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

Percentage Accurate: 85.4% → 93.6%

Time: 12.9s

Alternatives: 21

Speedup: 0.9×

• 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: 85.4% 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: 93.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+19} \lor \neg \left(t \leq 1.2 \cdot 10^{-46}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot x, y \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, t\_1\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma c b (* (* -4.0 x) i))))
   (if (or (<= t -1e+19) (not (<= t 1.2e-46)))
     (fma (* -27.0 j) k (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t t_1))
     (-
      (fma (* 18.0 x) (* y (* t z)) (fma (* -4.0 a) t t_1))
      (* (* j 27.0) k)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(c, b, ((-4.0 * x) * i));
	double tmp;
	if ((t <= -1e+19) || !(t <= 1.2e-46)) {
		tmp = fma((-27.0 * j), k, fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, t_1));
	} else {
		tmp = fma((18.0 * x), (y * (t * z)), fma((-4.0 * a), t, t_1)) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(c, b, Float64(Float64(-4.0 * x) * i))
	tmp = 0.0
	if ((t <= -1e+19) || !(t <= 1.2e-46))
		tmp = fma(Float64(-27.0 * j), k, fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, t_1));
	else
		tmp = Float64(fma(Float64(18.0 * x), Float64(y * Float64(t * z)), fma(Float64(-4.0 * a), t, t_1)) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(c * b + N[(N[(-4.0 * x), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -1e+19], N[Not[LessEqual[t, 1.2e-46]], $MachinePrecision]], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(18.0 * x), $MachinePrecision] * N[(y * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(N[(-4.0 * a), $MachinePrecision] * t + t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1e19 or 1.20000000000000007e-46 < t

   1. Initial program 87.6%

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

   4. Applied rewrites 97.1%

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

   if -1e19 < t < 1.20000000000000007e-46

   1. Initial program 84.3%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

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

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

      7. associate-+l+ N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*l* N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. lower-fma.f64 N/A

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

   4. Applied rewrites 96.5%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+19} \lor \neg \left(t \leq 1.2 \cdot 10^{-46}\right):\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot x, y \cdot \left(t \cdot z\right), \mathsf{fma}\left(-4 \cdot a, t, \mathsf{fma}\left(c, b, \left(-4 \cdot x\right) \cdot i\right)\right)\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot 18\right) \cdot y\\ \mathbf{if}\;\left(\left(\left(t\_1 \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 10^{+271}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(b, c, t \cdot \mathsf{fma}\left(t\_1, z, a \cdot -4\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* x 18.0) y)))
   (if (<=
        (- (+ (- (* (* t_1 z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))
        1e+271)
     (fma
      (* -27.0 j)
      k
      (fma (* i x) -4.0 (fma b c (* t (fma t_1 z (* a -4.0))))))
     (fma (* -4.0 x) i (fma (fma -4.0 a (* (* (* z y) x) 18.0)) t (* c b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (x * 18.0) * y;
	double tmp;
	if ((((((t_1 * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) <= 1e+271) {
		tmp = fma((-27.0 * j), k, fma((i * x), -4.0, fma(b, c, (t * fma(t_1, z, (a * -4.0))))));
	} else {
		tmp = fma((-4.0 * x), i, fma(fma(-4.0, a, (((z * y) * x) * 18.0)), t, (c * b)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(x * 18.0) * y)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(t_1 * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) <= 1e+271)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(i * x), -4.0, fma(b, c, Float64(t * fma(t_1, z, Float64(a * -4.0))))));
	else
		tmp = fma(Float64(-4.0 * x), i, fma(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)), t, Float64(c * b)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(t$95$1 * 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], 1e+271], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(b * c + N[(t * N[(t$95$1 * z + N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 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)) < 9.99999999999999953e270

   1. Initial program 94.9%

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

   4. Applied rewrites 95.5%

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

   6. Applied rewrites 95.5%

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

   if 9.99999999999999953e270 < (-.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 67.4%

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

   3. Taylor expanded in j around 0

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

   5. Applied rewrites 89.3%

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

Alternative 3: 82.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+127} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+149}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (or (<= t_1 -5e+127) (not (<= t_1 5e+149)))
     (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t (* (* k j) -27.0))
     (fma (* -4.0 x) i (fma (fma -4.0 a (* (* (* z y) x) 18.0)) t (* c b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if ((t_1 <= -5e+127) || !(t_1 <= 5e+149)) {
		tmp = fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, ((k * j) * -27.0));
	} else {
		tmp = fma((-4.0 * x), i, fma(fma(-4.0, a, (((z * y) * x) * 18.0)), t, (c * b)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if ((t_1 <= -5e+127) || !(t_1 <= 5e+149))
		tmp = fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, Float64(Float64(k * j) * -27.0));
	else
		tmp = fma(Float64(-4.0 * x), i, fma(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)), t, Float64(c * b)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+127], N[Not[LessEqual[t$95$1, 5e+149]], $MachinePrecision]], N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision], N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -5.0000000000000004e127 or 4.9999999999999999e149 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 80.3%

