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

Percentage Accurate: 85.6% → 93.8%

Time: 6.5s

Alternatives: 18

Speedup: 1.2×

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

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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: 85.6% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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: 93.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(\left(y \cdot 18\right) \cdot t, z, -4 \cdot i\right), x, \mathsf{fma}\left(-4 \cdot a, t, c \cdot b\right)\right)\right)\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, \left(-27 \cdot j\right) \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(b, c, x \cdot \mathsf{fma}\left(z, t \cdot \left(18 \cdot y\right), i \cdot -4\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < -inf.0

   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. Applied rewrites 89.7%

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

   if -inf.0 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < +inf.0

   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. Applied rewrites 89.0%

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

   if +inf.0 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i))

   1. Initial program 85.6%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 72.9

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 79.2%

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

Alternative 2: 93.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k)) < +inf.0

   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. Applied rewrites 89.0%

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

   if +inf.0 < (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) (*.f64 (*.f64 j #s(literal 27 binary64)) k))

   1. Initial program 85.6%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 72.9

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 79.2%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. distribute-lft-neg-out N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. metadata-eval N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r* N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*r* N/A

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

      12. distribute-lft-neg-in N/A

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

      13. distribute-rgt-neg-out N/A

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

      14. metadata-eval N/A

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

      15. lift-*.f64 N/A

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

      16. lower-fma.f64 N/A

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

      17. associate-*l* N/A

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

      18. *-commutative N/A

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

      19. associate-*r* N/A

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

      20. lower-*.f64 N/A

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

      21. lower-*.f64 79.8

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 79.8

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

   8. Applied rewrites 79.8%

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

Alternative 3: 88.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-15}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(b, c, x \cdot \mathsf{fma}\left(\left(z \cdot 18\right) \cdot t, y, -4 \cdot i\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-70}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-4, a, z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right), t, \mathsf{fma}\left(-27, j \cdot k, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(b, c, x \cdot \mathsf{fma}\left(z, t \cdot \left(18 \cdot y\right), i \cdot -4\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -2.1e-15)
   (fma (* k -27.0) j (fma b c (* x (fma (* (* z 18.0) t) y (* -4.0 i)))))
   (if (<= x 1.3e-70)
     (fma (fma -4.0 a (* z (* y (* 18.0 x)))) t (fma -27.0 (* j k) (* b c)))
     (fma (* k -27.0) j (fma b c (* x (fma z (* t (* 18.0 y)) (* i -4.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -2.1e-15) {
		tmp = fma((k * -27.0), j, fma(b, c, (x * fma(((z * 18.0) * t), y, (-4.0 * i)))));
	} else if (x <= 1.3e-70) {
		tmp = fma(fma(-4.0, a, (z * (y * (18.0 * x)))), t, fma(-27.0, (j * k), (b * c)));
	} else {
		tmp = fma((k * -27.0), j, fma(b, c, (x * fma(z, (t * (18.0 * y)), (i * -4.0)))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -2.1e-15)
		tmp = fma(Float64(k * -27.0), j, fma(b, c, Float64(x * fma(Float64(Float64(z * 18.0) * t), y, Float64(-4.0 * i)))));
	elseif (x <= 1.3e-70)
		tmp = fma(fma(-4.0, a, Float64(z * Float64(y * Float64(18.0 * x)))), t, fma(-27.0, Float64(j * k), Float64(b * c)));
	else
		tmp = fma(Float64(k * -27.0), j, fma(b, c, Float64(x * fma(z, Float64(t * Float64(18.0 * y)), Float64(i * -4.0)))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -2.1e-15], N[(N[(k * -27.0), $MachinePrecision] * j + N[(b * c + N[(x * N[(N[(N[(z * 18.0), $MachinePrecision] * t), $MachinePrecision] * y + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e-70], N[(N[(-4.0 * a + N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + N[(-27.0 * N[(j * k), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * -27.0), $MachinePrecision] * j + N[(b * c + N[(x * N[(z * N[(t * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.09999999999999981e-15

   1. Initial program 85.6%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 72.9

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 79.2%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. distribute-lft-neg-out N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. metadata-eval N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r* N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*r* N/A

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

      12. distribute-lft-neg-in N/A

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

      13. distribute-rgt-neg-out N/A

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

      14. metadata-eval N/A

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

      15. lift-*.f64 N/A

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

      16. lower-fma.f64 N/A

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

      17. associate-*l* N/A

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

      18. *-commutative N/A

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

      19. associate-*r* N/A

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

      20. lower-*.f64 N/A

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

      21. lower-*.f64 79.8

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 79.8

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

   8. Applied rewrites 79.8%

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

   if -2.09999999999999981e-15 < x < 1.30000000000000001e-70

   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. Applied rewrites 88.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 77.9

