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

Percentage Accurate: 85.5% → 90.6%

Time: 9.4s

Alternatives: 17

Speedup: 0.5×

• 51.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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: 90.6% accurate, 0.5× speedup

Math

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

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 (* a t) -4.0 (* b c)) (* (* (* 18.0 (* x y)) t) z)) t_1)
      t_2)
     (* (fma (* (* z y) x) 18.0 (* -4.0 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 * 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((a * t), -4.0, (b * c)) + (((18.0 * (x * y)) * t) * z)) - t_1) - t_2;
	} else {
		tmp = fma(((z * y) * x), 18.0, (-4.0 * a)) * 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(Float64(fma(Float64(a * t), -4.0, Float64(b * c)) + Float64(Float64(Float64(18.0 * Float64(x * y)) * t) * z)) - t_1) - t_2);
	else
		tmp = Float64(fma(Float64(Float64(z * y) * x), 18.0, Float64(-4.0 * a)) * 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[(N[(N[(a * t), $MachinePrecision] * -4.0 + N[(b * c), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(18.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $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 95.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      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

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-neg.f64 N/A

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

      18. lower-*.f64 93.0

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

   3. Applied rewrites 93.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-neg.f64 N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. lower-fma.f64 N/A

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

   5. Applied rewrites 93.0%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

      15. lower-+.f64 N/A

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

   7. Applied rewrites 94.8%

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

   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. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 55.0

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

   4. Applied rewrites 55.0%

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

Alternative 2: 87.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ t_2 := \mathsf{fma}\left(a, t, i \cdot x\right)\\ t_3 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+286}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, t\_1, c \cdot b - 4 \cdot t\_2\right)\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+263}:\\ \;\;\;\;c \cdot b - \mathsf{fma}\left(4, t\_2, \left(k \cdot j\right) \cdot 27\right)\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(t\_1 \cdot t, 18, \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, t \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, 18, -4 \cdot a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* z y) x))
        (t_2 (fma a t (* i x)))
        (t_3
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i))))
   (if (<= t_3 -2e+286)
     (fma (* 18.0 t) t_1 (- (* c b) (* 4.0 t_2)))
     (if (<= t_3 2e+263)
       (- (* c b) (fma 4.0 t_2 (* (* k j) 27.0)))
       (if (<= t_3 INFINITY)
         (fma (* t_1 t) 18.0 (fma c b (* -4.0 (fma i x (* t a)))))
         (* (fma t_1 18.0 (* -4.0 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 = (z * y) * x;
	double t_2 = fma(a, t, (i * x));
	double t_3 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_3 <= -2e+286) {
		tmp = fma((18.0 * t), t_1, ((c * b) - (4.0 * t_2)));
	} else if (t_3 <= 2e+263) {
		tmp = (c * b) - fma(4.0, t_2, ((k * j) * 27.0));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = fma((t_1 * t), 18.0, fma(c, b, (-4.0 * fma(i, x, (t * a)))));
	} else {
		tmp = fma(t_1, 18.0, (-4.0 * a)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(z * y) * x)
	t_2 = fma(a, t, Float64(i * x))
	t_3 = 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_3 <= -2e+286)
		tmp = fma(Float64(18.0 * t), t_1, Float64(Float64(c * b) - Float64(4.0 * t_2)));
	elseif (t_3 <= 2e+263)
		tmp = Float64(Float64(c * b) - fma(4.0, t_2, Float64(Float64(k * j) * 27.0)));
	elseif (t_3 <= Inf)
		tmp = fma(Float64(t_1 * t), 18.0, fma(c, b, Float64(-4.0 * fma(i, x, Float64(t * a)))));
	else
		tmp = Float64(fma(t_1, 18.0, Float64(-4.0 * a)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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$3, -2e+286], N[(N[(18.0 * t), $MachinePrecision] * t$95$1 + N[(N[(c * b), $MachinePrecision] - N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+263], N[(N[(c * b), $MachinePrecision] - N[(4.0 * t$95$2 + N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(N[(t$95$1 * t), $MachinePrecision] * 18.0 + N[(c * b + N[(-4.0 * N[(i * x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 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)) < -2.00000000000000007e286

