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

Percentage Accurate: 84.8% → 92.1%

Time: 8.1s

Alternatives: 20

Speedup: 0.6×

• 51.5% 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: 84.8% 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: 92.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* x 4.0) i)) (t_2 (* (* j 27.0) k)))
   (if (<=
        (-
         (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) t_1)
         t_2)
        INFINITY)
     (- (- (fma c b (* (fma (* (* y x) z) 18.0 (* -4.0 a)) t)) t_1) t_2)
     (fma c b (fma (* i -4.0) x (* (fma (* (* z y) x) 18.0 (* a -4.0)) t))))))

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

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

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

      14. associate-*l* N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. *-commutative N/A

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

   4. Applied rewrites 95.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 96.5

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

   6. Applied rewrites 96.5%

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

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

   1. Initial program 0.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

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

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

      14. associate-*l* N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. *-commutative N/A

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

   4. Applied rewrites 29.4%

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

   5. Taylor expanded in j around 0

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

   7. Applied rewrites 47.1%

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

   9. Applied rewrites 70.6%

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

Alternative 2: 64.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)\\ t_2 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -50000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+61}:\\ \;\;\;\;c \cdot b - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t\_2 \leq 10^{+297}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot y\right) \cdot z, 18, -4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma c b (* -4.0 (fma i x (* a t)))))
        (t_2
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i))))
   (if (<= t_2 -50000000000000.0)
     t_1
     (if (<= t_2 5e+61)
       (- (* c b) (* (* j 27.0) k))
       (if (<= t_2 1e+297) t_1 (* (fma (* (* t y) z) 18.0 (* -4.0 i)) x))))))

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 * fma(i, x, (a * t))));
	double t_2 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_2 <= -50000000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 5e+61) {
		tmp = (c * b) - ((j * 27.0) * k);
	} else if (t_2 <= 1e+297) {
		tmp = t_1;
	} else {
		tmp = fma(((t * y) * z), 18.0, (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t))))
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if (t_2 <= -50000000000000.0)
		tmp = t_1;
	elseif (t_2 <= 5e+61)
		tmp = Float64(Float64(c * b) - Float64(Float64(j * 27.0) * k));
	elseif (t_2 <= 1e+297)
		tmp = t_1;
	else
		tmp = Float64(fma(Float64(Float64(t * y) * z), 18.0, Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -50000000000000.0], t$95$1, If[LessEqual[t$95$2, 5e+61], N[(N[(c * b), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+297], t$95$1, N[(N[(N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < -5e13 or 5.00000000000000018e61 < (-.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)) < 1e297

   1. Initial program 91.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 80.8

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

   5. Applied rewrites 80.8%

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

   6. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. metadata-eval N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 69.1

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

   8. Applied rewrites 69.1%

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

   if -5e13 < (-.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)) < 5.00000000000000018e61

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 80.0

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

   5. Applied rewrites 80.0%

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

   if 1e297 < (-.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 63.5%

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

   3. Taylor expanded in i around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

   5. Applied rewrites 78.7%

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

   6. Taylor expanded in x around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 67.8

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

   8. Applied rewrites 67.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 70.4

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

   10. Applied rewrites 70.4%

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

Alternative 3: 63.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)\\ t_2 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -50000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+61}:\\ \;\;\;\;c \cdot b - \left(j \cdot 27\right) \cdot k\\ \mathbf{elif}\;t\_2 \leq 10^{+297}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma c b (* -4.0 (fma i x (* a t)))))
        (t_2
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i))))
   (if (<= t_2 -50000000000000.0)
     t_1
     (if (<= t_2 5e+61)
       (- (* c b) (* (* j 27.0) k))
       (if (<= t_2 1e+297) t_1 (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x))))))

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 * fma(i, x, (a * t))));
	double t_2 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_2 <= -50000000000000.0) {
		tmp = t_1;
	} else if (t_2 <= 5e+61) {
		tmp = (c * b) - ((j * 27.0) * k);
	} else if (t_2 <= 1e+297) {
		tmp = t_1;
	} else {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t))))
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if (t_2 <= -50000000000000.0)
		tmp = t_1;
	elseif (t_2 <= 5e+61)
		tmp = Float64(Float64(c * b) - Float64(Float64(j * 27.0) * k));
	elseif (t_2 <= 1e+297)
		tmp = t_1;
	else
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -50000000000000.0], t$95$1, If[LessEqual[t$95$2, 5e+61], N[(N[(c * b), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+297], t$95$1, N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < -5e13 or 5.00000000000000018e61 < (-.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)) < 1e297

   1. Initial program 91.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 80.8

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

   5. Applied rewrites 80.8%

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

   6. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. metadata-eval N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 69.1

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

   8. Applied rewrites 69.1%

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

   if -5e13 < (-.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)) < 5.00000000000000018e61

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 80.0

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

   5. Applied rewrites 80.0%

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

   if 1e297 < (-.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 63.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

         \[\leadsto \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right) \cdot x \]

      4. associate-*r* N/A

         \[\leadsto \left(\left(18 \cdot t\right) \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(4\right)\right) \cdot i\right) \cdot x \]

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 67.8

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

   5. Applied rewrites 67.8%

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

Alternative 4: 87.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 4 \cdot 10^{+217}\right):\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(i \cdot -4, x, \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, a \cdot -4\right) \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+217)))
     (fma c b (fma (* i -4.0) x (* (fma (* (* z y) x) 18.0 (* a -4.0)) t)))
     (fma (* -27.0 j) k (fma c b (* -4.0 (fma i x (* a t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 4e+217)) {
		tmp = fma(c, b, fma((i * -4.0), x, (fma(((z * y) * x), 18.0, (a * -4.0)) * t)));
	} else {
		tmp = fma((-27.0 * j), k, fma(c, b, (-4.0 * fma(i, x, (a * t)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 4e+217))
		tmp = fma(c, b, fma(Float64(i * -4.0), x, Float64(fma(Float64(Float64(z * y) * x), 18.0, Float64(a * -4.0)) * t)));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 4e+217]], $MachinePrecision]], N[(c * b + N[(N[(i * -4.0), $MachinePrecision] * x + N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $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)) < -inf.0 or 3.99999999999999984e217 < (-.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 72.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