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

   6. Applied rewrites 77.9%

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

   if 1.30000000000000001e-70 < x

   1. Initial program 85.6%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 72.9

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 79.2%

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

Alternative 4: 84.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-15}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(b, c, x \cdot \mathsf{fma}\left(\left(z \cdot 18\right) \cdot t, y, -4 \cdot i\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-94}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4, a \cdot t, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(b, c, x \cdot \mathsf{fma}\left(z, t \cdot \left(18 \cdot y\right), i \cdot -4\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -1.85e-15)
   (fma (* k -27.0) j (fma b c (* x (fma (* (* z 18.0) t) y (* -4.0 i)))))
   (if (<= x 1.1e-94)
     (fma (* -27.0 j) k (fma -4.0 (* a t) (* b c)))
     (fma (* k -27.0) j (fma b c (* x (fma z (* t (* 18.0 y)) (* i -4.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -1.85e-15) {
		tmp = fma((k * -27.0), j, fma(b, c, (x * fma(((z * 18.0) * t), y, (-4.0 * i)))));
	} else if (x <= 1.1e-94) {
		tmp = fma((-27.0 * j), k, fma(-4.0, (a * t), (b * c)));
	} else {
		tmp = fma((k * -27.0), j, fma(b, c, (x * fma(z, (t * (18.0 * y)), (i * -4.0)))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -1.85e-15)
		tmp = fma(Float64(k * -27.0), j, fma(b, c, Float64(x * fma(Float64(Float64(z * 18.0) * t), y, Float64(-4.0 * i)))));
	elseif (x <= 1.1e-94)
		tmp = fma(Float64(-27.0 * j), k, fma(-4.0, Float64(a * t), Float64(b * c)));
	else
		tmp = fma(Float64(k * -27.0), j, fma(b, c, Float64(x * fma(z, Float64(t * Float64(18.0 * y)), Float64(i * -4.0)))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -1.85e-15], N[(N[(k * -27.0), $MachinePrecision] * j + N[(b * c + N[(x * N[(N[(N[(z * 18.0), $MachinePrecision] * t), $MachinePrecision] * y + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e-94], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(-4.0 * N[(a * t), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * -27.0), $MachinePrecision] * j + N[(b * c + N[(x * N[(z * N[(t * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.85000000000000008e-15

   1. Initial program 85.6%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 72.9

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 79.2%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. distribute-lft-neg-out N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. metadata-eval N/A

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

      7. fp-cancel-sub-sign-inv N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r* N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*r* N/A

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

      12. distribute-lft-neg-in N/A

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

      13. distribute-rgt-neg-out N/A

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

      14. metadata-eval N/A

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

      15. lift-*.f64 N/A

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

      16. lower-fma.f64 N/A

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

      17. associate-*l* N/A

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

      18. *-commutative N/A

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

      19. associate-*r* N/A

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

      20. lower-*.f64 N/A

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

      21. lower-*.f64 79.8

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

      22. lift-*.f64 N/A

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

      23. *-commutative N/A

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

      24. lower-*.f64 79.8

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

   8. Applied rewrites 79.8%

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

   if -1.85000000000000008e-15 < x < 1.10000000000000001e-94

   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. Applied rewrites 89.7%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 61.2

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

   6. Applied rewrites 61.2%

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

   if 1.10000000000000001e-94 < x

   1. Initial program 85.6%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 72.9

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 79.2%

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

Alternative 5: 84.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(b, c, x \cdot \mathsf{fma}\left(z, t \cdot \left(18 \cdot y\right), i \cdot -4\right)\right)\right)\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-94}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4, a \cdot t, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (fma
          (* k -27.0)
          j
          (fma b c (* x (fma z (* t (* 18.0 y)) (* i -4.0)))))))
   (if (<= x -1.85e-15)
     t_1
     (if (<= x 1.1e-94) (fma (* -27.0 j) k (fma -4.0 (* a t) (* b c))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((k * -27.0), j, fma(b, c, (x * fma(z, (t * (18.0 * y)), (i * -4.0)))));
	double tmp;
	if (x <= -1.85e-15) {
		tmp = t_1;
	} else if (x <= 1.1e-94) {
		tmp = fma((-27.0 * j), k, fma(-4.0, (a * t), (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(k * -27.0), j, fma(b, c, Float64(x * fma(z, Float64(t * Float64(18.0 * y)), Float64(i * -4.0)))))
	tmp = 0.0
	if (x <= -1.85e-15)
		tmp = t_1;
	elseif (x <= 1.1e-94)
		tmp = fma(Float64(-27.0 * j), k, fma(-4.0, Float64(a * t), Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(k * -27.0), $MachinePrecision] * j + N[(b * c + N[(x * N[(z * N[(t * N[(18.0 * y), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.85e-15], t$95$1, If[LessEqual[x, 1.1e-94], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(-4.0 * N[(a * t), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.85000000000000008e-15 or 1.10000000000000001e-94 < x

   1. Initial program 85.6%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 72.9

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 79.2%

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

   if -1.85000000000000008e-15 < x < 1.10000000000000001e-94

   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. Applied rewrites 89.7%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 61.2

