0 * (t * (x * (z * y))));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * -27.0) * k
	t_2 = t_1 + (x * (-4.0 * i))
	tmp = 0
	if x <= -1.45e+252:
		tmp = t_1 + ((t * 18.0) * (z * (x * y)))
	elif x <= -1.4e+214:
		tmp = (b * c) - (4.0 * (x * i))
	elif x <= -2.9e+191:
		tmp = t_1 + (18.0 * (x * (t * (z * y))))
	elif x <= -8.5e+80:
		tmp = t_2
	elif x <= 1.1e+56:
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0))
	elif x <= 1.7e+232:
		tmp = t_1 + (x * (t * (z * (18.0 * y))))
	elif x <= 4.9e+287:
		tmp = t_2
	else:
		tmp = t_1 + (18.0 * (t * (x * (z * y))))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * -27.0) * k)
	t_2 = Float64(t_1 + Float64(x * Float64(-4.0 * i)))
	tmp = 0.0
	if (x <= -1.45e+252)
		tmp = Float64(t_1 + Float64(Float64(t * 18.0) * Float64(z * Float64(x * y))));
	elseif (x <= -1.4e+214)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (x <= -2.9e+191)
		tmp = Float64(t_1 + Float64(18.0 * Float64(x * Float64(t * Float64(z * y)))));
	elseif (x <= -8.5e+80)
		tmp = t_2;
	elseif (x <= 1.1e+56)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(t * a))) - Float64(k * Float64(j * 27.0)));
	elseif (x <= 1.7e+232)
		tmp = Float64(t_1 + Float64(x * Float64(t * Float64(z * Float64(18.0 * y)))));
	elseif (x <= 4.9e+287)
		tmp = t_2;
	else
		tmp = Float64(t_1 + Float64(18.0 * Float64(t * Float64(x * Float64(z * y)))));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * -27.0) * k;
	t_2 = t_1 + (x * (-4.0 * i));
	tmp = 0.0;
	if (x <= -1.45e+252)
		tmp = t_1 + ((t * 18.0) * (z * (x * y)));
	elseif (x <= -1.4e+214)
		tmp = (b * c) - (4.0 * (x * i));
	elseif (x <= -2.9e+191)
		tmp = t_1 + (18.0 * (x * (t * (z * y))));
	elseif (x <= -8.5e+80)
		tmp = t_2;
	elseif (x <= 1.1e+56)
		tmp = ((b * c) - (4.0 * (t * a))) - (k * (j * 27.0));
	elseif (x <= 1.7e+232)
		tmp = t_1 + (x * (t * (z * (18.0 * y))));
	elseif (x <= 4.9e+287)
		tmp = t_2;
	else
		tmp = t_1 + (18.0 * (t * (x * (z * y))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.45e+252], N[(t$95$1 + N[(N[(t * 18.0), $MachinePrecision] * N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.4e+214], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.9e+191], N[(t$95$1 + N[(18.0 * N[(x * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.5e+80], t$95$2, If[LessEqual[x, 1.1e+56], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(j * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+232], N[(t$95$1 + N[(x * N[(t * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.9e+287], t$95$2, N[(t$95$1 + N[(18.0 * N[(t * N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -1.44999999999999998e252

   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 77.6%

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

   4. Taylor expanded in z around inf 73.3%

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

      1. associate-*r* 73.3%

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

      2. associate-*r* 73.3%

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

   6. Simplified 73.3%

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

   if -1.44999999999999998e252 < x < -1.3999999999999999e214

   1. Initial program 62.8%

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

      1. associate-*l* 62.8%

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

      2. associate--l+ 62.8%

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

      3. distribute-rgt-out-- 62.8%

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

      4. associate-*l* 69.1%

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

      5. associate-*l* 69.1%

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

   3. Simplified 69.1%

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

   4. Taylor expanded in t around 0 62.9%

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

   5. Taylor expanded in j around 0 63.0%

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

   if -1.3999999999999999e214 < x < -2.9000000000000001e191

   1. Initial program 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in z around inf 62.5%

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

      1. expm1-log1p-u 41.2%

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

      2. expm1-udef 41.2%

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

      3. *-commutative 41.2%

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

   6. Applied egg-rr 41.2%

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

      1. expm1-def 41.2%

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

      2. expm1-log1p 62.5%

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

      3. *-commutative 62.5%

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

      4. associate-*l* 80.9%

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

      5. *-commutative 80.9%

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

      6. *-commutative 80.9%

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

   8. Simplified 80.9%

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

   if -2.9000000000000001e191 < x < -8.50000000000000007e80 or 1.6999999999999999e232 < x < 4.89999999999999993e287