   1. Initial program 86.4%

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

   2. Taylor expanded in j around 0

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

      1. associate--l+ N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. distribute-lft-out N/A

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

      13. lower-*.f64 N/A

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

      14. lower-fma.f64 N/A

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

      15. lower-*.f64 90.4

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

   4. Applied rewrites 90.4%

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

   if -2.00000000000000007e286 < (-.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)) < 2.00000000000000003e263

   1. Initial program 99.5%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   3. 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 89.5

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

   4. Applied rewrites 89.5%

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

   if 2.00000000000000003e263 < (-.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 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. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 12.6

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

   4. Applied rewrites 12.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      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 12.7

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

   6. Applied rewrites 12.7%

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

   7. Taylor expanded in j around 0

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

      1. distribute-lft-in N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

   9. Applied rewrites 89.3%

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

   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. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 60.1

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

   4. Applied rewrites 60.1%

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

Alternative 3: 87.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot y\right) \cdot x\\ t_2 := \mathsf{fma}\left(t\_1 \cdot t, 18, \mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, t \cdot a\right)\right)\right)\\ t_3 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+286}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+263}:\\ \;\;\;\;c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, i \cdot x\right), \left(k \cdot j\right) \cdot 27\right)\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, 18, -4 \cdot a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* z y) x))
        (t_2 (fma (* t_1 t) 18.0 (fma c b (* -4.0 (fma i x (* t a))))))
        (t_3
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i))))
   (if (<= t_3 -2e+286)
     t_2
     (if (<= t_3 2e+263)
       (- (* c b) (fma 4.0 (fma a t (* i x)) (* (* k j) 27.0)))
       (if (<= t_3 INFINITY) t_2 (* (fma t_1 18.0 (* -4.0 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 = (z * y) * x;
	double t_2 = fma((t_1 * t), 18.0, fma(c, b, (-4.0 * fma(i, x, (t * a)))));
	double t_3 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_3 <= -2e+286) {
		tmp = t_2;
	} else if (t_3 <= 2e+263) {
		tmp = (c * b) - fma(4.0, fma(a, t, (i * x)), ((k * j) * 27.0));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = fma(t_1, 18.0, (-4.0 * a)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(z * y) * x)
	t_2 = fma(Float64(t_1 * t), 18.0, fma(c, b, Float64(-4.0 * fma(i, x, Float64(t * a)))))
	t_3 = 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_3 <= -2e+286)
		tmp = t_2;
	elseif (t_3 <= 2e+263)
		tmp = Float64(Float64(c * b) - fma(4.0, fma(a, t, Float64(i * x)), Float64(Float64(k * j) * 27.0)));
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(fma(t_1, 18.0, Float64(-4.0 * a)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 * t), $MachinePrecision] * 18.0 + N[(c * b + N[(-4.0 * N[(i * x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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$3, -2e+286], t$95$2, If[LessEqual[t$95$3, 2e+263], N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision] + N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$2, N[(N[(t$95$1 * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $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)) < -2.00000000000000007e286 or 2.00000000000000003e263 < (-.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 86.3%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 12.4

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

   4. Applied rewrites 12.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      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 12.4

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

   6. Applied rewrites 12.4%

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

   7. Taylor expanded in j around 0

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

      1. distribute-lft-in N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

   9. Applied rewrites 89.9%

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

   if -2.00000000000000007e286 < (-.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)) < 2.00000000000000003e263

   1. Initial program 99.5%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   3. 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 89.5

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

   4. Applied rewrites 89.5%

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

   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. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 60.1