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

   4. Applied rewrites 88.2%

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

   5. Taylor expanded in j around inf

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

   7. Applied rewrites 76.8%

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

   if -5.0000000000000004e127 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999999e149

   1. Initial program 88.5%

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

   3. Taylor expanded in j around 0

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

   5. Applied rewrites 88.5%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -5 \cdot 10^{+127} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 5 \cdot 10^{+149}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, \left(k \cdot j\right) \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -0.002:\\ \;\;\;\;\mathsf{fma}\left(z \cdot \left(18 \cdot t\right), y \cdot x, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right) - t\_1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+149}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -0.002)
     (- (fma (* z (* 18.0 t)) (* y x) (* -4.0 (fma i x (* a t)))) t_1)
     (if (<= t_1 5e+149)
       (fma (* -4.0 x) i (fma (fma -4.0 a (* (* (* z y) x) 18.0)) t (* c b)))
       (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t (* (* k j) -27.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -0.002) {
		tmp = fma((z * (18.0 * t)), (y * x), (-4.0 * fma(i, x, (a * t)))) - t_1;
	} else if (t_1 <= 5e+149) {
		tmp = fma((-4.0 * x), i, fma(fma(-4.0, a, (((z * y) * x) * 18.0)), t, (c * b)));
	} else {
		tmp = fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, ((k * j) * -27.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_1 <= -0.002)
		tmp = Float64(fma(Float64(z * Float64(18.0 * t)), Float64(y * x), Float64(-4.0 * fma(i, x, Float64(a * t)))) - t_1);
	elseif (t_1 <= 5e+149)
		tmp = fma(Float64(-4.0 * x), i, fma(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)), t, Float64(c * b)));
	else
		tmp = fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, Float64(Float64(k * j) * -27.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -0.002], N[(N[(N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision] * N[(y * x), $MachinePrecision] + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 5e+149], N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e-3

   1. Initial program 81.6%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 75.7%

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

   if -2e-3 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 4.9999999999999999e149

   1. Initial program 89.1%

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

   3. Taylor expanded in j around 0

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

   5. Applied rewrites 90.8%

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

   if 4.9999999999999999e149 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.9%

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

   4. Applied rewrites 87.4%

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

   5. Taylor expanded in j around inf

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

   7. Applied rewrites 75.4%

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

Alternative 5: 80.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+39} \lor \neg \left(a \leq 4.5 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(\left(\left(z \cdot y\right) \cdot 18\right) \cdot x, t, \mathsf{fma}\left(c, b, -4 \cdot \left(x \cdot i\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= a -1.3e+39) (not (<= a 4.5e+18)))
   (fma (* -4.0 x) i (fma (fma -4.0 a (* (* (* z y) x) 18.0)) t (* c b)))
   (fma
    (* k j)
    -27.0
    (fma (* (* (* z y) 18.0) x) t (fma c b (* -4.0 (* x i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((a <= -1.3e+39) || !(a <= 4.5e+18)) {
		tmp = fma((-4.0 * x), i, fma(fma(-4.0, a, (((z * y) * x) * 18.0)), t, (c * b)));
	} else {
		tmp = fma((k * j), -27.0, fma((((z * y) * 18.0) * x), t, fma(c, b, (-4.0 * (x * i)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((a <= -1.3e+39) || !(a <= 4.5e+18))
		tmp = fma(Float64(-4.0 * x), i, fma(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)), t, Float64(c * b)));
	else
		tmp = fma(Float64(k * j), -27.0, fma(Float64(Float64(Float64(z * y) * 18.0) * x), t, fma(c, b, Float64(-4.0 * Float64(x * i)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[a, -1.3e+39], N[Not[LessEqual[a, 4.5e+18]], $MachinePrecision]], N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(N[(N[(N[(z * y), $MachinePrecision] * 18.0), $MachinePrecision] * x), $MachinePrecision] * t + N[(c * b + N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3e39 or 4.5e18 < a