   1. Initial program 79.1%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in i around inf 80.5%

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

      1. associate-*r* 80.5%

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

      2. *-commutative 80.5%

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

   6. Simplified 80.5%

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

   if -8.50000000000000007e80 < x < 1.10000000000000008e56

   1. Initial program 90.6%

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

   2. Taylor expanded in x around 0 74.6%

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

   if 1.10000000000000008e56 < x < 1.6999999999999999e232

   1. Initial program 59.4%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in z around inf 53.4%

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

      1. *-commutative 53.4%

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

      2. associate-*r* 66.4%

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

      3. associate-*l* 66.5%

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

      4. *-commutative 66.5%

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

      5. *-commutative 66.5%

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

      6. associate-*l* 66.5%

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

      7. associate-*r* 66.5%

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

      8. *-commutative 66.5%

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

      9. associate-*l* 66.5%

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

   6. Simplified 66.5%

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

   if 4.89999999999999993e287 < x

   1. Initial program 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in z around inf 63.2%

      \[\leadsto \color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)} + k \cdot \left(j \cdot -27\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+252}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + \left(t \cdot 18\right) \cdot \left(z \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+214}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+191}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + 18 \cdot \left(x \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+80}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+56}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(t \cdot a\right)\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+232}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + x \cdot \left(t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+287}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + x \cdot \left(-4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + 18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 13: 81.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := j \cdot \left(k \cdot 27\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{-72} \lor \neg \left(t \leq 5.4 \cdot 10^{-96}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* j (* k 27.0))))
   (if (or (<= t -8.5e-72) (not (<= t 5.4e-96)))
     (- (+ (* b c) (* t (- (* 18.0 (* x (* z y))) (* a 4.0)))) t_1)
     (- (- (* b c) (* 4.0 (* x i))) t_1))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * 27.0);
	double tmp;
	if ((t <= -8.5e-72) || !(t <= 5.4e-96)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (z * y))) - (a * 4.0)))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (k * 27.0d0)
    if ((t <= (-8.5d-72)) .or. (.not. (t <= 5.4d-96))) then
        tmp = ((b * c) + (t * ((18.0d0 * (x * (z * y))) - (a * 4.0d0)))) - t_1
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - t_1
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = j * (k * 27.0);
	double tmp;
	if ((t <= -8.5e-72) || !(t <= 5.4e-96)) {
		tmp = ((b * c) + (t * ((18.0 * (x * (z * y))) - (a * 4.0)))) - t_1;
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = j * (k * 27.0)
	tmp = 0
	if (t <= -8.5e-72) or not (t <= 5.4e-96):
		tmp = ((b * c) + (t * ((18.0 * (x * (z * y))) - (a * 4.0)))) - t_1
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - t_1
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(j * Float64(k * 27.0))
	tmp = 0.0
	if ((t <= -8.5e-72) || !(t <= 5.4e-96))
		tmp = Float64(Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(z * y))) - Float64(a * 4.0)))) - t_1);
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - t_1);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = j * (k * 27.0);
	tmp = 0.0;
	if ((t <= -8.5e-72) || ~((t <= 5.4e-96)))
		tmp = ((b * c) + (t * ((18.0 * (x * (z * y))) - (a * 4.0)))) - t_1;
	else
		tmp = ((b * c) - (4.0 * (x * i))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -8.5e-72], N[Not[LessEqual[t, 5.4e-96]], $MachinePrecision]], N[(N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.50000000000000008e-72 or 5.3999999999999999e-96 < t

   1. Initial program 84.4%

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

      1. associate-*l* 84.3%

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

      2. associate--l+ 84.3%

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

      3. distribute-rgt-out-- 86.8%

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

      4. associate-*l* 85.1%

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

      5. associate-*l* 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in i around 0 78.3%

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

   if -8.50000000000000008e-72 < t < 5.3999999999999999e-96

   1. Initial program 78.7%

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

      1. associate-*l* 78.7%

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

      2. associate--l+ 78.7%

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

      3. distribute-rgt-out-- 78.7%

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

      4. associate-*l* 80.8%

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

      5. associate-*l* 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in t around 0 82.2%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-72} \lor \neg \left(t \leq 5.4 \cdot 10^{-96}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - j \cdot \left(k \cdot 27\right)\\ \end{array} \]