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

   4. Applied rewrites 60.1%

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

Alternative 4: 89.0% accurate, 0.5× speedup

Math

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

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 (* (* y x) 18.0) (* t z) (fma (* a t) -4.0 (* c b))) t_1) t_2)
     (* (fma (* (* z y) x) 18.0 (* -4.0 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 * 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(((y * x) * 18.0), (t * z), fma((a * t), -4.0, (c * b))) - t_1) - t_2;
	} else {
		tmp = fma(((z * y) * x), 18.0, (-4.0 * a)) * 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(Float64(Float64(y * x) * 18.0), Float64(t * z), fma(Float64(a * t), -4.0, Float64(c * b))) - t_1) - t_2);
	else
		tmp = Float64(fma(Float64(Float64(z * y) * x), 18.0, Float64(-4.0 * a)) * 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[(N[(N[(y * x), $MachinePrecision] * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] * -4.0 + N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $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 95.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      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

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-neg.f64 N/A

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

      18. lower-*.f64 93.0

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

   3. Applied rewrites 93.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-neg.f64 N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. lower-fma.f64 N/A

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

   5. Applied rewrites 93.0%

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

   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. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 55.0

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

   4. Applied rewrites 55.0%

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

Alternative 5: 77.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7.5 \cdot 10^{+84}:\\ \;\;\;\;c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, i \cdot x\right), \left(k \cdot j\right) \cdot 27\right)\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+265}:\\ \;\;\;\;\left(\mathsf{fma}\left(\left(y \cdot x\right) \cdot 18, t \cdot z, b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(y \cdot x\right) \cdot z, 18, -4 \cdot a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z 7.5e+84)
   (- (* c b) (fma 4.0 (fma a t (* i x)) (* (* k j) 27.0)))
   (if (<= z 8.4e+265)
     (-
      (- (fma (* (* y x) 18.0) (* t z) (* b c)) (* (* x 4.0) i))
      (* (* j 27.0) k))
     (* (fma (* (* y x) z) 18.0 (* -4.0 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 (z <= 7.5e+84) {
		tmp = (c * b) - fma(4.0, fma(a, t, (i * x)), ((k * j) * 27.0));
	} else if (z <= 8.4e+265) {
		tmp = (fma(((y * x) * 18.0), (t * z), (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	} else {
		tmp = fma(((y * x) * z), 18.0, (-4.0 * a)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= 7.5e+84)
		tmp = Float64(Float64(c * b) - fma(4.0, fma(a, t, Float64(i * x)), Float64(Float64(k * j) * 27.0)));
	elseif (z <= 8.4e+265)
		tmp = Float64(Float64(fma(Float64(Float64(y * x) * 18.0), Float64(t * z), Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(fma(Float64(Float64(y * x) * z), 18.0, Float64(-4.0 * a)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, 7.5e+84], N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision] + N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.4e+265], N[(N[(N[(N[(N[(y * x), $MachinePrecision] * 18.0), $MachinePrecision] * N[(t * z), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < 7.5000000000000001e84

   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. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   3. 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 79.3

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

   4. Applied rewrites 79.3%

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

   if 7.5000000000000001e84 < z < 8.3999999999999993e265

   1. Initial program 82.4%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      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

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-neg.f64 N/A

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

      18. lower-*.f64 77.8

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

   3. Applied rewrites 77.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-neg.f64 N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. lower-fma.f64 N/A