   1. Initial program 82.8%

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

   3. Taylor expanded in j around 0

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

   5. Applied rewrites 88.0%

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

   if -1.3e39 < a < 4.5e18

   1. Initial program 89.0%

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

   4. Applied rewrites 90.5%

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

   6. Applied rewrites 89.0%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 83.3%

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

       1. lift-fma.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-*l* N/A

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

       4. *-commutative N/A

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

       5. lift-*.f64 N/A

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

       6. *-commutative N/A

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

       7. lower-fma.f64 83.3

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

       8. lift-fma.f64 N/A

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

       9. lift-fma.f64 N/A

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

       10. associate-+r+ N/A

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

       11. +-commutative N/A

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

   11. Applied rewrites 84.8%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+39} \lor \neg \left(a \leq 4.5 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(\left(\left(z \cdot y\right) \cdot 18\right) \cdot x, t, \mathsf{fma}\left(c, b, -4 \cdot \left(x \cdot i\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\\ \mathbf{if}\;k \leq 1.95 \cdot 10^{+95}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, t\_1\right), t, c \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{+261}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(b, c, t \cdot t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* (* z y) x) 18.0)))
   (if (<= k 1.95e+95)
     (fma (* -4.0 x) i (fma (fma -4.0 a t_1) t (* c b)))
     (if (<= k 1.55e+261)
       (fma (* -27.0 j) k (fma (* i x) -4.0 (fma b c (* t t_1))))
       (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t (* (* k j) -27.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((z * y) * x) * 18.0;
	double tmp;
	if (k <= 1.95e+95) {
		tmp = fma((-4.0 * x), i, fma(fma(-4.0, a, t_1), t, (c * b)));
	} else if (k <= 1.55e+261) {
		tmp = fma((-27.0 * j), k, fma((i * x), -4.0, fma(b, c, (t * t_1))));
	} else {
		tmp = fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, ((k * j) * -27.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(z * y) * x) * 18.0)
	tmp = 0.0
	if (k <= 1.95e+95)
		tmp = fma(Float64(-4.0 * x), i, fma(fma(-4.0, a, t_1), t, Float64(c * b)));
	elseif (k <= 1.55e+261)
		tmp = fma(Float64(-27.0 * j), k, fma(Float64(i * x), -4.0, fma(b, c, Float64(t * t_1))));
	else
		tmp = fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, Float64(Float64(k * j) * -27.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]}, If[LessEqual[k, 1.95e+95], N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(-4.0 * a + t$95$1), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 1.55e+261], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(b * c + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if k < 1.9499999999999999e95

   1. Initial program 88.7%

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

   3. Taylor expanded in j around 0

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

   5. Applied rewrites 81.7%

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

   if 1.9499999999999999e95 < k < 1.55e261

   1. Initial program 72.8%

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

   4. Applied rewrites 83.1%

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

   6. Applied rewrites 83.1%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 77.6%

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

   if 1.55e261 < k

   1. Initial program 66.7%

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

   4. Applied rewrites 88.9%

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

   5. Taylor expanded in j around inf

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

   7. Applied rewrites 99.8%

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

Alternative 7: 76.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;k \leq 2.6 \cdot 10^{+95}:\\ \;\;\;\;\mathsf{fma}\left(-4 \cdot x, i, \mathsf{fma}\left(\mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right), t, c \cdot b\right)\right)\\ \mathbf{elif}\;k \leq 9.8 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\left(\left(y \cdot z\right) \cdot x\right) \cdot t, 18, b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= k 2.6e+95)
   (fma (* -4.0 x) i (fma (fma -4.0 a (* (* (* z y) x) 18.0)) t (* c b)))
   (if (<= k 9.8e+204)
     (fma
      (* k j)
      -27.0
      (fma (* i x) -4.0 (fma (* (* (* y z) x) t) 18.0 (* b c))))
     (- (fma (* a t) -4.0 (* c b)) (* (* j 27.0) k)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (k <= 2.6e+95) {
		tmp = fma((-4.0 * x), i, fma(fma(-4.0, a, (((z * y) * x) * 18.0)), t, (c * b)));
	} else if (k <= 9.8e+204) {
		tmp = fma((k * j), -27.0, fma((i * x), -4.0, fma((((y * z) * x) * t), 18.0, (b * c))));
	} else {
		tmp = fma((a * t), -4.0, (c * b)) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (k <= 2.6e+95)
		tmp = fma(Float64(-4.0 * x), i, fma(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)), t, Float64(c * b)));
	elseif (k <= 9.8e+204)
		tmp = fma(Float64(k * j), -27.0, fma(Float64(i * x), -4.0, fma(Float64(Float64(Float64(y * z) * x) * t), 18.0, Float64(b * c))));
	else
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(c * b)) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[k, 2.6e+95], N[(N[(-4.0 * x), $MachinePrecision] * i + N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[k, 9.8e+204], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(N[(i * x), $MachinePrecision] * -4.0 + N[(N[(N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if k < 2.5999999999999999e95

   1. Initial program 88.7%

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

   3. Taylor expanded in j around 0

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

   5. Applied rewrites 81.7%

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

   if 2.5999999999999999e95 < k < 9.7999999999999995e204

   1. Initial program 88.2%

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

   4. Applied rewrites 88.2%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 90.4%

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

   if 9.7999999999999995e204 < k

   1. Initial program 59.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 69.1%

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

Alternative 8: 71.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right)\\ \mathbf{if}\;b \cdot c \leq -6 \cdot 10^{+101} \lor \neg \left(b \cdot c \leq 10^{+41}\right):\\ \;\;\;\;\mathsf{fma}\left(t\_1, t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, t, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma z (* y (* 18.0 x)) (* -4.0 a))))
   (if (or (<= (* b c) -6e+101) (not (<= (* b c) 1e+41)))
     (fma t_1 t (* b c))
     (fma t_1 t (* (* k j) -27.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(z, (y * (18.0 * x)), (-4.0 * a));
	double tmp;
	if (((b * c) <= -6e+101) || !((b * c) <= 1e+41)) {
		tmp = fma(t_1, t, (b * c));
	} else {
		tmp = fma(t_1, t, ((k * j) * -27.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a))
	tmp = 0.0
	if ((Float64(b * c) <= -6e+101) || !(Float64(b * c) <= 1e+41))
		tmp = fma(t_1, t, Float64(b * c));
	else
		tmp = fma(t_1, t, Float64(Float64(k * j) * -27.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(b * c), $MachinePrecision], -6e+101], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1e+41]], $MachinePrecision]], N[(t$95$1 * t + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * t + N[(N[(k * j), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -5.99999999999999986e101 or 1.00000000000000001e41 < (*.f64 b c)