Alternative 14: 64.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := \left(j \cdot -27\right) \cdot k\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{-112}:\\ \;\;\;\;t_1 + 18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+189}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+240}:\\ \;\;\;\;t_1 + x \cdot \left(t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j -27.0) k)))
   (if (<= z -1.8e-112)
     (+ t_1 (* 18.0 (* (* x z) (* t y))))
     (if (<= z 4.3e+189)
       (- (- (* b c) (* 4.0 (* x i))) (* j (* k 27.0)))
       (if (<= z 2.25e+240)
         (+ t_1 (* x (* t (* z (* 18.0 y)))))
         (+ t_1 (* 18.0 (* t (* y (* x z))))))))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double tmp;
	if (z <= -1.8e-112) {
		tmp = t_1 + (18.0 * ((x * z) * (t * y)));
	} else if (z <= 4.3e+189) {
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (k * 27.0));
	} else if (z <= 2.25e+240) {
		tmp = t_1 + (x * (t * (z * (18.0 * y))));
	} else {
		tmp = t_1 + (18.0 * (t * (y * (x * z))));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (-27.0d0)) * k
    if (z <= (-1.8d-112)) then
        tmp = t_1 + (18.0d0 * ((x * z) * (t * y)))
    else if (z <= 4.3d+189) then
        tmp = ((b * c) - (4.0d0 * (x * i))) - (j * (k * 27.0d0))
    else if (z <= 2.25d+240) then
        tmp = t_1 + (x * (t * (z * (18.0d0 * y))))
    else
        tmp = t_1 + (18.0d0 * (t * (y * (x * z))))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double tmp;
	if (z <= -1.8e-112) {
		tmp = t_1 + (18.0 * ((x * z) * (t * y)));
	} else if (z <= 4.3e+189) {
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (k * 27.0));
	} else if (z <= 2.25e+240) {
		tmp = t_1 + (x * (t * (z * (18.0 * y))));
	} else {
		tmp = t_1 + (18.0 * (t * (y * (x * z))));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * -27.0) * k
	tmp = 0
	if z <= -1.8e-112:
		tmp = t_1 + (18.0 * ((x * z) * (t * y)))
	elif z <= 4.3e+189:
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (k * 27.0))
	elif z <= 2.25e+240:
		tmp = t_1 + (x * (t * (z * (18.0 * y))))
	else:
		tmp = t_1 + (18.0 * (t * (y * (x * z))))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * -27.0) * k)
	tmp = 0.0
	if (z <= -1.8e-112)
		tmp = Float64(t_1 + Float64(18.0 * Float64(Float64(x * z) * Float64(t * y))));
	elseif (z <= 4.3e+189)
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(j * Float64(k * 27.0)));
	elseif (z <= 2.25e+240)
		tmp = Float64(t_1 + Float64(x * Float64(t * Float64(z * Float64(18.0 * y)))));
	else
		tmp = Float64(t_1 + Float64(18.0 * Float64(t * Float64(y * Float64(x * z)))));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * -27.0) * k;
	tmp = 0.0;
	if (z <= -1.8e-112)
		tmp = t_1 + (18.0 * ((x * z) * (t * y)));
	elseif (z <= 4.3e+189)
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (k * 27.0));
	elseif (z <= 2.25e+240)
		tmp = t_1 + (x * (t * (z * (18.0 * y))));
	else
		tmp = t_1 + (18.0 * (t * (y * (x * z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[z, -1.8e-112], N[(t$95$1 + N[(18.0 * N[(N[(x * z), $MachinePrecision] * N[(t * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e+189], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e+240], N[(t$95$1 + N[(x * N[(t * N[(z * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(18.0 * N[(t * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8e-112

   1. Initial program 74.7%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in z around inf 53.5%

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

      1. expm1-log1p-u 31.2%

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

      2. expm1-udef 30.7%

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

      3. *-commutative 30.7%

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

   6. Applied egg-rr 30.7%

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

      1. expm1-def 31.2%

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

      2. expm1-log1p 53.5%

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

      3. associate-*r* 52.2%

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

   8. Simplified 52.2%

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

   9. Taylor expanded in t around 0 53.5%

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

       1. *-commutative 53.5%

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

       2. associate-*r* 52.2%

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

       3. associate-*l* 57.3%

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

       4. *-commutative 57.3%

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

       5. associate-*l* 48.0%

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

   11. Simplified 48.0%

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

   if -1.8e-112 < z < 4.29999999999999998e189

   1. Initial program 86.7%

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

      1. associate-*l* 86.7%

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

      2. associate--l+ 86.7%

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

      3. distribute-rgt-out-- 86.7%

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

      4. associate-*l* 87.5%

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

      5. associate-*l* 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in t around 0 70.3%

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

   if 4.29999999999999998e189 < z < 2.24999999999999989e240

   1. Initial program 76.1%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in z around inf 57.2%

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

      1. *-commutative 57.2%

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

      2. associate-*r* 76.2%

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

      3. associate-*l* 76.3%

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

      4. *-commutative 76.3%

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

      5. *-commutative 76.3%

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

      6. associate-*l* 76.2%

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

      7. associate-*r* 76.3%

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

      8. *-commutative 76.3%

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

      9. associate-*l* 76.3%

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

   6. Simplified 76.3%

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

   if 2.24999999999999989e240 < z

   1. Initial program 84.9%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in z around inf 51.9%

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

      1. expm1-log1p-u 35.8%

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

      2. expm1-udef 35.8%

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

      3. *-commutative 35.8%

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

   6. Applied egg-rr 35.8%

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

      1. expm1-def 35.8%

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

      2. expm1-log1p 51.9%

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

      3. associate-*r* 66.0%

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

   8. Simplified 66.0%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-112}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + 18 \cdot \left(\left(x \cdot z\right) \cdot \left(t \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+189}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+240}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + x \cdot \left(t \cdot \left(z \cdot \left(18 \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ \end{array} \]