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

   5. Applied rewrites 77.9%

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

   6. Taylor expanded in t around 0

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

      1. lower-*.f64 74.9

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

   8. Applied rewrites 74.9%

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

   if 8.3999999999999993e265 < z

   1. Initial program 75.4%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 54.2

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

   4. Applied rewrites 54.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 57.0

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

   6. Applied rewrites 57.0%

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

Alternative 6: 79.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4.4 \cdot 10^{+79}:\\ \;\;\;\;c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, i \cdot x\right), \left(k \cdot j\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(18 \cdot \left(x \cdot y\right)\right) \cdot t\right) \cdot z\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z 4.4e+79)
   (- (* c b) (fma 4.0 (fma a t (* i x)) (* (* k j) 27.0)))
   (-
    (- (+ (* c b) (* (* (* 18.0 (* x y)) t) z)) (* (* x 4.0) i))
    (* (* j 27.0) k))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if (z <= 4.4e+79) {
		tmp = (c * b) - fma(4.0, fma(a, t, (i * x)), ((k * j) * 27.0));
	} else {
		tmp = (((c * b) + (((18.0 * (x * y)) * t) * z)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= 4.4e+79)
		tmp = Float64(Float64(c * b) - fma(4.0, fma(a, t, Float64(i * x)), Float64(Float64(k * j) * 27.0)));
	else
		tmp = Float64(Float64(Float64(Float64(c * b) + Float64(Float64(Float64(18.0 * Float64(x * y)) * t) * z)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, 4.4e+79], N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision] + N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(c * b), $MachinePrecision] + N[(N[(N[(18.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.3999999999999998e79

   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. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   3. 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 79.4

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

   4. Applied rewrites 79.4%

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

   if 4.3999999999999998e79 < z

   1. Initial program 81.1%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      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

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

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

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

      9. associate-*l* N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-neg.f64 N/A

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

      18. lower-*.f64 77.2

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

   3. Applied rewrites 77.2%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-+l+ N/A

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

      6. lift-*.f64 N/A

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

      7. lift-neg.f64 N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. lower-fma.f64 N/A

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

   5. Applied rewrites 77.4%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. *-commutative N/A

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

      14. associate-*l* N/A

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

      15. lower-+.f64 N/A

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

   7. Applied rewrites 85.7%

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

   8. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lift-*.f64 79.5

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

   10. Applied rewrites 79.5%

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

Alternative 7: 68.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+234}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right) - t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+165}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -1e+234)
     (- (* -4.0 (* a t)) t_1)
     (if (<= t_1 2e+165)
       (fma c b (* -4.0 (fma i x (* t a))))
       (- (* c b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+234) {
		tmp = (-4.0 * (a * t)) - t_1;
	} else if (t_1 <= 2e+165) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (t * a))));
	} else {
		tmp = (c * b) - t_1;
	}
	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 <= -1e+234)
		tmp = Float64(Float64(-4.0 * Float64(a * t)) - t_1);
	elseif (t_1 <= 2e+165)
		tmp = fma(c, b, Float64(-4.0 * fma(i, x, Float64(t * a))));
	else
		tmp = Float64(Float64(c * b) - t_1);
	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, -1e+234], N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 2e+165], N[(c * b + N[(-4.0 * N[(i * x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * b), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000002e234

   1. Initial program 77.9%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 74.1

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

   4. Applied rewrites 74.1%

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

   if -1.00000000000000002e234 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999998e165

   1. Initial program 87.5%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   3. 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 75.4

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

   4. Applied rewrites 75.4%

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

   5. Taylor expanded in j around 0

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)} \]
   6. 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. *-commutative N/A

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

      9. lower-*.f64 68.1

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

   7. Applied rewrites 68.1%

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

   if 1.9999999999999998e165 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.7%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 69.2

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

   4. Applied rewrites 69.2%

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

Alternative 8: 68.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+244}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+165}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b - t\_1\\ \end{array} \end{array} \]

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+244)
     (* -27.0 (* k j))
     (if (<= t_1 2e+165)
       (fma c b (* -4.0 (fma i x (* t a))))
       (- (* c b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -2e+244) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 2e+165) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (t * a))));
	} else {
		tmp = (c * b) - t_1;
	}
	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+244)
		tmp = Float64(-27.0 * Float64(k * j));
	elseif (t_1 <= 2e+165)
		tmp = fma(c, b, Float64(-4.0 * fma(i, x, Float64(t * a))));
	else
		tmp = Float64(Float64(c * b) - t_1);
	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+244], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+165], N[(c * b + N[(-4.0 * N[(i * x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * b), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -2.00000000000000015e244