   1. Initial program 83.6%

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

   4. Applied rewrites 91.8%

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

   5. Taylor expanded in b around inf

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

   7. Applied rewrites 83.3%

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

   if -5.99999999999999986e101 < (*.f64 b c) < 1.00000000000000001e41

   1. Initial program 87.6%

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

   4. Applied rewrites 90.2%

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

   5. Taylor expanded in j around inf

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

   7. Applied rewrites 74.5%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -6 \cdot 10^{+101} \lor \neg \left(b \cdot c \leq 10^{+41}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, \left(k \cdot j\right) \cdot -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right)\\ \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(t \cdot a\right) \cdot -4\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+132}:\\ \;\;\;\;\left(t \cdot \left(\left(y \cdot x\right) \cdot 18\right)\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* -27.0 j) k (* b c))))
   (if (<= (* b c) -4e+92)
     t_1
     (if (<= (* b c) 1e+53)
       (fma (* -27.0 j) k (* (* t a) -4.0))
       (if (<= (* b c) 2e+132) (* (* t (* (* y x) 18.0)) z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-27.0 * j), k, (b * c));
	double tmp;
	if ((b * c) <= -4e+92) {
		tmp = t_1;
	} else if ((b * c) <= 1e+53) {
		tmp = fma((-27.0 * j), k, ((t * a) * -4.0));
	} else if ((b * c) <= 2e+132) {
		tmp = (t * ((y * x) * 18.0)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-27.0 * j), k, Float64(b * c))
	tmp = 0.0
	if (Float64(b * c) <= -4e+92)
		tmp = t_1;
	elseif (Float64(b * c) <= 1e+53)
		tmp = fma(Float64(-27.0 * j), k, Float64(Float64(t * a) * -4.0));
	elseif (Float64(b * c) <= 2e+132)
		tmp = Float64(Float64(t * Float64(Float64(y * x) * 18.0)) * z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-27.0 * j), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -4e+92], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 1e+53], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+132], N[(N[(t * N[(N[(y * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -4.0000000000000002e92 or 1.99999999999999998e132 < (*.f64 b c)

   1. Initial program 80.5%

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

   4. Applied rewrites 90.8%

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

   5. Taylor expanded in b around inf

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

   7. Applied rewrites 61.2%

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

   if -4.0000000000000002e92 < (*.f64 b c) < 9.9999999999999999e52

   1. Initial program 88.9%

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

   4. Applied rewrites 92.0%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 54.1%

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

   if 9.9999999999999999e52 < (*.f64 b c) < 1.99999999999999998e132

   1. Initial program 90.9%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 61.9%

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

   7. Applied rewrites 71.1%

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

   9. Applied rewrites 71.0%

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

   11. Applied rewrites 71.2%

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

Alternative 10: 72.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-71}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, y \cdot \left(18 \cdot x\right), -4 \cdot a\right), t, b \cdot c\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)))
   (if (<= x -9.5e+100)
     t_1
     (if (<= x -6.4e-71)
       (fma (fma z (* y (* 18.0 x)) (* -4.0 a)) t (* b c))
       (if (<= x 1.3e+18)
         (- (fma (* a t) -4.0 (* c b)) (* (* j 27.0) k))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	double tmp;
	if (x <= -9.5e+100) {
		tmp = t_1;
	} else if (x <= -6.4e-71) {
		tmp = fma(fma(z, (y * (18.0 * x)), (-4.0 * a)), t, (b * c));
	} else if (x <= 1.3e+18) {
		tmp = fma((a * t), -4.0, (c * b)) - ((j * 27.0) * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x)
	tmp = 0.0
	if (x <= -9.5e+100)
		tmp = t_1;
	elseif (x <= -6.4e-71)
		tmp = fma(fma(z, Float64(y * Float64(18.0 * x)), Float64(-4.0 * a)), t, Float64(b * c));
	elseif (x <= 1.3e+18)
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(c * b)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -9.5e+100], t$95$1, If[LessEqual[x, -6.4e-71], N[(N[(z * N[(y * N[(18.0 * x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+18], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.4999999999999995e100 or 1.3e18 < x