Alternative 15: 74.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{-59} \lor \neg \left(t \leq 3.6 \cdot 10^{-86}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - j \cdot \left(k \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.26e-59) (not (<= t 3.6e-86)))
   (+ (* b c) (* t (- (* 18.0 (* x (* z y))) (* a 4.0))))
   (- (- (* b c) (* 4.0 (* x i))) (* j (* k 27.0)))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.26e-59) || !(t <= 3.6e-86)) {
		tmp = (b * c) + (t * ((18.0 * (x * (z * y))) - (a * 4.0)));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (k * 27.0));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((t <= (-1.26d-59)) .or. (.not. (t <= 3.6d-86))) then
        tmp = (b * c) + (t * ((18.0d0 * (x * (z * y))) - (a * 4.0d0)))
    else
        tmp = ((b * c) - (4.0d0 * (x * i))) - (j * (k * 27.0d0))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((t <= -1.26e-59) || !(t <= 3.6e-86)) {
		tmp = (b * c) + (t * ((18.0 * (x * (z * y))) - (a * 4.0)));
	} else {
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (k * 27.0));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (t <= -1.26e-59) or not (t <= 3.6e-86):
		tmp = (b * c) + (t * ((18.0 * (x * (z * y))) - (a * 4.0)))
	else:
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (k * 27.0))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.26e-59) || !(t <= 3.6e-86))
		tmp = Float64(Float64(b * c) + Float64(t * Float64(Float64(18.0 * Float64(x * Float64(z * y))) - Float64(a * 4.0))));
	else
		tmp = Float64(Float64(Float64(b * c) - Float64(4.0 * Float64(x * i))) - Float64(j * Float64(k * 27.0)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((t <= -1.26e-59) || ~((t <= 3.6e-86)))
		tmp = (b * c) + (t * ((18.0 * (x * (z * y))) - (a * 4.0)));
	else
		tmp = ((b * c) - (4.0 * (x * i))) - (j * (k * 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.26e-59], N[Not[LessEqual[t, 3.6e-86]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] + N[(t * N[(N[(18.0 * N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2599999999999999e-59 or 3.59999999999999966e-86 < t

   1. Initial program 84.0%

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

      1. associate-*l* 84.0%

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

      2. associate--l+ 84.0%

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

      3. distribute-rgt-out-- 86.5%

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

      4. associate-*l* 84.8%

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

      5. associate-*l* 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in i around 0 78.3%

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

   5. Taylor expanded in j around 0 71.9%

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

   if -1.2599999999999999e-59 < t < 3.59999999999999966e-86

   1. Initial program 79.5%

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

      1. associate-*l* 79.5%

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

      2. associate--l+ 79.5%

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

      3. distribute-rgt-out-- 79.5%

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

      4. associate-*l* 81.5%

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

      5. associate-*l* 81.5%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in t around 0 82.0%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{-59} \lor \neg \left(t \leq 3.6 \cdot 10^{-86}\right):\\ \;\;\;\;b \cdot c + t \cdot \left(18 \cdot \left(x \cdot \left(z \cdot y\right)\right) - a \cdot 4\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c - 4 \cdot \left(x \cdot i\right)\right) - j \cdot \left(k \cdot 27\right)\\ \end{array} \]

Alternative 16: 54.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_1 := \left(j \cdot -27\right) \cdot k\\ \mathbf{if}\;b \cdot c \leq -580000000000:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 4.1 \cdot 10^{+75}:\\ \;\;\;\;t_1 + x \cdot \left(-4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j -27.0) k)))
   (if (<= (* b c) -580000000000.0)
     (- (* b c) (* 4.0 (* x i)))
     (if (<= (* b c) 4.1e+75) (+ t_1 (* x (* -4.0 i))) (+ (* b c) t_1)))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double tmp;
	if ((b * c) <= -580000000000.0) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= 4.1e+75) {
		tmp = t_1 + (x * (-4.0 * i));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * (-27.0d0)) * k
    if ((b * c) <= (-580000000000.0d0)) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else if ((b * c) <= 4.1d+75) then
        tmp = t_1 + (x * ((-4.0d0) * i))
    else
        tmp = (b * c) + t_1
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * -27.0) * k;
	double tmp;
	if ((b * c) <= -580000000000.0) {
		tmp = (b * c) - (4.0 * (x * i));
	} else if ((b * c) <= 4.1e+75) {
		tmp = t_1 + (x * (-4.0 * i));
	} else {
		tmp = (b * c) + t_1;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * -27.0) * k
	tmp = 0
	if (b * c) <= -580000000000.0:
		tmp = (b * c) - (4.0 * (x * i))
	elif (b * c) <= 4.1e+75:
		tmp = t_1 + (x * (-4.0 * i))
	else:
		tmp = (b * c) + t_1
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * -27.0) * k)
	tmp = 0.0
	if (Float64(b * c) <= -580000000000.0)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	elseif (Float64(b * c) <= 4.1e+75)
		tmp = Float64(t_1 + Float64(x * Float64(-4.0 * i)));
	else
		tmp = Float64(Float64(b * c) + t_1);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * -27.0) * k;
	tmp = 0.0;
	if ((b * c) <= -580000000000.0)
		tmp = (b * c) - (4.0 * (x * i));
	elseif ((b * c) <= 4.1e+75)
		tmp = t_1 + (x * (-4.0 * i));
	else
		tmp = (b * c) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -580000000000.0], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 4.1e+75], N[(t$95$1 + N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -5.8e11