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

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

      14. associate-*l* N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. *-commutative N/A

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

   4. Applied rewrites 79.5%

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

   5. Taylor expanded in j around 0

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

   7. Applied rewrites 80.5%

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

   9. Applied rewrites 85.8%

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

   if -inf.0 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x #s(literal 18 binary64)) y) z) t) (*.f64 (*.f64 a #s(literal 4 binary64)) t)) (*.f64 b c)) (*.f64 (*.f64 x #s(literal 4 binary64)) i)) < 3.99999999999999984e217

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 93.6

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

   5. Applied rewrites 93.6%

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

   6. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. distribute-lft-in N/A

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

      4. associate--r+ N/A

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

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

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

      6. metadata-eval N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. +-commutative N/A

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

      11. metadata-eval N/A

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

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

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

      13. associate--r+ N/A

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

   8. Applied rewrites 93.6%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq -\infty \lor \neg \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 4 \cdot 10^{+217}\right):\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(i \cdot -4, x, \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, a \cdot -4\right) \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.4% accurate, 0.5× speedup

Math

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

FPCore

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

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 96.4%

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

   3. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 94.3%

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

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

   1. Initial program 0.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

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

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

      14. associate-*l* N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. *-commutative N/A

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

   4. Applied rewrites 29.4%

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

   5. Taylor expanded in j around 0

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

   7. Applied rewrites 47.1%

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

   9. Applied rewrites 70.6%

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

Alternative 6: 91.4% accurate, 0.6× speedup

Math

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

FPCore

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

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[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], Infinity], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(N[(18.0 * t), $MachinePrecision] * N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] + N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $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)) < +inf.0

   1. Initial program 91.9%

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

   3. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. associate--l+ N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

   5. Applied rewrites 93.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

   5. Applied rewrites 56.5%

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

   6. Taylor expanded in x around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 78.4

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

   8. Applied rewrites 78.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 78.4

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

   10. Applied rewrites 78.4%

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

Alternative 7: 48.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ t_3 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 10^{-55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+90}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{elif}\;t\_3 \leq 10^{+296}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* k j)))
        (t_2 (fma c b (* (* a t) -4.0)))
        (t_3 (* (* j 27.0) k)))
   (if (<= t_3 -2e+203)
     t_1
     (if (<= t_3 1e-55)
       t_2
       (if (<= t_3 5e+90) (* (* -4.0 i) x) (if (<= t_3 1e+296) t_2 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 = -27.0 * (k * j);
	double t_2 = fma(c, b, ((a * t) * -4.0));
	double t_3 = (j * 27.0) * k;
	double tmp;
	if (t_3 <= -2e+203) {
		tmp = t_1;
	} else if (t_3 <= 1e-55) {
		tmp = t_2;
	} else if (t_3 <= 5e+90) {
		tmp = (-4.0 * i) * x;
	} else if (t_3 <= 1e+296) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(k * j))
	t_2 = fma(c, b, Float64(Float64(a * t) * -4.0))
	t_3 = Float64(Float64(j * 27.0) * k)
	tmp = 0.0
	if (t_3 <= -2e+203)
		tmp = t_1;
	elseif (t_3 <= 1e-55)
		tmp = t_2;
	elseif (t_3 <= 5e+90)
		tmp = Float64(Float64(-4.0 * i) * x);
	elseif (t_3 <= 1e+296)
		tmp = t_2;
	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[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * b + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+203], t$95$1, If[LessEqual[t$95$3, 1e-55], t$95$2, If[LessEqual[t$95$3, 5e+90], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$3, 1e+296], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e203 or 9.99999999999999981e295 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 71.9%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 64.1

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

   5. Applied rewrites 64.1%

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

   if -2e203 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999995e-56 or 5.0000000000000004e90 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999981e295

   1. Initial program 87.1%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

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

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

      14. associate-*l* N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. *-commutative N/A

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

   4. Applied rewrites 89.5%

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

   5. Taylor expanded in j around 0

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

   7. Applied rewrites 82.8%

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

   8. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 51.8

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

   10. Applied rewrites 51.8%

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

       1. lift-*.f64 N/A

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

       2. lift-fma.f64 N/A

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

       3. +-commutative N/A

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

       4. *-commutative N/A

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

       5. lift-*.f64 N/A

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

       6. *-commutative N/A

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

       7. *-commutative N/A

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

       8. lower-fma.f64 N/A

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

       9. *-commutative N/A

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

       10. lower-*.f64 N/A

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

       11. lower-*.f64 51.8

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

   12. Applied rewrites 51.8%

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

   if 9.99999999999999995e-56 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.0000000000000004e90