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

   6. Applied rewrites 61.2%

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

Alternative 6: 81.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+133}:\\ \;\;\;\;\mathsf{fma}\left(j \cdot -27, k, \mathsf{fma}\left(x \cdot -4, i, b \cdot c\right)\right)\\ \mathbf{elif}\;t\_2 \leq 3 \cdot 10^{+227}:\\ \;\;\;\;\mathsf{fma}\left(-4, a \cdot t, \mathsf{fma}\left(b, c, x \cdot \mathsf{fma}\left(-4, i, t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, \mathsf{fma}\left(b, c, x \cdot t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* 18.0 (* t (* y z)))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -5e+133)
     (fma (* j -27.0) k (fma (* x -4.0) i (* b c)))
     (if (<= t_2 3e+227)
       (fma -4.0 (* a t) (fma b c (* x (fma -4.0 i t_1))))
       (fma (* k -27.0) j (fma b c (* x t_1)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = 18.0 * (t * (y * z));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+133) {
		tmp = fma((j * -27.0), k, fma((x * -4.0), i, (b * c)));
	} else if (t_2 <= 3e+227) {
		tmp = fma(-4.0, (a * t), fma(b, c, (x * fma(-4.0, i, t_1))));
	} else {
		tmp = fma((k * -27.0), j, fma(b, c, (x * t_1)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(18.0 * Float64(t * Float64(y * z)))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -5e+133)
		tmp = fma(Float64(j * -27.0), k, fma(Float64(x * -4.0), i, Float64(b * c)));
	elseif (t_2 <= 3e+227)
		tmp = fma(-4.0, Float64(a * t), fma(b, c, Float64(x * fma(-4.0, i, t_1))));
	else
		tmp = fma(Float64(k * -27.0), j, fma(b, c, Float64(x * t_1)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+133], N[(N[(j * -27.0), $MachinePrecision] * k + N[(N[(x * -4.0), $MachinePrecision] * i + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 3e+227], N[(-4.0 * N[(a * t), $MachinePrecision] + N[(b * c + N[(x * N[(-4.0 * i + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * -27.0), $MachinePrecision] * j + N[(b * c + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999961e133

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

      1. lift--.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate--r+ N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. metadata-eval N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      8. associate-*l* N/A

         \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right) \]

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + b \cdot c\right) - 27 \cdot \left(j \cdot k\right) \]

      12. *-commutative N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + c \cdot b\right) - 27 \cdot \left(j \cdot k\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + c \cdot b\right) - 27 \cdot \left(j \cdot k\right) \]

      14. lift-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. fp-cancel-sub-sign-inv N/A

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

      17. metadata-eval N/A

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

      18. lift-*.f64 N/A

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

      19. associate-*l* N/A

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

      20. lift-*.f64 N/A

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

      21. +-commutative N/A

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

   6. Applied rewrites 61.9%

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

   if -4.99999999999999961e133 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 2.99999999999999986e227

   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. Applied rewrites 89.7%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      5. lower-*.f64 42.8

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

   6. Applied rewrites 42.8%

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

   7. Taylor expanded in x around 0

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

      1. lower-*.f64 21.1

         \[\leadsto t \cdot \left(-4 \cdot a\right) \]

   9. Applied rewrites 21.1%

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

   10. Taylor expanded in j around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-fma.f64 N/A

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

       4. lower-*.f64 N/A

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

       5. lower-fma.f64 N/A

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

       6. lower-*.f64 N/A

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

       7. lower-*.f64 N/A

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

       8. lower-*.f64 72.4

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

   12. Applied rewrites 72.4%

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

   if 2.99999999999999986e227 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.6%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 72.9

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 79.2%

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

   7. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 63.0

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

   9. Applied rewrites 63.0%

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

Alternative 7: 76.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27, j \cdot k, x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4, a \cdot t, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma -27.0 (* j k) (* x (fma -4.0 i (* 18.0 (* t (* y z))))))))
   (if (<= x -1.75e+64)
     t_1
     (if (<= x 1.25e+56) (fma (* -27.0 j) k (fma -4.0 (* a t) (* b c))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-27.0, (j * k), (x * fma(-4.0, i, (18.0 * (t * (y * z))))));
	double tmp;
	if (x <= -1.75e+64) {
		tmp = t_1;
	} else if (x <= 1.25e+56) {
		tmp = fma((-27.0 * j), k, fma(-4.0, (a * t), (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(-27.0, Float64(j * k), Float64(x * fma(-4.0, i, Float64(18.0 * Float64(t * Float64(y * z))))))
	tmp = 0.0
	if (x <= -1.75e+64)
		tmp = t_1;
	elseif (x <= 1.25e+56)
		tmp = fma(Float64(-27.0 * j), k, fma(-4.0, Float64(a * t), Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision] + N[(x * N[(-4.0 * i + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.75e+64], t$95$1, If[LessEqual[x, 1.25e+56], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(-4.0 * N[(a * t), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7499999999999999e64 or 1.25000000000000006e56 < x

   1. Initial program 85.6%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 72.9

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 79.2%

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

   7. Taylor expanded in b around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 60.0

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

   9. Applied rewrites 60.0%

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

   if -1.7499999999999999e64 < x < 1.25000000000000006e56

   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. Applied rewrites 89.7%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 61.2