   1. Initial program 75.4%

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

      1. associate-*l* 75.4%

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

      2. associate--l+ 75.4%

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

      3. distribute-rgt-out-- 75.4%

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

      4. associate-*l* 74.2%

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

      5. associate-*l* 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in t around 0 68.9%

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

   5. Taylor expanded in j around 0 64.4%

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

   if -5.8e11 < (*.f64 b c) < 4.0999999999999998e75

   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 88.0%

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

   4. Taylor expanded in i around inf 49.3%

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

      1. associate-*r* 49.3%

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

      2. *-commutative 49.3%

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

   6. Simplified 49.3%

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

   if 4.0999999999999998e75 < (*.f64 b c)

   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 89.8%

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

   4. Taylor expanded in b around inf 64.3%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -580000000000:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 4.1 \cdot 10^{+75}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + x \cdot \left(-4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(j \cdot -27\right) \cdot k\\ \end{array} \]

Alternative 17: 35.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.1 \cdot 10^{+120}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 3.6 \cdot 10^{-130}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2.02 \cdot 10^{+49}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1.1e+120)
   (* b c)
   (if (<= (* b c) 3.6e-130)
     (* x (* -4.0 i))
     (if (<= (* b c) 2.02e+49) (* j (* -27.0 k)) (* b c)))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.1e+120) {
		tmp = b * c;
	} else if ((b * c) <= 3.6e-130) {
		tmp = x * (-4.0 * i);
	} else if ((b * c) <= 2.02e+49) {
		tmp = j * (-27.0 * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((b * c) <= (-1.1d+120)) then
        tmp = b * c
    else if ((b * c) <= 3.6d-130) then
        tmp = x * ((-4.0d0) * i)
    else if ((b * c) <= 2.02d+49) then
        tmp = j * ((-27.0d0) * k)
    else
        tmp = b * c
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -1.1e+120) {
		tmp = b * c;
	} else if ((b * c) <= 3.6e-130) {
		tmp = x * (-4.0 * i);
	} else if ((b * c) <= 2.02e+49) {
		tmp = j * (-27.0 * k);
	} else {
		tmp = b * c;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -1.1e+120:
		tmp = b * c
	elif (b * c) <= 3.6e-130:
		tmp = x * (-4.0 * i)
	elif (b * c) <= 2.02e+49:
		tmp = j * (-27.0 * k)
	else:
		tmp = b * c
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -1.1e+120)
		tmp = Float64(b * c);
	elseif (Float64(b * c) <= 3.6e-130)
		tmp = Float64(x * Float64(-4.0 * i));
	elseif (Float64(b * c) <= 2.02e+49)
		tmp = Float64(j * Float64(-27.0 * k));
	else
		tmp = Float64(b * c);
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -1.1e+120)
		tmp = b * c;
	elseif ((b * c) <= 3.6e-130)
		tmp = x * (-4.0 * i);
	elseif ((b * c) <= 2.02e+49)
		tmp = j * (-27.0 * k);
	else
		tmp = b * c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -1.1e+120], N[(b * c), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 3.6e-130], N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2.02e+49], N[(j * N[(-27.0 * k), $MachinePrecision]), $MachinePrecision], N[(b * c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -1.1000000000000001e120 or 2.02000000000000004e49 < (*.f64 b c)

   1. Initial program 80.6%

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

      1. associate-*l* 80.6%

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

      2. associate--l+ 80.6%

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

      3. distribute-rgt-out-- 81.7%

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

      4. associate-*l* 81.7%

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

      5. associate-*l* 81.7%

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

   3. Simplified 81.7%

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

   4. Taylor expanded in i around 0 76.2%

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

      1. associate--l+ 76.2%

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

      2. cancel-sign-sub-inv 76.2%

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

      3. associate-*r* 76.2%

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

      4. fma-def 76.2%

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

      5. metadata-eval 76.2%

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

   6. Applied egg-rr 76.2%

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

   7. Taylor expanded in b around inf 50.8%

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

   if -1.1000000000000001e120 < (*.f64 b c) < 3.6000000000000001e-130

   1. Initial program 83.1%

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

      1. associate-*l* 83.1%

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

      2. associate--l+ 83.1%

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

      3. distribute-rgt-out-- 84.7%

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

      4. associate-*l* 84.1%

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

      5. associate-*l* 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in t around 0 56.7%