   1. Initial program 86.2%

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

   3. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 50.4

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

   5. Applied rewrites 50.4%

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

Alternative 8: 35.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -1 \cdot 10^{+129}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{+22}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{elif}\;b \cdot c \leq -5.5 \cdot 10^{-164}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-188}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-11}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -1e+129)
   (* c b)
   (if (<= (* b c) -2e+22)
     (* (* -4.0 i) x)
     (if (<= (* b c) -5.5e-164)
       (* (* -27.0 j) k)
       (if (<= (* b c) 5e-188)
         (* -4.0 (* a t))
         (if (<= (* b c) 2e-11) (* -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) <= -1e+129) {
		tmp = c * b;
	} else if ((b * c) <= -2e+22) {
		tmp = (-4.0 * i) * x;
	} else if ((b * c) <= -5.5e-164) {
		tmp = (-27.0 * j) * k;
	} else if ((b * c) <= 5e-188) {
		tmp = -4.0 * (a * t);
	} else if ((b * c) <= 2e-11) {
		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) <= (-1d+129)) then
        tmp = c * b
    else if ((b * c) <= (-2d+22)) then
        tmp = ((-4.0d0) * i) * x
    else if ((b * c) <= (-5.5d-164)) then
        tmp = ((-27.0d0) * j) * k
    else if ((b * c) <= 5d-188) then
        tmp = (-4.0d0) * (a * t)
    else if ((b * c) <= 2d-11) 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) <= -1e+129) {
		tmp = c * b;
	} else if ((b * c) <= -2e+22) {
		tmp = (-4.0 * i) * x;
	} else if ((b * c) <= -5.5e-164) {
		tmp = (-27.0 * j) * k;
	} else if ((b * c) <= 5e-188) {
		tmp = -4.0 * (a * t);
	} else if ((b * c) <= 2e-11) {
		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) <= -1e+129:
		tmp = c * b
	elif (b * c) <= -2e+22:
		tmp = (-4.0 * i) * x
	elif (b * c) <= -5.5e-164:
		tmp = (-27.0 * j) * k
	elif (b * c) <= 5e-188:
		tmp = -4.0 * (a * t)
	elif (b * c) <= 2e-11:
		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) <= -1e+129)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= -2e+22)
		tmp = Float64(Float64(-4.0 * i) * x);
	elseif (Float64(b * c) <= -5.5e-164)
		tmp = Float64(Float64(-27.0 * j) * k);
	elseif (Float64(b * c) <= 5e-188)
		tmp = Float64(-4.0 * Float64(a * t));
	elseif (Float64(b * c) <= 2e-11)
		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) <= -1e+129)
		tmp = c * b;
	elseif ((b * c) <= -2e+22)
		tmp = (-4.0 * i) * x;
	elseif ((b * c) <= -5.5e-164)
		tmp = (-27.0 * j) * k;
	elseif ((b * c) <= 5e-188)
		tmp = -4.0 * (a * t);
	elseif ((b * c) <= 2e-11)
		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], -1e+129], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2e+22], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5.5e-164], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e-188], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e-11], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 b c) < -1e129 or 1.99999999999999988e-11 < (*.f64 b c)

   1. Initial program 77.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 54.0

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

   5. Applied rewrites 54.0%

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

   if -1e129 < (*.f64 b c) < -2e22

   1. Initial program 85.4%

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

   3. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 42.4

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

   5. Applied rewrites 42.4%

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

   if -2e22 < (*.f64 b c) < -5.50000000000000027e-164

   1. Initial program 88.8%

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 45.6

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

   5. Applied rewrites 45.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 45.7

         \[\leadsto \left(-27 \cdot j\right) \cdot k \]

   7. Applied rewrites 45.7%

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

   if -5.50000000000000027e-164 < (*.f64 b c) < 5.0000000000000001e-188

   1. Initial program 89.8%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 33.5

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

   5. Applied rewrites 33.5%

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

   if 5.0000000000000001e-188 < (*.f64 b c) < 1.99999999999999988e-11

   1. Initial program 82.3%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 37.2

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

   5. Applied rewrites 37.2%

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

Alternative 9: 66.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, x, a \cdot t\right)\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+306}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot y\right) \cdot z, 18, -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-11}:\\ \;\;\;\;-\mathsf{fma}\left(t\_1, 4, \left(k \cdot j\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma i x (* a t))))
   (if (<= (* b c) -5e+306)
     (* c b)
     (if (<= (* b c) -2e+59)
       (* (fma (* (* t y) z) 18.0 (* -4.0 i)) x)
       (if (<= (* b c) 2e-11)
         (- (fma t_1 4.0 (* (* k j) 27.0)))
         (fma c b (* -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(i, x, (a * t));
	double tmp;
	if ((b * c) <= -5e+306) {
		tmp = c * b;
	} else if ((b * c) <= -2e+59) {
		tmp = fma(((t * y) * z), 18.0, (-4.0 * i)) * x;
	} else if ((b * c) <= 2e-11) {
		tmp = -fma(t_1, 4.0, ((k * j) * 27.0));
	} else {
		tmp = fma(c, b, (-4.0 * t_1));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = fma(i, x, Float64(a * t))
	tmp = 0.0
	if (Float64(b * c) <= -5e+306)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= -2e+59)
		tmp = Float64(fma(Float64(Float64(t * y) * z), 18.0, Float64(-4.0 * i)) * x);
	elseif (Float64(b * c) <= 2e-11)
		tmp = Float64(-fma(t_1, 4.0, Float64(Float64(k * j) * 27.0)));
	else
		tmp = fma(c, b, Float64(-4.0 * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5e+306], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2e+59], N[(N[(N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e-11], (-N[(t$95$1 * 4.0 + N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), N[(c * b + N[(-4.0 * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -4.99999999999999993e306

   1. Initial program 61.1%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 89.7

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

   5. Applied rewrites 89.7%

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

   if -4.99999999999999993e306 < (*.f64 b c) < -1.99999999999999994e59

   1. Initial program 69.9%

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

   3. Taylor expanded in i around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

   5. Applied rewrites 91.5%

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

   6. Taylor expanded in x around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 61.8

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

   8. Applied rewrites 61.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 65.9

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

   10. Applied rewrites 65.9%

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

   if -1.99999999999999994e59 < (*.f64 b c) < 1.99999999999999988e-11

   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 y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 73.5

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

   5. Applied rewrites 73.5%

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

   6. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. distribute-lft-in N/A

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

      3. associate-+r+ N/A

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

      4. lower-neg.f64 N/A

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

      5. associate-+r+ N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lift-*.f64 71.6

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

   8. Applied rewrites 71.6%

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

   if 1.99999999999999988e-11 < (*.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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 77.2

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

   5. Applied rewrites 77.2%

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

   6. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. metadata-eval N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 78.8