   1. Initial program 76.9%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 75.9

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

   4. Applied rewrites 75.9%

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

   if -2.00000000000000015e244 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 1.9999999999999998e165

   1. Initial program 87.5%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   3. 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 75.4

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

   4. Applied rewrites 75.4%

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

   5. Taylor expanded in j around 0

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)} \]
   6. 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. *-commutative N/A

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

      9. lower-*.f64 67.9

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

   7. Applied rewrites 67.9%

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

   if 1.9999999999999998e165 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 79.7%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 69.2

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

   4. Applied rewrites 69.2%

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

Alternative 9: 52.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+234}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+237}:\\ \;\;\;\;c \cdot b - \left(i \cdot x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;\left(-27 \cdot j\right) \cdot k\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (* j 27.0) k)))
   (if (<= t_1 -1e+234)
     (* -27.0 (* k j))
     (if (<= t_1 5e+237) (- (* c b) (* (* i x) 4.0)) (* (* -27.0 j) k)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+234) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 5e+237) {
		tmp = (c * b) - ((i * x) * 4.0);
	} else {
		tmp = (-27.0 * j) * k;
	}
	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 = (j * 27.0d0) * k
    if (t_1 <= (-1d+234)) then
        tmp = (-27.0d0) * (k * j)
    else if (t_1 <= 5d+237) then
        tmp = (c * b) - ((i * x) * 4.0d0)
    else
        tmp = ((-27.0d0) * j) * k
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (j * 27.0) * k;
	double tmp;
	if (t_1 <= -1e+234) {
		tmp = -27.0 * (k * j);
	} else if (t_1 <= 5e+237) {
		tmp = (c * b) - ((i * x) * 4.0);
	} else {
		tmp = (-27.0 * j) * k;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (j * 27.0) * k
	tmp = 0
	if t_1 <= -1e+234:
		tmp = -27.0 * (k * j)
	elif t_1 <= 5e+237:
		tmp = (c * b) - ((i * x) * 4.0)
	else:
		tmp = (-27.0 * j) * k
	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 <= -1e+234)
		tmp = Float64(-27.0 * Float64(k * j));
	elseif (t_1 <= 5e+237)
		tmp = Float64(Float64(c * b) - Float64(Float64(i * x) * 4.0));
	else
		tmp = Float64(Float64(-27.0 * j) * k);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (j * 27.0) * k;
	tmp = 0.0;
	if (t_1 <= -1e+234)
		tmp = -27.0 * (k * j);
	elseif (t_1 <= 5e+237)
		tmp = (c * b) - ((i * x) * 4.0);
	else
		tmp = (-27.0 * j) * k;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+234], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+237], N[(N[(c * b), $MachinePrecision] - N[(N[(i * x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(N[(-27.0 * j), $MachinePrecision] * k), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 j #s(literal 27 binary64)) k) < -1.00000000000000002e234

   1. Initial program 77.9%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 72.9

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

   4. Applied rewrites 72.9%

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

   if -1.00000000000000002e234 < (*.f64 (*.f64 j #s(literal 27 binary64)) k) < 5.0000000000000002e237

   1. Initial program 87.3%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   3. 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 75.4

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

   4. Applied rewrites 75.4%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-*.f64 47.1

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

   7. Applied rewrites 47.1%

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

   if 5.0000000000000002e237 < (*.f64 (*.f64 j #s(literal 27 binary64)) k)

   1. Initial program 77.4%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 74.3

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

   4. Applied rewrites 74.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      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 74.1