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

   5. Taylor expanded in i around inf 34.2%

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

      1. associate-*r* 34.2%

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

      2. metadata-eval 34.2%

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

      3. distribute-lft-neg-in 34.2%

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

      4. *-commutative 34.2%

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

      5. distribute-lft-neg-in 34.2%

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

      6. metadata-eval 34.2%

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

   7. Simplified 34.2%

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

   if 3.6000000000000001e-130 < (*.f64 b c) < 2.02000000000000004e49

   1. Initial program 83.3%

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

      1. associate-*l* 83.3%

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

      2. associate--l+ 83.3%

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

      3. distribute-rgt-out-- 86.1%

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

      4. associate-*l* 86.1%

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

      5. associate-*l* 86.1%

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

   3. Simplified 86.1%

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

      1. associate-*r* 86.1%

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

      2. distribute-rgt-out-- 83.3%

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

      3. associate-*l* 83.2%

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

      4. associate-*l* 80.4%

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

      5. *-commutative 80.4%

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

   5. Applied egg-rr 80.4%

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

   6. Taylor expanded in j around inf 32.2%

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

      1. associate-*r* 32.3%

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

      2. *-commutative 32.3%

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

      3. associate-*r* 32.2%

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

      4. *-commutative 32.2%

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

   8. Simplified 32.2%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1.1 \cdot 10^{+120}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \cdot c \leq 3.6 \cdot 10^{-130}:\\ \;\;\;\;x \cdot \left(-4 \cdot i\right)\\ \mathbf{elif}\;b \cdot c \leq 2.02 \cdot 10^{+49}:\\ \;\;\;\;j \cdot \left(-27 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 18: 48.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+110} \lor \neg \left(a \leq 6 \cdot 10^{+33}\right):\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= a -1.8e+110) (not (<= a 6e+33)))
   (+ (* (* j -27.0) k) (* -4.0 (* t a)))
   (- (* b c) (* 4.0 (* x i)))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((a <= -1.8e+110) || !(a <= 6e+33)) {
		tmp = ((j * -27.0) * k) + (-4.0 * (t * a));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((a <= (-1.8d+110)) .or. (.not. (a <= 6d+33))) then
        tmp = ((j * (-27.0d0)) * k) + ((-4.0d0) * (t * a))
    else
        tmp = (b * c) - (4.0d0 * (x * i))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((a <= -1.8e+110) || !(a <= 6e+33)) {
		tmp = ((j * -27.0) * k) + (-4.0 * (t * a));
	} else {
		tmp = (b * c) - (4.0 * (x * i));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (a <= -1.8e+110) or not (a <= 6e+33):
		tmp = ((j * -27.0) * k) + (-4.0 * (t * a))
	else:
		tmp = (b * c) - (4.0 * (x * i))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((a <= -1.8e+110) || !(a <= 6e+33))
		tmp = Float64(Float64(Float64(j * -27.0) * k) + Float64(-4.0 * Float64(t * a)));
	else
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((a <= -1.8e+110) || ~((a <= 6e+33)))
		tmp = ((j * -27.0) * k) + (-4.0 * (t * a));
	else
		tmp = (b * c) - (4.0 * (x * i));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[a, -1.8e+110], N[Not[LessEqual[a, 6e+33]], $MachinePrecision]], N[(N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.7999999999999998e110 or 5.99999999999999967e33 < a

   1. Initial program 76.5%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in a around inf 56.3%

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

      1. *-commutative 56.3%

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

   6. Simplified 56.3%

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

   if -1.7999999999999998e110 < a < 5.99999999999999967e33

   1. Initial program 85.3%

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

      1. associate-*l* 85.3%

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

      2. associate--l+ 85.3%

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

      3. distribute-rgt-out-- 85.3%

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

      4. associate-*l* 84.8%

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

      5. associate-*l* 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in t around 0 65.9%