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

   8. Applied rewrites 78.8%

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

Alternative 10: 35.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+122}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq -5.5 \cdot 10^{-164}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-188}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-11}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -5e+122)
   (* c b)
   (if (<= (* b c) -5.5e-164)
     (* (* -27.0 j) k)
     (if (<= (* b c) 5e-188)
       (* -4.0 (* a t))
       (if (<= (* b c) 2e-11) (* -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) <= -5e+122) {
		tmp = c * b;
	} else if ((b * c) <= -5.5e-164) {
		tmp = (-27.0 * j) * k;
	} else if ((b * c) <= 5e-188) {
		tmp = -4.0 * (a * t);
	} else if ((b * c) <= 2e-11) {
		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) <= (-5d+122)) then
        tmp = c * b
    else if ((b * c) <= (-5.5d-164)) then
        tmp = ((-27.0d0) * j) * k
    else if ((b * c) <= 5d-188) then
        tmp = (-4.0d0) * (a * t)
    else if ((b * c) <= 2d-11) 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) <= -5e+122) {
		tmp = c * b;
	} else if ((b * c) <= -5.5e-164) {
		tmp = (-27.0 * j) * k;
	} else if ((b * c) <= 5e-188) {
		tmp = -4.0 * (a * t);
	} else if ((b * c) <= 2e-11) {
		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) <= -5e+122:
		tmp = c * b
	elif (b * c) <= -5.5e-164:
		tmp = (-27.0 * j) * k
	elif (b * c) <= 5e-188:
		tmp = -4.0 * (a * t)
	elif (b * c) <= 2e-11:
		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) <= -5e+122)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= -5.5e-164)
		tmp = Float64(Float64(-27.0 * j) * k);
	elseif (Float64(b * c) <= 5e-188)
		tmp = Float64(-4.0 * Float64(a * t));
	elseif (Float64(b * c) <= 2e-11)
		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) <= -5e+122)
		tmp = c * b;
	elseif ((b * c) <= -5.5e-164)
		tmp = (-27.0 * j) * k;
	elseif ((b * c) <= 5e-188)
		tmp = -4.0 * (a * t);
	elseif ((b * c) <= 2e-11)
		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], -5e+122], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5.5e-164], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e-188], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e-11], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 b c) < -4.99999999999999989e122 or 1.99999999999999988e-11 < (*.f64 b c)

   1. Initial program 76.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 53.5

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

   5. Applied rewrites 53.5%

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

   if -4.99999999999999989e122 < (*.f64 b c) < -5.50000000000000027e-164

   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 inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 34.1

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

   5. Applied rewrites 34.1%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 34.2

         \[\leadsto \left(-27 \cdot j\right) \cdot k \]

   7. Applied rewrites 34.2%

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

   if -5.50000000000000027e-164 < (*.f64 b c) < 5.0000000000000001e-188

   1. Initial program 89.8%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 33.5

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

   5. Applied rewrites 33.5%

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

   if 5.0000000000000001e-188 < (*.f64 b c) < 1.99999999999999988e-11

   1. Initial program 82.3%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 37.2

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

   5. Applied rewrites 37.2%

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

Alternative 11: 35.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+122}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq -5.5 \cdot 10^{-164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{-188}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* -27.0 (* k j))))
   (if (<= (* b c) -5e+122)
     (* c b)
     (if (<= (* b c) -5.5e-164)
       t_1
       (if (<= (* b c) 5e-188)
         (* -4.0 (* a t))
         (if (<= (* b c) 2e-11) t_1 (* 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 = -27.0 * (k * j);
	double tmp;
	if ((b * c) <= -5e+122) {
		tmp = c * b;
	} else if ((b * c) <= -5.5e-164) {
		tmp = t_1;
	} else if ((b * c) <= 5e-188) {
		tmp = -4.0 * (a * t);
	} else if ((b * c) <= 2e-11) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (-27.0d0) * (k * j)
    if ((b * c) <= (-5d+122)) then
        tmp = c * b
    else if ((b * c) <= (-5.5d-164)) then
        tmp = t_1
    else if ((b * c) <= 5d-188) then
        tmp = (-4.0d0) * (a * t)
    else if ((b * c) <= 2d-11) then
        tmp = t_1
    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 t_1 = -27.0 * (k * j);
	double tmp;
	if ((b * c) <= -5e+122) {
		tmp = c * b;
	} else if ((b * c) <= -5.5e-164) {
		tmp = t_1;
	} else if ((b * c) <= 5e-188) {
		tmp = -4.0 * (a * t);
	} else if ((b * c) <= 2e-11) {
		tmp = t_1;
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = -27.0 * (k * j)
	tmp = 0
	if (b * c) <= -5e+122:
		tmp = c * b
	elif (b * c) <= -5.5e-164:
		tmp = t_1
	elif (b * c) <= 5e-188:
		tmp = -4.0 * (a * t)
	elif (b * c) <= 2e-11:
		tmp = t_1
	else:
		tmp = c * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(-27.0 * Float64(k * j))
	tmp = 0.0
	if (Float64(b * c) <= -5e+122)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= -5.5e-164)
		tmp = t_1;
	elseif (Float64(b * c) <= 5e-188)
		tmp = Float64(-4.0 * Float64(a * t));
	elseif (Float64(b * c) <= 2e-11)
		tmp = t_1;
	else
		tmp = Float64(c * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = -27.0 * (k * j);
	tmp = 0.0;
	if ((b * c) <= -5e+122)
		tmp = c * b;
	elseif ((b * c) <= -5.5e-164)
		tmp = t_1;
	elseif ((b * c) <= 5e-188)
		tmp = -4.0 * (a * t);
	elseif ((b * c) <= 2e-11)
		tmp = t_1;
	else
		tmp = c * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * c), $MachinePrecision], -5e+122], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -5.5e-164], t$95$1, If[LessEqual[N[(b * c), $MachinePrecision], 5e-188], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e-11], t$95$1, N[(c * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -4.99999999999999989e122 or 1.99999999999999988e-11 < (*.f64 b c)

   1. Initial program 76.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 53.5

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

   5. Applied rewrites 53.5%

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

   if -4.99999999999999989e122 < (*.f64 b c) < -5.50000000000000027e-164 or 5.0000000000000001e-188 < (*.f64 b c) < 1.99999999999999988e-11

   1. Initial program 86.5%

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 35.3

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

   5. Applied rewrites 35.3%

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

   if -5.50000000000000027e-164 < (*.f64 b c) < 5.0000000000000001e-188

   1. Initial program 89.8%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 33.5

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

   5. Applied rewrites 33.5%

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

Alternative 12: 66.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+281} \lor \neg \left(t\_1 \leq 10^{+296}\right):\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)\\ \end{array} \end{array} \]

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 -4e+281) (not (<= t_1 1e+296)))
     (* -27.0 (* k j))
     (fma c b (* -4.0 (fma i x (* a t)))))))