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

   6. Applied rewrites 61.2%

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

Alternative 8: 73.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -4.9 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.38 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(-4, a \cdot t, b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (fma -4.0 i (* 18.0 (* t (* y z)))))))
   (if (<= x -4.9e+58)
     t_1
     (if (<= x 1.38e+75) (fma (* -27.0 j) k (fma -4.0 (* a t) (* b c))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * fma(-4.0, i, (18.0 * (t * (y * z))));
	double tmp;
	if (x <= -4.9e+58) {
		tmp = t_1;
	} else if (x <= 1.38e+75) {
		tmp = fma((-27.0 * j), k, fma(-4.0, (a * t), (b * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * fma(-4.0, i, Float64(18.0 * Float64(t * Float64(y * z)))))
	tmp = 0.0
	if (x <= -4.9e+58)
		tmp = t_1;
	elseif (x <= 1.38e+75)
		tmp = fma(Float64(-27.0 * j), k, fma(-4.0, Float64(a * t), Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(-4.0 * i + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.9e+58], t$95$1, If[LessEqual[x, 1.38e+75], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(-4.0 * N[(a * t), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.90000000000000018e58 or 1.3799999999999999e75 < x

   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. Applied rewrites 89.7%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 43.0

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

   6. Applied rewrites 43.0%

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

   if -4.90000000000000018e58 < x < 1.3799999999999999e75

   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. Applied rewrites 89.7%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 61.2

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

   6. Applied rewrites 61.2%

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

Alternative 9: 70.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(\left(z \cdot x\right) \cdot 18, y, -4 \cdot a\right)\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-63}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(x \cdot -4, i, \left(k \cdot j\right) \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (fma (* (* z x) 18.0) y (* -4.0 a)))))
   (if (<= t -9.5e+127)
     t_1
     (if (<= t 1.45e-63) (fma c b (fma (* x -4.0) i (* (* k j) -27.0))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * fma(((z * x) * 18.0), y, (-4.0 * a));
	double tmp;
	if (t <= -9.5e+127) {
		tmp = t_1;
	} else if (t <= 1.45e-63) {
		tmp = fma(c, b, fma((x * -4.0), i, ((k * j) * -27.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * fma(Float64(Float64(z * x) * 18.0), y, Float64(-4.0 * a)))
	tmp = 0.0
	if (t <= -9.5e+127)
		tmp = t_1;
	elseif (t <= 1.45e-63)
		tmp = fma(c, b, fma(Float64(x * -4.0), i, Float64(Float64(k * j) * -27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(N[(z * x), $MachinePrecision] * 18.0), $MachinePrecision] * y + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+127], t$95$1, If[LessEqual[t, 1.45e-63], N[(c * b + N[(N[(x * -4.0), $MachinePrecision] * i + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.49999999999999975e127 or 1.44999999999999987e-63 < t

   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. Applied rewrites 89.7%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      5. lower-*.f64 42.8

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

   6. Applied rewrites 42.8%

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

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

          \[\leadsto t \cdot \mathsf{fma}\left(z \cdot \left(x \cdot 18\right), y, -4 \cdot a\right) \]

      12. associate-*r* N/A

          \[\leadsto t \cdot \mathsf{fma}\left(\left(z \cdot x\right) \cdot 18, y, -4 \cdot a\right) \]

      13. lower-*.f64 N/A

          \[\leadsto t \cdot \mathsf{fma}\left(\left(z \cdot x\right) \cdot 18, y, -4 \cdot a\right) \]

      14. lower-*.f64 N/A

          \[\leadsto t \cdot \mathsf{fma}\left(\left(z \cdot x\right) \cdot 18, y, -4 \cdot a\right) \]

      15. lower-*.f64 43.4

          \[\leadsto t \cdot \mathsf{fma}\left(\left(z \cdot x\right) \cdot 18, y, -4 \cdot a\right) \]

   8. Applied rewrites 43.4%

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

   if -9.49999999999999975e127 < t < 1.44999999999999987e-63

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      8. fp-cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) - \left(\mathsf{neg}\left(27\right)\right) \cdot \left(j \cdot k\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) - -27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      10. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) - -27 \cdot \left(j \cdot k\right)\right)\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) - \left(-27 \cdot j\right) \cdot k\right)\right)\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, \mathsf{neg}\left(\left(4 \cdot \left(i \cdot x\right) - \left(-27 \cdot j\right) \cdot k\right)\right)\right) \]

      13. sub-negate N/A

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

      14. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(-27 \cdot j\right) \cdot k - \left(\mathsf{neg}\left(-4\right)\right) \cdot \left(i \cdot x\right)\right) \]

      15. fp-cancel-sign-sub-inv N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. associate-*l* N/A