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

   6. Applied rewrites 74.1%

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

Alternative 10: 35.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -5 \cdot 10^{+160}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq -2 \cdot 10^{-273}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+108}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -5e+160)
   (* c b)
   (if (<= (* b c) -2e-273)
     (* (* -4.0 i) x)
     (if (<= (* b c) 2e+108) (* -4.0 (* a t)) (* c b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -5e+160) {
		tmp = c * b;
	} else if ((b * c) <= -2e-273) {
		tmp = (-4.0 * i) * x;
	} else if ((b * c) <= 2e+108) {
		tmp = -4.0 * (a * t);
	} 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+160)) then
        tmp = c * b
    else if ((b * c) <= (-2d-273)) then
        tmp = ((-4.0d0) * i) * x
    else if ((b * c) <= 2d+108) then
        tmp = (-4.0d0) * (a * t)
    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+160) {
		tmp = c * b;
	} else if ((b * c) <= -2e-273) {
		tmp = (-4.0 * i) * x;
	} else if ((b * c) <= 2e+108) {
		tmp = -4.0 * (a * t);
	} 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+160:
		tmp = c * b
	elif (b * c) <= -2e-273:
		tmp = (-4.0 * i) * x
	elif (b * c) <= 2e+108:
		tmp = -4.0 * (a * t)
	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+160)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= -2e-273)
		tmp = Float64(Float64(-4.0 * i) * x);
	elseif (Float64(b * c) <= 2e+108)
		tmp = Float64(-4.0 * Float64(a * t));
	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+160)
		tmp = c * b;
	elseif ((b * c) <= -2e-273)
		tmp = (-4.0 * i) * x;
	elseif ((b * c) <= 2e+108)
		tmp = -4.0 * (a * t);
	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+160], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], -2e-273], N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+108], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 b c) < -5.0000000000000002e160 or 2.0000000000000001e108 < (*.f64 b c)

   1. Initial program 81.3%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 60.4

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

   4. Applied rewrites 60.4%

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

   if -5.0000000000000002e160 < (*.f64 b c) < -2e-273

   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. Taylor expanded in i around inf

      \[\leadsto \color{blue}{-4 \cdot \left(i \cdot x\right)} \]
   3. 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 24.4

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

   4. Applied rewrites 24.4%

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

   if -2e-273 < (*.f64 b c) < 2.0000000000000001e108

   1. Initial program 87.5%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 24.7

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

   4. Applied rewrites 24.7%

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

Alternative 11: 71.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(y \cdot x\right) \cdot z, 18, -4 \cdot a\right) \cdot t\\ \mathbf{if}\;t \leq -420000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+122}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \left(-4 \cdot i\right) \cdot x\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* (fma (* (* y x) z) 18.0 (* -4.0 a)) t)))
   (if (<= t -420000000.0)
     t_1
     (if (<= t 6e+122) (- (fma c b (* (* -4.0 i) x)) (* (* 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(((y * x) * z), 18.0, (-4.0 * a)) * t;
	double tmp;
	if (t <= -420000000.0) {
		tmp = t_1;
	} else if (t <= 6e+122) {
		tmp = fma(c, b, ((-4.0 * i) * x)) - ((j * 27.0) * k);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(fma(Float64(Float64(y * x) * z), 18.0, Float64(-4.0 * a)) * t)
	tmp = 0.0
	if (t <= -420000000.0)
		tmp = t_1;
	elseif (t <= 6e+122)
		tmp = Float64(fma(c, b, Float64(Float64(-4.0 * i) * x)) - Float64(Float64(j * 27.0) * k));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision] * 18.0 + N[(-4.0 * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -420000000.0], t$95$1, If[LessEqual[t, 6e+122], N[(N[(c * b + N[(N[(-4.0 * i), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.2e8 or 5.99999999999999972e122 < 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. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. *-commutative N/A

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

      5. metadata-eval N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 68.3

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

   4. Applied rewrites 68.3%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 68.4

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

   6. Applied rewrites 68.4%

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

   if -4.2e8 < t < 5.99999999999999972e122

   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. Taylor expanded in t around 0