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 <= -4e+281) || !(t_1 <= 1e+296)) {
		tmp = -27.0 * (k * j);
	} else {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t))));
	}
	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 <= -4e+281) || !(t_1 <= 1e+296))
		tmp = Float64(-27.0 * Float64(k * j));
	else
		tmp = fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t))));
	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, -4e+281], N[Not[LessEqual[t$95$1, 1e+296]], $MachinePrecision]], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -4.0000000000000001e281 or 9.99999999999999981e295 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 68.1%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 73.5

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

   5. Applied rewrites 73.5%

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

   if -4.0000000000000001e281 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999981e295

   1. Initial program 86.8%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 74.0

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

   5. Applied rewrites 74.0%

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

   6. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. metadata-eval N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 66.9

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

   8. Applied rewrites 66.9%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(j \cdot 27\right) \cdot k \leq -4 \cdot 10^{+281} \lor \neg \left(\left(j \cdot 27\right) \cdot k \leq 10^{+296}\right):\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+203}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x - j \cdot \left(k \cdot 27\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+296}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -2e+203)
     (- (* (* -4.0 i) x) (* j (* k 27.0)))
     (if (<= t_1 1e+296)
       (fma c b (* -4.0 (fma i x (* a t))))
       (* -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 t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+203) {
		tmp = ((-4.0 * i) * x) - (j * (k * 27.0));
	} else if (t_1 <= 1e+296) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (a * t))));
	} else {
		tmp = -27.0 * (k * j);
	}
	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 <= -2e+203)
		tmp = Float64(Float64(Float64(-4.0 * i) * x) - Float64(j * Float64(k * 27.0)));
	elseif (t_1 <= 1e+296)
		tmp = fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t))));
	else
		tmp = Float64(-27.0 * Float64(k * j));
	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, -2e+203], N[(N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+296], N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2e203

   1. Initial program 72.5%

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

   3. Taylor expanded in i around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 63.6

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

   5. Applied rewrites 63.6%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 63.6

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

   7. Applied rewrites 63.6%

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

   if -2e203 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 9.99999999999999981e295

   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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 74.2

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

   5. Applied rewrites 74.2%

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

   6. Taylor expanded in j around 0

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

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

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. metadata-eval N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 67.7

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

   8. Applied rewrites 67.7%

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

   if 9.99999999999999981e295 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 70.5%

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

   3. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 77.3

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

   5. Applied rewrites 77.3%

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

Alternative 14: 75.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-68} \lor \neg \left(t \leq 3.1 \cdot 10^{-52}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, a \cdot -4\right), t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= t -1.15e-68) (not (<= t 3.1e-52)))
   (fma (fma (* (* z y) x) 18.0 (* a -4.0)) t (* b c))
   (- (* c b) (fma (* i x) 4.0 (* (* 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 tmp;
	if ((t <= -1.15e-68) || !(t <= 3.1e-52)) {
		tmp = fma(fma(((z * y) * x), 18.0, (a * -4.0)), t, (b * c));
	} else {
		tmp = (c * b) - fma((i * x), 4.0, ((k * j) * 27.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((t <= -1.15e-68) || !(t <= 3.1e-52))
		tmp = fma(fma(Float64(Float64(z * y) * x), 18.0, Float64(a * -4.0)), t, Float64(b * c));
	else
		tmp = Float64(Float64(c * b) - fma(Float64(i * x), 4.0, Float64(Float64(k * j) * 27.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[t, -1.15e-68], N[Not[LessEqual[t, 3.1e-52]], $MachinePrecision]], N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(c * b), $MachinePrecision] - N[(N[(i * x), $MachinePrecision] * 4.0 + N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.14999999999999998e-68 or 3.0999999999999999e-52 < t

   1. Initial program 83.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

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

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

      14. associate-*l* N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. *-commutative N/A

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

   4. Applied rewrites 88.5%

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

   5. Taylor expanded in j around 0

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

   7. Applied rewrites 79.5%

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

   8. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 74.6

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

   10. Applied rewrites 74.6%

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

   if -1.14999999999999998e-68 < t < 3.0999999999999999e-52

   1. Initial program 84.5%

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

   3. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 81.7

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

   5. Applied rewrites 81.7%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-68} \lor \neg \left(t \leq 3.1 \cdot 10^{-52}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, a \cdot -4\right), t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b - \mathsf{fma}\left(i \cdot x, 4, \left(k \cdot j\right) \cdot 27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 71.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot y\right) \cdot z, 18, -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+42}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t\right)\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(z \cdot y\right) \cdot t, 18, -4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= x -2.1e-19)
   (* (fma (* (* t y) z) 18.0 (* -4.0 i)) x)
   (if (<= x 1.05e+42)
     (- (fma c b (* -4.0 (* a t))) (* (* j 27.0) k))
     (* (fma (* (* z y) t) 18.0 (* -4.0 i)) x))))

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 <= -2.1e-19) {
		tmp = fma(((t * y) * z), 18.0, (-4.0 * i)) * x;
	} else if (x <= 1.05e+42) {
		tmp = fma(c, b, (-4.0 * (a * t))) - ((j * 27.0) * k);
	} else {
		tmp = fma(((z * y) * t), 18.0, (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (x <= -2.1e-19)
		tmp = Float64(fma(Float64(Float64(t * y) * z), 18.0, Float64(-4.0 * i)) * x);
	elseif (x <= 1.05e+42)
		tmp = Float64(fma(c, b, Float64(-4.0 * Float64(a * t))) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(fma(Float64(Float64(z * y) * t), 18.0, Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[x, -2.1e-19], N[(N[(N[(N[(t * y), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 1.05e+42], N[(N[(c * b + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(z * y), $MachinePrecision] * t), $MachinePrecision] * 18.0 + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.0999999999999999e-19

   1. Initial program 75.1%

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

   3. Taylor expanded in i around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

   5. Applied rewrites 84.8%

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

   6. Taylor expanded in x around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 67.9

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

   8. Applied rewrites 67.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 68.1

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

   10. Applied rewrites 68.1%

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

   if -2.0999999999999999e-19 < x < 1.04999999999999998e42

   1. Initial program 93.0%

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 78.2

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

   5. Applied rewrites 78.2%

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

   if 1.04999999999999998e42 < x

   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

   3. Taylor expanded in i around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

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

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

   5. Applied rewrites 85.5%

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

   6. Taylor expanded in x around inf

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

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

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 80.7

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

   8. Applied rewrites 80.7%

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

Alternative 16: 79.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+202}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, a \cdot -4\right), t, b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-27 \cdot j, k, \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= y -2.9e+202)
   (fma (fma (* (* z y) x) 18.0 (* a -4.0)) t (* b c))
   (fma (* -27.0 j) k (fma c b (* -4.0 (fma i x (* a t)))))))