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

      19. lift-*.f64 N/A

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

   6. Applied rewrites 61.8%

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

Alternative 10: 60.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(\left(z \cdot x\right) \cdot 18, y, -4 \cdot a\right)\\ \mathbf{if}\;t \leq -1.18 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-249}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, -4 \cdot \left(i \cdot x\right)\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-64}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (fma (* (* z x) 18.0) y (* -4.0 a)))))
   (if (<= t -1.18e-48)
     t_1
     (if (<= t 9.5e-249)
       (fma -27.0 (* j k) (* -4.0 (* i x)))
       (if (<= t 5.4e-64) (- (* b c) (* 4.0 (* i x))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * fma(((z * x) * 18.0), y, (-4.0 * a));
	double tmp;
	if (t <= -1.18e-48) {
		tmp = t_1;
	} else if (t <= 9.5e-249) {
		tmp = fma(-27.0, (j * k), (-4.0 * (i * x)));
	} else if (t <= 5.4e-64) {
		tmp = (b * c) - (4.0 * (i * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * fma(Float64(Float64(z * x) * 18.0), y, Float64(-4.0 * a)))
	tmp = 0.0
	if (t <= -1.18e-48)
		tmp = t_1;
	elseif (t <= 9.5e-249)
		tmp = fma(-27.0, Float64(j * k), Float64(-4.0 * Float64(i * x)));
	elseif (t <= 5.4e-64)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(i * x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(N[(N[(z * x), $MachinePrecision] * 18.0), $MachinePrecision] * y + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.18e-48], t$95$1, If[LessEqual[t, 9.5e-249], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e-64], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.18000000000000007e-48 or 5.39999999999999971e-64 < t

   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. Applied rewrites 89.7%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      5. lower-*.f64 42.8

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

   6. Applied rewrites 42.8%

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

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

          \[\leadsto t \cdot \mathsf{fma}\left(z \cdot \left(x \cdot 18\right), y, -4 \cdot a\right) \]

      12. associate-*r* N/A

          \[\leadsto t \cdot \mathsf{fma}\left(\left(z \cdot x\right) \cdot 18, y, -4 \cdot a\right) \]

      13. lower-*.f64 N/A

          \[\leadsto t \cdot \mathsf{fma}\left(\left(z \cdot x\right) \cdot 18, y, -4 \cdot a\right) \]

      14. lower-*.f64 N/A

          \[\leadsto t \cdot \mathsf{fma}\left(\left(z \cdot x\right) \cdot 18, y, -4 \cdot a\right) \]

      15. lower-*.f64 43.4

          \[\leadsto t \cdot \mathsf{fma}\left(\left(z \cdot x\right) \cdot 18, y, -4 \cdot a\right) \]

   8. Applied rewrites 43.4%

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

   if -1.18000000000000007e-48 < t < 9.4999999999999997e-249

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

      1. lift--.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate--r+ N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. metadata-eval N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      8. associate-*l* N/A

         \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right) \]

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + b \cdot c\right) - 27 \cdot \left(j \cdot k\right) \]

      12. *-commutative N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + c \cdot b\right) - 27 \cdot \left(j \cdot k\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + c \cdot b\right) - 27 \cdot \left(j \cdot k\right) \]

      14. lift-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. fp-cancel-sub-sign-inv N/A

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

      17. metadata-eval N/A

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

      18. lift-*.f64 N/A

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

      19. associate-*l* N/A

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

      20. lift-*.f64 N/A

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

      21. +-commutative N/A

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

   6. Applied rewrites 61.9%

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

   7. Taylor expanded in b around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, -4 \cdot \left(i \cdot x\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, -4 \cdot \left(i \cdot x\right)\right) \]

      4. lower-*.f64 41.7

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, -4 \cdot \left(i \cdot x\right)\right) \]

   9. Applied rewrites 41.7%

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

   if 9.4999999999999997e-249 < t < 5.39999999999999971e-64

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 41.4

         \[\leadsto b \cdot c - 4 \cdot \left(i \cdot x\right) \]

   7. Applied rewrites 41.4%

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

Alternative 11: 57.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-249}:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, -4 \cdot \left(i \cdot x\right)\right)\\ \mathbf{elif}\;t \leq 1650:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* t (fma -4.0 a (* 18.0 (* x (* y z)))))))
   (if (<= t -1.05e-55)
     t_1
     (if (<= t 9.5e-249)
       (fma -27.0 (* j k) (* -4.0 (* i x)))
       (if (<= t 1650.0) (- (* b c) (* 4.0 (* i x))) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = t * fma(-4.0, a, (18.0 * (x * (y * z))));
	double tmp;
	if (t <= -1.05e-55) {
		tmp = t_1;
	} else if (t <= 9.5e-249) {
		tmp = fma(-27.0, (j * k), (-4.0 * (i * x)));
	} else if (t <= 1650.0) {
		tmp = (b * c) - (4.0 * (i * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(t * fma(-4.0, a, Float64(18.0 * Float64(x * Float64(y * z)))))
	tmp = 0.0
	if (t <= -1.05e-55)
		tmp = t_1;
	elseif (t <= 9.5e-249)
		tmp = fma(-27.0, Float64(j * k), Float64(-4.0 * Float64(i * x)));
	elseif (t <= 1650.0)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(i * x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(t * N[(-4.0 * a + N[(18.0 * N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e-55], t$95$1, If[LessEqual[t, 9.5e-249], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1650.0], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.0500000000000001e-55 or 1650 < t

   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. Applied rewrites 89.7%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      5. lower-*.f64 42.8