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

   5. Taylor expanded in j around 0 54.1%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+110} \lor \neg \left(a \leq 6 \cdot 10^{+33}\right):\\ \;\;\;\;\left(j \cdot -27\right) \cdot k + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 19: 37.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -24000000000 \lor \neg \left(b \cdot c \leq 2 \cdot 10^{+49}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -24000000000.0) (not (<= (* b c) 2e+49)))
   (* b c)
   (* -27.0 (* j k))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -24000000000.0) || !((b * c) <= 2e+49)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if (((b * c) <= (-24000000000.0d0)) .or. (.not. ((b * c) <= 2d+49))) then
        tmp = b * c
    else
        tmp = (-27.0d0) * (j * k)
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -24000000000.0) || !((b * c) <= 2e+49)) {
		tmp = b * c;
	} else {
		tmp = -27.0 * (j * k);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -24000000000.0) or not ((b * c) <= 2e+49):
		tmp = b * c
	else:
		tmp = -27.0 * (j * k)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -24000000000.0) || !(Float64(b * c) <= 2e+49))
		tmp = Float64(b * c);
	else
		tmp = Float64(-27.0 * Float64(j * k));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -24000000000.0) || ~(((b * c) <= 2e+49)))
		tmp = b * c;
	else
		tmp = -27.0 * (j * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -24000000000.0], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2e+49]], $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) < -2.4e10 or 1.99999999999999989e49 < (*.f64 b c)

   1. Initial program 78.4%

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

      1. associate-*l* 78.4%

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

      2. associate--l+ 78.4%

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

      3. distribute-rgt-out-- 79.3%

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

      4. associate-*l* 78.5%

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

      5. associate-*l* 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in i around 0 72.0%

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

      1. associate--l+ 72.0%

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

      2. cancel-sign-sub-inv 72.0%

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

      3. associate-*r* 72.0%

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

      4. fma-def 72.0%

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

      5. metadata-eval 72.0%

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

   6. Applied egg-rr 72.0%

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

   7. Taylor expanded in b around inf 44.1%

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

   if -2.4e10 < (*.f64 b c) < 1.99999999999999989e49

   1. Initial program 85.6%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in k around inf 25.0%

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

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -24000000000 \lor \neg \left(b \cdot c \leq 2 \cdot 10^{+49}\right):\\ \;\;\;\;b \cdot c\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 20: 47.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+80} \lor \neg \left(x \leq 4.5 \cdot 10^{+174}\right):\\ \;\;\;\;x \cdot \left(-4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(j \cdot -27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -6.5e+80) (not (<= x 4.5e+174)))
   (* x (* -4.0 i))
   (+ (* b c) (* (* j -27.0) k))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -6.5e+80) || !(x <= 4.5e+174)) {
		tmp = x * (-4.0 * i);
	} else {
		tmp = (b * c) + ((j * -27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((x <= (-6.5d+80)) .or. (.not. (x <= 4.5d+174))) then
        tmp = x * ((-4.0d0) * i)
    else
        tmp = (b * c) + ((j * (-27.0d0)) * k)
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -6.5e+80) || !(x <= 4.5e+174)) {
		tmp = x * (-4.0 * i);
	} else {
		tmp = (b * c) + ((j * -27.0) * k);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (x <= -6.5e+80) or not (x <= 4.5e+174):
		tmp = x * (-4.0 * i)
	else:
		tmp = (b * c) + ((j * -27.0) * k)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -6.5e+80) || !(x <= 4.5e+174))
		tmp = Float64(x * Float64(-4.0 * i));
	else
		tmp = Float64(Float64(b * c) + Float64(Float64(j * -27.0) * k));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((x <= -6.5e+80) || ~((x <= 4.5e+174)))
		tmp = x * (-4.0 * i);
	else
		tmp = (b * c) + ((j * -27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -6.5e+80], N[Not[LessEqual[x, 4.5e+174]], $MachinePrecision]], N[(x * N[(-4.0 * i), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.4999999999999998e80 or 4.50000000000000042e174 < x

   1. Initial program 73.4%

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

      1. associate-*l* 73.4%

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

      2. associate--l+ 73.4%

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

      3. distribute-rgt-out-- 74.5%

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

      4. associate-*l* 76.7%

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

      5. associate-*l* 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in t around 0 59.1%

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

   5. Taylor expanded in i around inf 49.8%

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

      1. associate-*r* 49.8%

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

      2. metadata-eval 49.8%

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

      3. distribute-lft-neg-in 49.8%

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

      4. *-commutative 49.8%

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

      5. distribute-lft-neg-in 49.8%

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

      6. metadata-eval 49.8%

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

   7. Simplified 49.8%

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

   if -6.4999999999999998e80 < x < 4.50000000000000042e174

   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 87.8%

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

   4. Taylor expanded in b around inf 51.1%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+80} \lor \neg \left(x \leq 4.5 \cdot 10^{+174}\right):\\ \;\;\;\;x \cdot \left(-4 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(j \cdot -27\right) \cdot k\\ \end{array} \]