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 (y <= -2.9e+202) {
		tmp = fma(fma(((z * y) * x), 18.0, (a * -4.0)), t, (b * c));
	} else {
		tmp = fma((-27.0 * j), k, fma(c, b, (-4.0 * fma(i, x, (a * t)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (y <= -2.9e+202)
		tmp = fma(fma(Float64(Float64(z * y) * x), 18.0, Float64(a * -4.0)), t, Float64(b * c));
	else
		tmp = fma(Float64(-27.0 * j), k, fma(c, b, Float64(-4.0 * fma(i, x, Float64(a * t)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[y, -2.9e+202], N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(a * -4.0), $MachinePrecision]), $MachinePrecision] * t + N[(b * c), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k + N[(c * b + N[(-4.0 * N[(i * x + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8999999999999999e202

   1. Initial program 70.4%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

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

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

      14. associate-*l* N/A

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

      15. *-commutative N/A

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

      16. associate-*r* N/A

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

      17. *-commutative N/A

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

   4. Applied rewrites 74.1%

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

   5. Taylor expanded in j around 0

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

   7. Applied rewrites 74.9%

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

   8. Taylor expanded in i around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 78.6

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

   10. Applied rewrites 78.6%

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

   if -2.8999999999999999e202 < y

   1. Initial program 85.2%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. distribute-lft-out N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 76.4

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

   5. Applied rewrites 76.4%

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

   6. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. distribute-lft-in N/A

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

      4. associate--r+ N/A

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

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

         \[\leadsto \left(-27 \cdot j\right) \cdot k + \left(\left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(\color{blue}{i} \cdot x\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot k + \left(\left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(i \cdot x\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \left(-27 \cdot j\right) \cdot k + \left(\left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 4 \cdot \left(\color{blue}{i} \cdot x\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \left(-4 \cdot \left(a \cdot t\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \left(b \cdot c + -4 \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(i \cdot x\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \left(b \cdot c + \left(\mathsf{neg}\left(4\right)\right) \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(i \cdot x\right)\right) \]

      12. fp-cancel-sub-sign-inv N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, \left(b \cdot c - 4 \cdot \left(a \cdot t\right)\right) - 4 \cdot \left(i \cdot x\right)\right) \]

      13. associate--r+ N/A

          \[\leadsto \mathsf{fma}\left(-27 \cdot j, k, b \cdot c - \left(4 \cdot \left(a \cdot t\right) + 4 \cdot \left(i \cdot x\right)\right)\right) \]

   8. Applied rewrites 80.4%

      \[\leadsto \mathsf{fma}\left(-27 \cdot j, \color{blue}{k}, \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, a \cdot t\right)\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 50.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-276}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot -4, x, b \cdot c\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-38}:\\ \;\;\;\;c \cdot b - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (fma c b (* (* a t) -4.0))))
   (if (<= a -3.2e+166)
     t_1
     (if (<= a -7.5e-276)
       (fma (* i -4.0) x (* b c))
       (if (<= a 1.02e-38) (- (* 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(c, b, ((a * t) * -4.0));
	double tmp;
	if (a <= -3.2e+166) {
		tmp = t_1;
	} else if (a <= -7.5e-276) {
		tmp = fma((i * -4.0), x, (b * c));
	} else if (a <= 1.02e-38) {
		tmp = (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 = fma(c, b, Float64(Float64(a * t) * -4.0))
	tmp = 0.0
	if (a <= -3.2e+166)
		tmp = t_1;
	elseif (a <= -7.5e-276)
		tmp = fma(Float64(i * -4.0), x, Float64(b * c));
	elseif (a <= 1.02e-38)
		tmp = Float64(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[(c * b + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e+166], t$95$1, If[LessEqual[a, -7.5e-276], N[(N[(i * -4.0), $MachinePrecision] * x + N[(b * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e-38], N[(N[(c * b), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.19999999999999968e166 or 1.01999999999999998e-38 < a

   1. Initial program 84.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      2. lift--.f64 N/A

         \[\leadsto \left(\left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\color{blue}{\left(x \cdot 18\right)} \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \color{blue}{\left(a \cdot 4\right)} \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \color{blue}{\left(a \cdot 4\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{b \cdot c}\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      10. +-commutative N/A

          \[\leadsto \left(\color{blue}{\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      11. *-commutative N/A

          \[\leadsto \left(\left(\color{blue}{c \cdot b} + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      12. lower-fma.f64 N/A

          \[\leadsto \left(\color{blue}{\mathsf{fma}\left(c, b, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      13. distribute-rgt-out-- N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)}\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      14. associate-*l* N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      15. *-commutative N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, t \cdot \left(\color{blue}{\left(18 \cdot x\right)} \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      16. associate-*r* N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, t \cdot \left(\color{blue}{18 \cdot \left(x \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      17. *-commutative N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{4 \cdot a}\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 88.5%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in j around 0

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   7. Applied rewrites 80.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right), t, c \cdot b\right)\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto -4 \cdot \left(a \cdot t\right) + \color{blue}{b \cdot c} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot t\right) \cdot -4 + b \cdot c \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(a \cdot t, -4, b \cdot c\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right) \]

      5. lower-*.f64 59.1

         \[\leadsto \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right) \]

   10. Applied rewrites 59.1%

       \[\leadsto \mathsf{fma}\left(t \cdot a, \color{blue}{-4}, b \cdot c\right) \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right) \]

       2. lift-fma.f64 N/A

          \[\leadsto \left(t \cdot a\right) \cdot -4 + b \cdot \color{blue}{c} \]

       3. +-commutative N/A

          \[\leadsto b \cdot c + \left(t \cdot a\right) \cdot \color{blue}{-4} \]