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

   6. Applied rewrites 42.8%

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

   if -1.0500000000000001e-55 < t < 9.4999999999999997e-249

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

      1. lift--.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate--r+ N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. metadata-eval N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      8. associate-*l* N/A

         \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right) \]

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + b \cdot c\right) - 27 \cdot \left(j \cdot k\right) \]

      12. *-commutative N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + c \cdot b\right) - 27 \cdot \left(j \cdot k\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + c \cdot b\right) - 27 \cdot \left(j \cdot k\right) \]

      14. lift-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. fp-cancel-sub-sign-inv N/A

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

      17. metadata-eval N/A

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

      18. lift-*.f64 N/A

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

      19. associate-*l* N/A

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

      20. lift-*.f64 N/A

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

      21. +-commutative N/A

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

   6. Applied rewrites 61.9%

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

   7. Taylor expanded in b around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, -4 \cdot \left(i \cdot x\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, -4 \cdot \left(i \cdot x\right)\right) \]

      4. lower-*.f64 41.7

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, -4 \cdot \left(i \cdot x\right)\right) \]

   9. Applied rewrites 41.7%

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

   if 9.4999999999999997e-249 < t < 1650

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 41.4

         \[\leadsto b \cdot c - 4 \cdot \left(i \cdot x\right) \]

   7. Applied rewrites 41.4%

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

Alternative 12: 57.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := x \cdot \mathsf{fma}\left(-4, i, 18 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{if}\;x \leq -4.9 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* x (fma -4.0 i (* 18.0 (* t (* y z)))))))
   (if (<= x -4.9e+58)
     t_1
     (if (<= x 4.4e+74) (fma (* k -27.0) j (* b c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = x * fma(-4.0, i, (18.0 * (t * (y * z))));
	double tmp;
	if (x <= -4.9e+58) {
		tmp = t_1;
	} else if (x <= 4.4e+74) {
		tmp = fma((k * -27.0), j, (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(x * fma(-4.0, i, Float64(18.0 * Float64(t * Float64(y * z)))))
	tmp = 0.0
	if (x <= -4.9e+58)
		tmp = t_1;
	elseif (x <= 4.4e+74)
		tmp = fma(Float64(k * -27.0), j, Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(x * N[(-4.0 * i + N[(18.0 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.9e+58], t$95$1, If[LessEqual[x, 4.4e+74], N[(N[(k * -27.0), $MachinePrecision] * j + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.90000000000000018e58 or 4.4000000000000002e74 < x

   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. Applied rewrites 89.7%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 43.0

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

   6. Applied rewrites 43.0%

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

   if -4.90000000000000018e58 < x < 4.4000000000000002e74

   1. Initial program 85.6%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 72.9

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 79.2%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(k \cdot -27, j, b \cdot c\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 44.6

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, b \cdot c\right) \]

   9. Applied rewrites 44.6%

      \[\leadsto \mathsf{fma}\left(k \cdot -27, j, b \cdot c\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 54.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -7 \cdot 10^{+169}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \mathbf{elif}\;b \cdot c \leq 2050:\\ \;\;\;\;\mathsf{fma}\left(-27, j \cdot k, -4 \cdot \left(i \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -7e+169)
   (- (* b c) (* 4.0 (* i x)))
   (if (<= (* b c) 2050.0)
     (fma -27.0 (* j k) (* -4.0 (* i x)))
     (fma (* k -27.0) j (* b c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -7e+169) {
		tmp = (b * c) - (4.0 * (i * x));
	} else if ((b * c) <= 2050.0) {
		tmp = fma(-27.0, (j * k), (-4.0 * (i * x)));
	} else {
		tmp = fma((k * -27.0), j, (b * c));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -7e+169)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(i * x)));
	elseif (Float64(b * c) <= 2050.0)
		tmp = fma(-27.0, Float64(j * k), Float64(-4.0 * Float64(i * x)));
	else
		tmp = fma(Float64(k * -27.0), j, Float64(b * c));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -7e+169], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2050.0], N[(-27.0 * N[(j * k), $MachinePrecision] + N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * -27.0), $MachinePrecision] * j + N[(b * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -7.00000000000000038e169

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 41.4

         \[\leadsto b \cdot c - 4 \cdot \left(i \cdot x\right) \]

   7. Applied rewrites 41.4%

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

   if -7.00000000000000038e169 < (*.f64 b c) < 2050

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

      1. lift--.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate--r+ N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. metadata-eval N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(i \cdot x\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      7. *-commutative N/A

         \[\leadsto \left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) - 27 \cdot \left(j \cdot k\right) \]

      8. associate-*l* N/A

         \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(b \cdot c + \left(-4 \cdot x\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right) \]

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + b \cdot c\right) - 27 \cdot \left(j \cdot k\right) \]

      12. *-commutative N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + c \cdot b\right) - 27 \cdot \left(j \cdot k\right) \]

      13. lift-*.f64 N/A

          \[\leadsto \left(\left(-4 \cdot x\right) \cdot i + c \cdot b\right) - 27 \cdot \left(j \cdot k\right) \]