   1. Initial program 78.1%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 78.6%

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

   if -9.4999999999999995e100 < x < -6.3999999999999998e-71

   1. Initial program 83.3%

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

   4. Applied rewrites 83.3%

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

   5. Taylor expanded in b around inf

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

   7. Applied rewrites 70.2%

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

   if -6.3999999999999998e-71 < x < 1.3e18

   1. Initial program 92.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 81.3%

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

Alternative 11: 49.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-27 \cdot j, k, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1700000000:\\ \;\;\;\;\left(y \cdot \left(\left(18 \cdot x\right) \cdot t\right)\right) \cdot z\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+170}:\\ \;\;\;\;\left(t \cdot \left(\left(y \cdot x\right) \cdot 18\right)\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma (* -27.0 j) k (* (* i x) -4.0))))
   (if (<= x -1.1e+182)
     t_1
     (if (<= x -1700000000.0)
       (* (* y (* (* 18.0 x) t)) z)
       (if (<= x 1.3e+18)
         (fma (* -27.0 j) k (* b c))
         (if (<= x 3.2e+170) (* (* t (* (* y x) 18.0)) z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma((-27.0 * j), k, ((i * x) * -4.0));
	double tmp;
	if (x <= -1.1e+182) {
		tmp = t_1;
	} else if (x <= -1700000000.0) {
		tmp = (y * ((18.0 * x) * t)) * z;
	} else if (x <= 1.3e+18) {
		tmp = fma((-27.0 * j), k, (b * c));
	} else if (x <= 3.2e+170) {
		tmp = (t * ((y * x) * 18.0)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(Float64(-27.0 * j), k, Float64(Float64(i * x) * -4.0))
	tmp = 0.0
	if (x <= -1.1e+182)
		tmp = t_1;
	elseif (x <= -1700000000.0)
		tmp = Float64(Float64(y * Float64(Float64(18.0 * x) * t)) * z);
	elseif (x <= 1.3e+18)
		tmp = fma(Float64(-27.0 * j), k, Float64(b * c));
	elseif (x <= 3.2e+170)
		tmp = Float64(Float64(t * Float64(Float64(y * x) * 18.0)) * z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+182], t$95$1, If[LessEqual[x, -1700000000.0], N[(N[(y * N[(N[(18.0 * x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, 1.3e+18], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+170], N[(N[(t * N[(N[(y * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.09999999999999998e182 or 3.19999999999999979e170 < x

   1. Initial program 67.6%

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

   4. Applied rewrites 79.9%

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

   5. Taylor expanded in i around inf

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

   7. Applied rewrites 63.2%

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

   if -1.09999999999999998e182 < x < -1.7e9

   1. Initial program 80.3%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 43.0%

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

   7. Applied rewrites 52.4%

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

   9. Applied rewrites 48.3%

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

   if -1.7e9 < x < 1.3e18

   1. Initial program 93.4%

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in b around inf

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

   7. Applied rewrites 52.9%

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

   if 1.3e18 < x < 3.19999999999999979e170

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 51.4%

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

   7. Applied rewrites 54.5%

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

   9. Applied rewrites 51.4%

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

   11. Applied rewrites 61.0%

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

Alternative 12: 59.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-4, a, \left(\left(z \cdot y\right) \cdot x\right) \cdot 18\right) \cdot t\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-284}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(i \cdot x\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma -4.0 a (* (* (* z y) x) 18.0)) t)))
   (if (<= t -5.4e-33)
     t_1
     (if (<= t 1.2e-284)
       (fma (* -27.0 j) k (* b c))
       (if (<= t 4e-27) (fma (* -27.0 j) k (* (* i x) -4.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = fma(-4.0, a, (((z * y) * x) * 18.0)) * t;
	double tmp;
	if (t <= -5.4e-33) {
		tmp = t_1;
	} else if (t <= 1.2e-284) {
		tmp = fma((-27.0 * j), k, (b * c));
	} else if (t <= 4e-27) {
		tmp = fma((-27.0 * j), k, ((i * x) * -4.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(-4.0, a, Float64(Float64(Float64(z * y) * x) * 18.0)) * t)
	tmp = 0.0
	if (t <= -5.4e-33)
		tmp = t_1;
	elseif (t <= 1.2e-284)
		tmp = fma(Float64(-27.0 * j), k, Float64(b * c));
	elseif (t <= 4e-27)
		tmp = fma(Float64(-27.0 * j), k, Float64(Float64(i * x) * -4.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(-4.0 * a + N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -5.4e-33], t$95$1, If[LessEqual[t, 1.2e-284], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-27], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(i * x), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.4000000000000002e-33 or 4.0000000000000002e-27 < t