Alternative 21: 50.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -2.6 \cdot 10^{+33} \lor \neg \left(i \leq 7 \cdot 10^{-81}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(j \cdot -27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= i -2.6e+33) (not (<= i 7e-81)))
   (- (* b c) (* 4.0 (* x i)))
   (+ (* b c) (* (* j -27.0) k))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -2.6e+33) || !(i <= 7e-81)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) + ((j * -27.0) * k);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((i <= (-2.6d+33)) .or. (.not. (i <= 7d-81))) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = (b * c) + ((j * (-27.0d0)) * k)
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -2.6e+33) || !(i <= 7e-81)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) + ((j * -27.0) * k);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (i <= -2.6e+33) or not (i <= 7e-81):
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = (b * c) + ((j * -27.0) * k)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((i <= -2.6e+33) || !(i <= 7e-81))
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(b * c) + Float64(Float64(j * -27.0) * k));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((i <= -2.6e+33) || ~((i <= 7e-81)))
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = (b * c) + ((j * -27.0) * k);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[i, -2.6e+33], N[Not[LessEqual[i, 7e-81]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.5999999999999997e33 or 6.99999999999999973e-81 < i

   1. Initial program 81.0%

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

      1. associate-*l* 81.0%

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

      2. associate--l+ 81.0%

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

      3. distribute-rgt-out-- 82.4%

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

      4. associate-*l* 81.2%

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

      5. associate-*l* 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in t around 0 66.9%

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

   5. Taylor expanded in j around 0 56.1%

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

   if -2.5999999999999997e33 < i < 6.99999999999999973e-81

   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 87.5%

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

   4. Taylor expanded in b around inf 46.1%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.6 \cdot 10^{+33} \lor \neg \left(i \leq 7 \cdot 10^{-81}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(j \cdot -27\right) \cdot k\\ \end{array} \]

Alternative 22: 50.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -4.6 \cdot 10^{+33} \lor \neg \left(i \leq 3.5 \cdot 10^{-80}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= i -4.6e+33) (not (<= i 3.5e-80)))
   (- (* b c) (* 4.0 (* x i)))
   (- (* b c) (* 27.0 (* j k)))))

C

assert(y < z);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -4.6e+33) || !(i <= 3.5e-80)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((i <= (-4.6d+33)) .or. (.not. (i <= 3.5d-80))) then
        tmp = (b * c) - (4.0d0 * (x * i))
    else
        tmp = (b * c) - (27.0d0 * (j * k))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((i <= -4.6e+33) || !(i <= 3.5e-80)) {
		tmp = (b * c) - (4.0 * (x * i));
	} else {
		tmp = (b * c) - (27.0 * (j * k));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (i <= -4.6e+33) or not (i <= 3.5e-80):
		tmp = (b * c) - (4.0 * (x * i))
	else:
		tmp = (b * c) - (27.0 * (j * k))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((i <= -4.6e+33) || !(i <= 3.5e-80))
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(x * i)));
	else
		tmp = Float64(Float64(b * c) - Float64(27.0 * Float64(j * k)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((i <= -4.6e+33) || ~((i <= 3.5e-80)))
		tmp = (b * c) - (4.0 * (x * i));
	else
		tmp = (b * c) - (27.0 * (j * k));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[i, -4.6e+33], N[Not[LessEqual[i, 3.5e-80]], $MachinePrecision]], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] - N[(27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -4.60000000000000021e33 or 3.50000000000000015e-80 < i

   1. Initial program 81.0%

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

      1. associate-*l* 81.0%

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

      2. associate--l+ 81.0%

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

      3. distribute-rgt-out-- 82.4%

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

      4. associate-*l* 81.2%

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

      5. associate-*l* 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in t around 0 66.9%

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

   5. Taylor expanded in j around 0 56.1%

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

   if -4.60000000000000021e33 < i < 3.50000000000000015e-80

   1. Initial program 83.9%

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

      1. associate-*l* 83.8%

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

      2. associate--l+ 83.8%

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

      3. distribute-rgt-out-- 85.6%

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

      4. associate-*l* 86.5%

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

      5. associate-*l* 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in i around 0 84.4%

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

   5. Taylor expanded in t around 0 46.1%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.6 \cdot 10^{+33} \lor \neg \left(i \leq 3.5 \cdot 10^{-80}\right):\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c - 27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 23: 23.7% accurate, 10.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.3%

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

   1. associate-*l* 82.2%

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

   2. associate--l+ 82.2%

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

   3. distribute-rgt-out-- 83.8%

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

   4. associate-*l* 83.5%

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

   5. associate-*l* 83.5%

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

3. Simplified 83.5%

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

4. Taylor expanded in i around 0 71.3%

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

   1. associate--l+ 71.3%

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

   2. cancel-sign-sub-inv 71.3%

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

   3. associate-*r* 71.3%

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

   4. fma-def 71.3%

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

   5. metadata-eval 71.3%

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

6. Applied egg-rr 71.3%

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

7. Taylor expanded in b around inf 22.8%

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

8. Final simplification 22.8%

   \[\leadsto b \cdot c \]

Developer target: 88.8% 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 2023336 
(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)))