      14. lift-fma.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. fp-cancel-sub-sign-inv N/A

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

      17. metadata-eval N/A

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

      18. lift-*.f64 N/A

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

      19. associate-*l* N/A

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

      20. lift-*.f64 N/A

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

      21. +-commutative N/A

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

   6. Applied rewrites 61.9%

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

   7. Taylor expanded in b around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, -4 \cdot \left(i \cdot x\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, -4 \cdot \left(i \cdot x\right)\right) \]

      4. lower-*.f64 41.7

         \[\leadsto \mathsf{fma}\left(-27, j \cdot k, -4 \cdot \left(i \cdot x\right)\right) \]

   9. Applied rewrites 41.7%

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

   if 2050 < (*.f64 b c)

   1. Initial program 85.6%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 72.9

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 79.2%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(k \cdot -27, j, b \cdot c\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 44.6

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, b \cdot c\right) \]

   9. Applied rewrites 44.6%

      \[\leadsto \mathsf{fma}\left(k \cdot -27, j, b \cdot c\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 53.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(k \cdot -27, j, b \cdot c\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+190}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* k -27.0) j (* b c))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -5e-16)
     t_1
     (if (<= t_2 1e+190) (- (* b c) (* 4.0 (* i x))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((k * -27.0), j, (b * c));
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e-16) {
		tmp = t_1;
	} else if (t_2 <= 1e+190) {
		tmp = (b * c) - (4.0 * (i * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(k * -27.0), j, Float64(b * c))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -5e-16)
		tmp = t_1;
	elseif (t_2 <= 1e+190)
		tmp = Float64(Float64(b * c) - Float64(4.0 * Float64(i * x)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(k * -27.0), $MachinePrecision] * j + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-16], t$95$1, If[LessEqual[t$95$2, 1e+190], N[(N[(b * c), $MachinePrecision] - N[(4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.0000000000000004e-16 or 1.0000000000000001e190 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.6%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 72.9

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 79.2%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(k \cdot -27, j, b \cdot c\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 44.6

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, b \cdot c\right) \]

   9. Applied rewrites 44.6%

      \[\leadsto \mathsf{fma}\left(k \cdot -27, j, b \cdot c\right) \]

   if -5.0000000000000004e-16 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.0000000000000001e190

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 60.8

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

   4. Applied rewrites 60.8%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 41.4

         \[\leadsto b \cdot c - 4 \cdot \left(i \cdot x\right) \]

   7. Applied rewrites 41.4%

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

Alternative 15: 47.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -4 \cdot \left(i \cdot x\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+167}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot -27, j, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -4.0 (* i x))))
   (if (<= x -4.8e+167)
     t_1
     (if (<= x 1.42e+78) (fma (* k -27.0) j (* b c)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -4.0 * (i * x);
	double tmp;
	if (x <= -4.8e+167) {
		tmp = t_1;
	} else if (x <= 1.42e+78) {
		tmp = fma((k * -27.0), j, (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-4.0 * Float64(i * x))
	tmp = 0.0
	if (x <= -4.8e+167)
		tmp = t_1;
	elseif (x <= 1.42e+78)
		tmp = fma(Float64(k * -27.0), j, Float64(b * c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.8e+167], t$95$1, If[LessEqual[x, 1.42e+78], N[(N[(k * -27.0), $MachinePrecision] * j + N[(b * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999998e167 or 1.42e78 < x

   1. Initial program 85.6%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 21.2

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

   4. Applied rewrites 21.2%

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

   if -4.79999999999999998e167 < x < 1.42e78

   1. Initial program 85.6%

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

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 72.9

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

   4. Applied rewrites 72.9%

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

   6. Applied rewrites 79.2%

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

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(k \cdot -27, j, b \cdot c\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 44.6

         \[\leadsto \mathsf{fma}\left(k \cdot -27, j, b \cdot c\right) \]

   9. Applied rewrites 44.6%

      \[\leadsto \mathsf{fma}\left(k \cdot -27, j, b \cdot c\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 34.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-234}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+193}:\\ \;\;\;\;-4 \cdot \left(i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -5e+133)
     t_1
     (if (<= t_2 1e-234)
       (* t (* -4.0 a))
       (if (<= t_2 5e+193) (* -4.0 (* i x)) t_1)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+133) {
		tmp = t_1;
	} else if (t_2 <= 1e-234) {
		tmp = t * (-4.0 * a);
	} else if (t_2 <= 5e+193) {
		tmp = -4.0 * (i * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-5d+133)) then
        tmp = t_1
    else if (t_2 <= 1d-234) then
        tmp = t * ((-4.0d0) * a)
    else if (t_2 <= 5d+193) then
        tmp = (-4.0d0) * (i * x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+133) {
		tmp = t_1;
	} else if (t_2 <= 1e-234) {
		tmp = t * (-4.0 * a);
	} else if (t_2 <= 5e+193) {
		tmp = -4.0 * (i * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -5e+133:
		tmp = t_1
	elif t_2 <= 1e-234:
		tmp = t * (-4.0 * a)
	elif t_2 <= 5e+193:
		tmp = -4.0 * (i * x)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -5e+133)
		tmp = t_1;
	elseif (t_2 <= 1e-234)
		tmp = Float64(t * Float64(-4.0 * a));
	elseif (t_2 <= 5e+193)
		tmp = Float64(-4.0 * Float64(i * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -5e+133)
		tmp = t_1;
	elseif (t_2 <= 1e-234)
		tmp = t * (-4.0 * a);
	elseif (t_2 <= 5e+193)
		tmp = -4.0 * (i * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+133], t$95$1, If[LessEqual[t$95$2, 1e-234], N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+193], N[(-4.0 * N[(i * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999961e133 or 4.99999999999999972e193 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.6%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.0