   1. Initial program 87.2%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 68.0%

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

   if -5.4000000000000002e-33 < t < 1.20000000000000001e-284

   1. Initial program 87.0%

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

   4. Applied rewrites 87.0%

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

   5. Taylor expanded in b around inf

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

   7. Applied rewrites 61.6%

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

   if 1.20000000000000001e-284 < t < 4.0000000000000002e-27

   1. Initial program 82.5%

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

   4. Applied rewrites 84.2%

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

   5. Taylor expanded in i around inf

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

   7. Applied rewrites 54.1%

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

Alternative 13: 35.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+106}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq 10^{-88}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 10^{+41}:\\ \;\;\;\;\left(j \cdot -27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -2e+106)
   (* c b)
   (if (<= (* b c) 1e-88)
     (* (* a t) -4.0)
     (if (<= (* b c) 1e+41) (* (* j -27.0) k) (* c b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2e+106) {
		tmp = c * b;
	} else if ((b * c) <= 1e-88) {
		tmp = (a * t) * -4.0;
	} else if ((b * c) <= 1e+41) {
		tmp = (j * -27.0) * k;
	} else {
		tmp = c * b;
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((b * c) <= (-2d+106)) then
        tmp = c * b
    else if ((b * c) <= 1d-88) then
        tmp = (a * t) * (-4.0d0)
    else if ((b * c) <= 1d+41) then
        tmp = (j * (-27.0d0)) * k
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2e+106) {
		tmp = c * b;
	} else if ((b * c) <= 1e-88) {
		tmp = (a * t) * -4.0;
	} else if ((b * c) <= 1e+41) {
		tmp = (j * -27.0) * k;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -2e+106:
		tmp = c * b
	elif (b * c) <= 1e-88:
		tmp = (a * t) * -4.0
	elif (b * c) <= 1e+41:
		tmp = (j * -27.0) * k
	else:
		tmp = c * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -2e+106)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= 1e-88)
		tmp = Float64(Float64(a * t) * -4.0);
	elseif (Float64(b * c) <= 1e+41)
		tmp = Float64(Float64(j * -27.0) * k);
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -2e+106)
		tmp = c * b;
	elseif ((b * c) <= 1e-88)
		tmp = (a * t) * -4.0;
	elseif ((b * c) <= 1e+41)
		tmp = (j * -27.0) * k;
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -2e+106], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e-88], N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+41], N[(N[(j * -27.0), $MachinePrecision] * k), $MachinePrecision], N[(c * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.00000000000000018e106 or 1.00000000000000001e41 < (*.f64 b c)

   1. Initial program 84.1%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

   5. Applied rewrites 52.0%

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

   if -2.00000000000000018e106 < (*.f64 b c) < 9.99999999999999934e-89

   1. Initial program 86.6%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 31.6%

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

   if 9.99999999999999934e-89 < (*.f64 b c) < 1.00000000000000001e41

   1. Initial program 90.0%

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

   4. Applied rewrites 93.4%

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

   5. Taylor expanded in j around inf

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

   7. Applied rewrites 44.6%

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

   9. Applied rewrites 44.6%

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

Alternative 14: 35.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+106}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq 10^{-88}:\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{elif}\;b \cdot c \leq 10^{+41}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -2e+106)
   (* c b)
   (if (<= (* b c) 1e-88)
     (* (* a t) -4.0)
     (if (<= (* b c) 1e+41) (* -27.0 (* k j)) (* c b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2e+106) {
		tmp = c * b;
	} else if ((b * c) <= 1e-88) {
		tmp = (a * t) * -4.0;
	} else if ((b * c) <= 1e+41) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = c * b;
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((b * c) <= (-2d+106)) then
        tmp = c * b
    else if ((b * c) <= 1d-88) then
        tmp = (a * t) * (-4.0d0)
    else if ((b * c) <= 1d+41) then
        tmp = (-27.0d0) * (k * j)
    else
        tmp = c * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -2e+106) {
		tmp = c * b;
	} else if ((b * c) <= 1e-88) {
		tmp = (a * t) * -4.0;
	} else if ((b * c) <= 1e+41) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -2e+106:
		tmp = c * b
	elif (b * c) <= 1e-88:
		tmp = (a * t) * -4.0
	elif (b * c) <= 1e+41:
		tmp = -27.0 * (k * j)
	else:
		tmp = c * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (Float64(b * c) <= -2e+106)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= 1e-88)
		tmp = Float64(Float64(a * t) * -4.0);
	elseif (Float64(b * c) <= 1e+41)
		tmp = Float64(-27.0 * Float64(k * j));
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if ((b * c) <= -2e+106)
		tmp = c * b;
	elseif ((b * c) <= 1e-88)
		tmp = (a * t) * -4.0;
	elseif ((b * c) <= 1e+41)
		tmp = -27.0 * (k * j);
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[N[(b * c), $MachinePrecision], -2e+106], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e-88], N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 1e+41], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -2.00000000000000018e106 or 1.00000000000000001e41 < (*.f64 b c)

   1. Initial program 84.1%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

   5. Applied rewrites 52.0%

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

   if -2.00000000000000018e106 < (*.f64 b c) < 9.99999999999999934e-89

   1. Initial program 86.6%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 31.6%

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

   if 9.99999999999999934e-89 < (*.f64 b c) < 1.00000000000000001e41

   1. Initial program 90.0%

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

   3. Taylor expanded in j around inf

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

   5. Applied rewrites 44.6%

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

Alternative 15: 72.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{+49} \lor \neg \left(x \leq 1.3 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -2.85e+49) (not (<= x 1.3e+18)))
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (- (fma (* a t) -4.0 (* c b)) (* (* j 27.0) k))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2.85e+49) || !(x <= 1.3e+18)) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else {
		tmp = fma((a * t), -4.0, (c * b)) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -2.85e+49) || !(x <= 1.3e+18))
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	else
		tmp = Float64(fma(Float64(a * t), -4.0, Float64(c * b)) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -2.85e+49], N[Not[LessEqual[x, 1.3e+18]], $MachinePrecision]], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8499999999999999e49 or 1.3e18 < x