       4. *-commutative N/A

          \[\leadsto c \cdot b + \left(t \cdot a\right) \cdot -4 \]

       5. lift-*.f64 N/A

          \[\leadsto c \cdot b + \left(t \cdot a\right) \cdot -4 \]

       6. *-commutative N/A

          \[\leadsto c \cdot b + \left(a \cdot t\right) \cdot -4 \]

       7. *-commutative N/A

          \[\leadsto c \cdot b + -4 \cdot \left(a \cdot \color{blue}{t}\right) \]

       8. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right) \]

       10. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right) \]

       11. lower-*.f64 60.0

           \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right) \]

   12. Applied rewrites 60.0%

       \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right) \]

   if -3.19999999999999968e166 < a < -7.500000000000001e-276

   1. Initial program 79.1%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      2. lift--.f64 N/A

         \[\leadsto \left(\left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\color{blue}{\left(x \cdot 18\right)} \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \color{blue}{\left(a \cdot 4\right)} \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \color{blue}{\left(a \cdot 4\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{b \cdot c}\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      10. +-commutative N/A

          \[\leadsto \left(\color{blue}{\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      11. *-commutative N/A

          \[\leadsto \left(\left(\color{blue}{c \cdot b} + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      12. lower-fma.f64 N/A

          \[\leadsto \left(\color{blue}{\mathsf{fma}\left(c, b, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      13. distribute-rgt-out-- N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)}\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      14. associate-*l* N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      15. *-commutative N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, t \cdot \left(\color{blue}{\left(18 \cdot x\right)} \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      16. associate-*r* N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, t \cdot \left(\color{blue}{18 \cdot \left(x \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      17. *-commutative N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{4 \cdot a}\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 83.4%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in j around 0

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   7. Applied rewrites 74.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right), t, c \cdot b\right)\right)} \]

   8. Taylor expanded in t around 0

      \[\leadsto -4 \cdot \left(i \cdot x\right) + \color{blue}{b \cdot c} \]
   9. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot x + b \cdot c \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, b \cdot c\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

      5. lower-*.f64 55.2

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

   10. Applied rewrites 55.2%

       \[\leadsto \mathsf{fma}\left(i \cdot -4, \color{blue}{x}, b \cdot c\right) \]

   if -7.500000000000001e-276 < a < 1.01999999999999998e-38

   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 b around inf

      \[\leadsto \color{blue}{b \cdot c} - \left(j \cdot 27\right) \cdot k \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{b} - \left(j \cdot 27\right) \cdot k \]

      2. lower-*.f64 56.8

         \[\leadsto c \cdot \color{blue}{b} - \left(j \cdot 27\right) \cdot k \]

   5. Applied rewrites 56.8%

      \[\leadsto \color{blue}{c \cdot b} - \left(j \cdot 27\right) \cdot k \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 37.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+122} \lor \neg \left(b \cdot c \leq 2 \cdot 10^{-11}\right):\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= (* b c) -5e+122) (not (<= (* b c) 2e-11)))
   (* 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) <= -5e+122) || !((b * c) <= 2e-11)) {
		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) <= (-5d+122)) .or. (.not. ((b * c) <= 2d-11))) 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) <= -5e+122) || !((b * c) <= 2e-11)) {
		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) <= -5e+122) or not ((b * c) <= 2e-11):
		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) <= -5e+122) || !(Float64(b * c) <= 2e-11))
		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) <= -5e+122) || ~(((b * c) <= 2e-11)))
		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], -5e+122], N[Not[LessEqual[N[(b * c), $MachinePrecision], 2e-11]], $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) < -4.99999999999999989e122 or 1.99999999999999988e-11 < (*.f64 b c)

   1. Initial program 76.8%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot c} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto c \cdot \color{blue}{b} \]

      2. lower-*.f64 53.5

         \[\leadsto c \cdot \color{blue}{b} \]

   5. Applied rewrites 53.5%

      \[\leadsto \color{blue}{c \cdot b} \]

   if -4.99999999999999989e122 < (*.f64 b c) < 1.99999999999999988e-11

   1. Initial program 87.9%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{-27 \cdot \left(j \cdot k\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -27 \cdot \color{blue}{\left(j \cdot k\right)} \]

      2. *-commutative N/A

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

      3. lower-*.f64 27.6

         \[\leadsto -27 \cdot \left(k \cdot \color{blue}{j}\right) \]

   5. Applied rewrites 27.6%

      \[\leadsto \color{blue}{-27 \cdot \left(k \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+122} \lor \neg \left(b \cdot c \leq 2 \cdot 10^{-11}\right):\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 48.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+166} \lor \neg \left(a \leq 5.4 \cdot 10^{+38}\right):\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot -4, x, b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (or (<= a -3.2e+166) (not (<= a 5.4e+38)))
   (fma c b (* (* a t) -4.0))
   (fma (* i -4.0) x (* 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 <= -3.2e+166) || !(a <= 5.4e+38)) {
		tmp = fma(c, b, ((a * t) * -4.0));
	} else {
		tmp = fma((i * -4.0), x, (b * c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if ((a <= -3.2e+166) || !(a <= 5.4e+38))
		tmp = fma(c, b, Float64(Float64(a * t) * -4.0));
	else
		tmp = fma(Float64(i * -4.0), x, Float64(b * c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[Or[LessEqual[a, -3.2e+166], N[Not[LessEqual[a, 5.4e+38]], $MachinePrecision]], N[(c * b + N[(N[(a * t), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision], N[(N[(i * -4.0), $MachinePrecision] * x + N[(b * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.19999999999999968e166 or 5.39999999999999992e38 < a

   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. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      2. lift--.f64 N/A

         \[\leadsto \left(\left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\color{blue}{\left(x \cdot 18\right)} \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \color{blue}{\left(a \cdot 4\right)} \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \color{blue}{\left(a \cdot 4\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{b \cdot c}\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      10. +-commutative N/A

          \[\leadsto \left(\color{blue}{\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      11. *-commutative N/A

          \[\leadsto \left(\left(\color{blue}{c \cdot b} + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      12. lower-fma.f64 N/A

          \[\leadsto \left(\color{blue}{\mathsf{fma}\left(c, b, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      13. distribute-rgt-out-- N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)}\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      14. associate-*l* N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      15. *-commutative N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, t \cdot \left(\color{blue}{\left(18 \cdot x\right)} \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      16. associate-*r* N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, t \cdot \left(\color{blue}{18 \cdot \left(x \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      17. *-commutative N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{4 \cdot a}\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 90.4%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in j around 0