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

   4. Applied rewrites 24.0%

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

   if -4.99999999999999961e133 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.9999999999999996e-235

   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. Applied rewrites 89.7%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      5. lower-*.f64 42.8

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

   6. Applied rewrites 42.8%

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

   7. Taylor expanded in x around 0

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

      1. lower-*.f64 21.1

         \[\leadsto t \cdot \left(-4 \cdot a\right) \]

   9. Applied rewrites 21.1%

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

   if 9.9999999999999996e-235 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.99999999999999972e193

   1. Initial program 85.6%

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

   2. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 21.2

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

   4. Applied rewrites 21.2%

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

Alternative 17: 34.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i, j, k] = \mathsf{sort}([x, y, z, t, a, b, c, i, j, k])\\ \\ \begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+227}:\\ \;\;\;\;t \cdot \left(-4 \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* j k))) (t_2 (* (* j 27.0) k)))
   (if (<= t_2 -5e+133) t_1 (if (<= t_2 5e+227) (* t (* -4.0 a)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k);
double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+133) {
		tmp = t_1;
	} else if (t_2 <= 5e+227) {
		tmp = t * (-4.0 * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-27.0d0) * (j * k)
    t_2 = (j * 27.0d0) * k
    if (t_2 <= (-5d+133)) then
        tmp = t_1
    else if (t_2 <= 5d+227) then
        tmp = t * ((-4.0d0) * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i && i < j && j < k;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = -27.0 * (j * k);
	double t_2 = (j * 27.0) * k;
	double tmp;
	if (t_2 <= -5e+133) {
		tmp = t_1;
	} else if (t_2 <= 5e+227) {
		tmp = t * (-4.0 * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (j * k)
	t_2 = (j * 27.0) * k
	tmp = 0
	if t_2 <= -5e+133:
		tmp = t_1
	elif t_2 <= 5e+227:
		tmp = t * (-4.0 * a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b, c, i, j, k = sort([x, y, z, t, a, b, c, i, j, k])
function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(j * k))
	t_2 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_2 <= -5e+133)
		tmp = t_1;
	elseif (t_2 <= 5e+227)
		tmp = Float64(t * Float64(-4.0 * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (j * k);
	t_2 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_2 <= -5e+133)
		tmp = t_1;
	elseif (t_2 <= 5e+227)
		tmp = t * (-4.0 * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(j * k), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+133], t$95$1, If[LessEqual[t$95$2, 5e+227], N[(t * N[(-4.0 * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.99999999999999961e133 or 4.9999999999999996e227 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 85.6%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.0

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

   4. Applied rewrites 24.0%

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

   if -4.99999999999999961e133 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999996e227

   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. Applied rewrites 89.7%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

      5. lower-*.f64 42.8

         \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

   6. Applied rewrites 42.8%

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

   7. Taylor expanded in x around 0

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

      1. lower-*.f64 21.1

         \[\leadsto t \cdot \left(-4 \cdot a\right) \]

   9. Applied rewrites 21.1%

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

Alternative 18: 21.1% accurate, 6.4× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, b, c, i, j, and k should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c, i, j, k)
use fmin_fmax_functions
    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 = t * ((-4.0d0) * a)
end function

Java

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

Python

[x, y, z, t, a, b, c, i, j, k] = sort([x, y, z, t, a, b, c, i, j, k])
def code(x, y, z, t, a, b, c, i, j, k):
	return t * (-4.0 * a)

Julia

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

MATLAB

x, y, z, t, a, b, c, i, j, k = num2cell(sort([x, y, z, t, a, b, c, i, j, k])){:}
function tmp = code(x, y, z, t, a, b, c, i, j, k)
	tmp = t * (-4.0 * a);
end

Wolfram

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

Derivation

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. Applied rewrites 89.7%

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

4. Taylor expanded in t around inf

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

   1. lower-*.f64 N/A

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

   2. lower-fma.f64 N/A

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

   3. lower-*.f64 N/A

      \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

   4. lower-*.f64 N/A

      \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

   5. lower-*.f64 42.8

      \[\leadsto t \cdot \mathsf{fma}\left(-4, a, 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right) \]

6. Applied rewrites 42.8%

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

7. Taylor expanded in x around 0

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

   1. lower-*.f64 21.1

      \[\leadsto t \cdot \left(-4 \cdot a\right) \]

9. Applied rewrites 21.1%

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

Reproduce

herbie shell --seed 2025156 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))