   1. Initial program 78.1%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 75.8%

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

   if -2.8499999999999999e49 < x < 1.3e18

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 78.3%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{+49} \lor \neg \left(x \leq 1.3 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot t, -4, c \cdot b\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 72.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{+49} \lor \neg \left(x \leq 1.3 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -2.85e+49) (not (<= x 1.3e+18)))
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (fma (* k j) -27.0 (fma (* t a) -4.0 (* b c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -2.85e+49) || !(x <= 1.3e+18)) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else {
		tmp = fma((k * j), -27.0, fma((t * a), -4.0, (b * c)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -2.85e+49) || !(x <= 1.3e+18))
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	else
		tmp = fma(Float64(k * j), -27.0, fma(Float64(t * a), -4.0, Float64(b * c)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -2.85e+49], N[Not[LessEqual[x, 1.3e+18]], $MachinePrecision]], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(k * j), $MachinePrecision] * -27.0 + N[(N[(t * a), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8499999999999999e49 or 1.3e18 < x

   1. Initial program 78.1%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 75.8%

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

   if -2.8499999999999999e49 < x < 1.3e18

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 78.3%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. associate-*l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

   7. Applied rewrites 78.2%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{+49} \lor \neg \left(x \leq 1.3 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(k \cdot j, -27, \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 58.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+62} \lor \neg \left(x \leq 1.2 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(t \cdot a\right) \cdot -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= x -7.2e+62) (not (<= x 1.2e+18)))
   (* (fma -4.0 i (* (* (* z y) t) 18.0)) x)
   (fma (* -27.0 j) k (* (* t a) -4.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((x <= -7.2e+62) || !(x <= 1.2e+18)) {
		tmp = fma(-4.0, i, (((z * y) * t) * 18.0)) * x;
	} else {
		tmp = fma((-27.0 * j), k, ((t * a) * -4.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((x <= -7.2e+62) || !(x <= 1.2e+18))
		tmp = Float64(fma(-4.0, i, Float64(Float64(Float64(z * y) * t) * 18.0)) * x);
	else
		tmp = fma(Float64(-27.0 * j), k, Float64(Float64(t * a) * -4.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[x, -7.2e+62], N[Not[LessEqual[x, 1.2e+18]], $MachinePrecision]], N[(N[(-4.0 * i + N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(t * a), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.2e62 or 1.2e18 < x

   1. Initial program 78.6%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 76.3%

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

   if -7.2e62 < x < 1.2e18

   1. Initial program 91.7%

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

   4. Applied rewrites 96.5%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 55.2%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+62} \lor \neg \left(x \leq 1.2 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(-4, i, \left(\left(z \cdot y\right) \cdot t\right) \cdot 18\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \left(t \cdot a\right) \cdot -4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+106} \lor \neg \left(b \cdot c \leq 10^{+41}\right):\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -2e+106) (not (<= (* b c) 1e+41)))
   (* c b)
   (* -27.0 (* k j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2e+106) || !((b * c) <= 1e+41)) {
		tmp = c * b;
	} else {
		tmp = -27.0 * (k * j);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (((b * c) <= (-2d+106)) .or. (.not. ((b * c) <= 1d+41))) then
        tmp = c * b
    else
        tmp = (-27.0d0) * (k * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (((b * c) <= -2e+106) || !((b * c) <= 1e+41)) {
		tmp = c * b;
	} else {
		tmp = -27.0 * (k * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if ((b * c) <= -2e+106) or not ((b * c) <= 1e+41):
		tmp = c * b
	else:
		tmp = -27.0 * (k * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((Float64(b * c) <= -2e+106) || !(Float64(b * c) <= 1e+41))
		tmp = Float64(c * b);
	else
		tmp = Float64(-27.0 * Float64(k * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0;
	if (((b * c) <= -2e+106) || ~(((b * c) <= 1e+41)))
		tmp = c * b;
	else
		tmp = -27.0 * (k * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[N[(b * c), $MachinePrecision], -2e+106], N[Not[LessEqual[N[(b * c), $MachinePrecision], 1e+41]], $MachinePrecision]], N[(c * b), $MachinePrecision], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -2.00000000000000018e106 or 1.00000000000000001e41 < (*.f64 b c)