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   7. Applied rewrites 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right), t, c \cdot b\right)\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto -4 \cdot \left(a \cdot t\right) + \color{blue}{b \cdot c} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot t\right) \cdot -4 + b \cdot c \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(a \cdot t, -4, b \cdot c\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right) \]

      5. lower-*.f64 59.2

         \[\leadsto \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right) \]

   10. Applied rewrites 59.2%

       \[\leadsto \mathsf{fma}\left(t \cdot a, \color{blue}{-4}, b \cdot c\right) \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(t \cdot a, -4, b \cdot c\right) \]

       2. lift-fma.f64 N/A

          \[\leadsto \left(t \cdot a\right) \cdot -4 + b \cdot \color{blue}{c} \]

       3. +-commutative N/A

          \[\leadsto b \cdot c + \left(t \cdot a\right) \cdot \color{blue}{-4} \]

       4. *-commutative N/A

          \[\leadsto c \cdot b + \left(t \cdot a\right) \cdot -4 \]

       5. lift-*.f64 N/A

          \[\leadsto c \cdot b + \left(t \cdot a\right) \cdot -4 \]

       6. *-commutative N/A

          \[\leadsto c \cdot b + \left(a \cdot t\right) \cdot -4 \]

       7. *-commutative N/A

          \[\leadsto c \cdot b + -4 \cdot \left(a \cdot \color{blue}{t}\right) \]

       8. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(c, b, -4 \cdot \left(a \cdot t\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right) \]

       10. lower-*.f64 N/A

           \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right) \]

       11. lower-*.f64 60.3

           \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right) \]

   12. Applied rewrites 60.3%

       \[\leadsto \mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right) \]

   if -3.19999999999999968e166 < a < 5.39999999999999992e38

   1. Initial program 82.2%

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \left(\color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      2. lift--.f64 N/A

         \[\leadsto \left(\left(\color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      4. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\color{blue}{\left(x \cdot 18\right)} \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right)} \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      7. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \color{blue}{\left(a \cdot 4\right)} \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \color{blue}{\left(a \cdot 4\right) \cdot t}\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \color{blue}{b \cdot c}\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      10. +-commutative N/A

          \[\leadsto \left(\color{blue}{\left(b \cdot c + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      11. *-commutative N/A

          \[\leadsto \left(\left(\color{blue}{c \cdot b} + \left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      12. lower-fma.f64 N/A

          \[\leadsto \left(\color{blue}{\mathsf{fma}\left(c, b, \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      13. distribute-rgt-out-- N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)}\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      14. associate-*l* N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      15. *-commutative N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, t \cdot \left(\color{blue}{\left(18 \cdot x\right)} \cdot \left(y \cdot z\right) - a \cdot 4\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      16. associate-*r* N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, t \cdot \left(\color{blue}{18 \cdot \left(x \cdot \left(y \cdot z\right)\right)} - a \cdot 4\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

      17. *-commutative N/A

          \[\leadsto \left(\mathsf{fma}\left(c, b, t \cdot \left(18 \cdot \left(x \cdot \left(y \cdot z\right)\right) - \color{blue}{4 \cdot a}\right)\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied rewrites 84.1%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right) \cdot t\right)} - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   5. Taylor expanded in j around 0

      \[\leadsto \color{blue}{\left(b \cdot c + t \cdot \left(-4 \cdot a + 18 \cdot \left(x \cdot \left(y \cdot z\right)\right)\right)\right) - 4 \cdot \left(i \cdot x\right)} \]

   7. Applied rewrites 70.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot x, -4, \mathsf{fma}\left(\mathsf{fma}\left(\left(z \cdot y\right) \cdot x, 18, -4 \cdot a\right), t, c \cdot b\right)\right)} \]

   8. Taylor expanded in t around 0

      \[\leadsto -4 \cdot \left(i \cdot x\right) + \color{blue}{b \cdot c} \]
   9. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-4 \cdot i\right) \cdot x + b \cdot c \]

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-4 \cdot i, x, b \cdot c\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

      5. lower-*.f64 51.4

         \[\leadsto \mathsf{fma}\left(i \cdot -4, x, b \cdot c\right) \]

   10. Applied rewrites 51.4%

       \[\leadsto \mathsf{fma}\left(i \cdot -4, \color{blue}{x}, b \cdot c\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+166} \lor \neg \left(a \leq 5.4 \cdot 10^{+38}\right):\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(a \cdot t\right) \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot -4, x, b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 23.6% 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 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

3. Taylor expanded in b around inf

   \[\leadsto \color{blue}{b \cdot c} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto c \cdot \color{blue}{b} \]

   2. lower-*.f64 23.1

      \[\leadsto c \cdot \color{blue}{b} \]

5. Applied rewrites 23.1%

   \[\leadsto \color{blue}{c \cdot b} \]
6. Add Preprocessing

Developer Target 1: 88.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot t + i \cdot x\right) \cdot 4\\ t_2 := \left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - t\_1\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - t\_1\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (+ (* a t) (* i x)) 4.0))
        (t_2
         (-
          (- (* (* 18.0 t) (* (* x y) z)) t_1)
          (- (* (* k j) 27.0) (* c b)))))
   (if (< t -1.6210815397541398e-69)
     t_2
     (if (< t 165.68027943805222)
       (+ (- (* (* 18.0 y) (* x (* z t))) t_1) (- (* c b) (* 27.0 (* k j))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((a * t) + (i * x)) * 4.0;
	double t_2 = (((18.0 * t) * ((x * y) * z)) - t_1) - (((k * j) * 27.0) - (c * b));
	double tmp;
	if (t < -1.6210815397541398e-69) {
		tmp = t_2;
	} else if (t < 165.68027943805222) {
		tmp = (((18.0 * y) * (x * (z * t))) - t_1) + ((c * b) - (27.0 * (k * j)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

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 2025052 
(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)))