   1. Initial program 84.1%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

   5. Applied rewrites 52.0%

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

   if -2.00000000000000018e106 < (*.f64 b c) < 1.00000000000000001e41

   1. Initial program 87.2%

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

   3. Taylor expanded in j around inf

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

   5. Applied rewrites 25.8%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -2 \cdot 10^{+106} \lor \neg \left(b \cdot c \leq 10^{+41}\right):\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 47.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1650000000:\\ \;\;\;\;y \cdot \left(\left(x \cdot 18\right) \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(y \cdot x\right) \cdot 18\right)\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -1650000000.0)
   (* y (* (* x 18.0) (* t z)))
   (if (<= x 1.3e+18)
     (fma (* -27.0 j) k (* b c))
     (* (* t (* (* y x) 18.0)) z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (x <= -1650000000.0) {
		tmp = y * ((x * 18.0) * (t * z));
	} else if (x <= 1.3e+18) {
		tmp = fma((-27.0 * j), k, (b * c));
	} else {
		tmp = (t * ((y * x) * 18.0)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -1650000000.0)
		tmp = Float64(y * Float64(Float64(x * 18.0) * Float64(t * z)));
	elseif (x <= 1.3e+18)
		tmp = fma(Float64(-27.0 * j), k, Float64(b * c));
	else
		tmp = Float64(Float64(t * Float64(Float64(y * x) * 18.0)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -1650000000.0], N[(y * N[(N[(x * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+18], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(y * x), $MachinePrecision] * 18.0), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65e9

   1. Initial program 73.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 40.3%

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

   7. Applied rewrites 47.4%

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

   if -1.65e9 < x < 1.3e18

   1. Initial program 93.4%

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in b around inf

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

   7. Applied rewrites 52.9%

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

   if 1.3e18 < x

   1. Initial program 83.1%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 46.8%

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

   7. Applied rewrites 46.6%

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

   9. Applied rewrites 44.8%

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

   11. Applied rewrites 54.0%

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

Alternative 20: 47.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+196} \lor \neg \left(a \leq 8.6 \cdot 10^{+167}\right):\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= a -1.35e+196) (not (<= a 8.6e+167)))
   (* (* a t) -4.0)
   (fma (* -27.0 j) k (* b c))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((a <= -1.35e+196) || !(a <= 8.6e+167)) {
		tmp = (a * t) * -4.0;
	} else {
		tmp = fma((-27.0 * j), k, (b * c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((a <= -1.35e+196) || !(a <= 8.6e+167))
		tmp = Float64(Float64(a * t) * -4.0);
	else
		tmp = fma(Float64(-27.0 * j), k, Float64(b * c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[a, -1.35e+196], N[Not[LessEqual[a, 8.6e+167]], $MachinePrecision]], N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(b * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.34999999999999998e196 or 8.6000000000000004e167 < a

   1. Initial program 83.9%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 67.6%

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

   if -1.34999999999999998e196 < a < 8.6000000000000004e167

   1. Initial program 86.7%

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

   4. Applied rewrites 90.7%

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

   5. Taylor expanded in b around inf

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

   7. Applied rewrites 45.7%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+196} \lor \neg \left(a \leq 8.6 \cdot 10^{+167}\right):\\ \;\;\;\;\left(a \cdot t\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 24.0% accurate, 11.3× speedup

Math

\[\begin{array}{l} \\ c \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b c i j k) :precision binary64 (* c b))

C

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

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 = c * b
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 c * b;
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(c * b), $MachinePrecision]

Derivation

1. Initial program 86.1%

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

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot c} \]
4. Step-by-step derivation

5. Applied rewrites 22.3%

   \[\leadsto \color{blue}{c \cdot b} \]
6. Add Preprocessing

Developer Target 1: 89.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

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 = ((a * t) + (i * x)) * 4.0d0
    t_2 = (((18.0d0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0d0) - (c * b))
    if (t < (-1.6210815397541398d-69)) then
        tmp = t_2
    else if (t < 165.68027943805222d0) then
        tmp = (((18.0d0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0d0 * (k * j)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((a * t) + (i * x)) * 4.0
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b))
	tmp = 0
	if t < -1.6210815397541398e-69:
		tmp = t_2
	elif t < 165.68027943805222:
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(a * t) + Float64(i * x)) * 4.0)
	t_2 = Float64(Float64(Float64(Float64(18.0 * t) * Float64(Float64(x * y) * z)) - t_1) - Float64(Float64(Float64(k * j) * 27.0) - Float64(c * b)))
	tmp = 0.0
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = Float64(Float64(Float64(Float64(18.0 * y) * Float64(x * Float64(z * t))) - t_1) + Float64(Float64(c * b) - Float64(27.0 * Float64(k * j))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((a * t) + (i * x)) * 4.0;
	t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	tmp = 0.0;
	if (t < -1.6210815397541398e-69)
		tmp = t_2;
	elseif (t < 165.68027943805222)
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(a * t), $MachinePrecision] + N[(i * x), $MachinePrecision]), $MachinePrecision] * 4.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(18.0 * t), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - N[(N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.6210815397541398e-69], t$95$2, If[Less[t, 165.68027943805222], N[(N[(N[(N[(18.0 * y), $MachinePrecision] * N[(x * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2025019 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8105407698770699/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 8284013971902611/50000000000000) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))))))

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