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

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

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

      2. *-commutative N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 73.9

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

   4. Applied rewrites 73.9%

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

Alternative 12: 76.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.26 \cdot 10^{+207}:\\ \;\;\;\;c \cdot b - \mathsf{fma}\left(4, \mathsf{fma}\left(a, t, i \cdot x\right), \left(k \cdot j\right) \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot 18\right) \cdot z, y, -4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z 1.26e+207)
   (- (* c b) (fma 4.0 (fma a t (* i x)) (* (* k j) 27.0)))
   (* (fma (* (* t 18.0) 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 tmp;
	if (z <= 1.26e+207) {
		tmp = (c * b) - fma(4.0, fma(a, t, (i * x)), ((k * j) * 27.0));
	} else {
		tmp = fma(((t * 18.0) * z), y, (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= 1.26e+207)
		tmp = Float64(Float64(c * b) - fma(4.0, fma(a, t, Float64(i * x)), Float64(Float64(k * j) * 27.0)));
	else
		tmp = Float64(fma(Float64(Float64(t * 18.0) * z), y, Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, 1.26e+207], N[(N[(c * b), $MachinePrecision] - N[(4.0 * N[(a * t + N[(i * x), $MachinePrecision]), $MachinePrecision] + N[(N[(k * j), $MachinePrecision] * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(t * 18.0), $MachinePrecision] * z), $MachinePrecision] * y + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.25999999999999999e207

   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. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   3. 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 77.9

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

   4. Applied rewrites 77.9%

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

   if 1.25999999999999999e207 < z

   1. Initial program 77.2%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   3. 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 55.8

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

   4. Applied rewrites 55.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-*.f64 56.7

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

   6. Applied rewrites 56.7%

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

Alternative 13: 59.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-69}:\\ \;\;\;\;\mathsf{fma}\left(18 \cdot t, z \cdot y, -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+207}:\\ \;\;\;\;\mathsf{fma}\left(c, b, -4 \cdot \mathsf{fma}\left(i, x, t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t \cdot 18\right) \cdot z, y, -4 \cdot i\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= z -9e-69)
   (* (fma (* 18.0 t) (* z y) (* -4.0 i)) x)
   (if (<= z 1.26e+207)
     (fma c b (* -4.0 (fma i x (* t a))))
     (* (fma (* (* t 18.0) 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 tmp;
	if (z <= -9e-69) {
		tmp = fma((18.0 * t), (z * y), (-4.0 * i)) * x;
	} else if (z <= 1.26e+207) {
		tmp = fma(c, b, (-4.0 * fma(i, x, (t * a))));
	} else {
		tmp = fma(((t * 18.0) * z), y, (-4.0 * i)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	tmp = 0.0
	if (z <= -9e-69)
		tmp = Float64(fma(Float64(18.0 * t), Float64(z * y), Float64(-4.0 * i)) * x);
	elseif (z <= 1.26e+207)
		tmp = fma(c, b, Float64(-4.0 * fma(i, x, Float64(t * a))));
	else
		tmp = Float64(fma(Float64(Float64(t * 18.0) * z), y, Float64(-4.0 * i)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := If[LessEqual[z, -9e-69], N[(N[(N[(18.0 * t), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 1.26e+207], N[(c * b + N[(-4.0 * N[(i * x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(t * 18.0), $MachinePrecision] * z), $MachinePrecision] * y + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.00000000000000019e-69

   1. Initial program 84.2%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   3. 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 49.8

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

   4. Applied rewrites 49.8%

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

   if -9.00000000000000019e-69 < z < 1.25999999999999999e207

   1. Initial program 87.2%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   3. 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 82.9

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

   4. Applied rewrites 82.9%

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

   5. Taylor expanded in j around 0

      \[\leadsto b \cdot c - \color{blue}{4 \cdot \left(a \cdot t + i \cdot x\right)} \]
   6. 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. *-commutative N/A

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

      9. lower-*.f64 65.0

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

   7. Applied rewrites 65.0%

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

   if 1.25999999999999999e207 < z

   1. Initial program 77.2%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(18 \cdot \left(t \cdot \left(y \cdot z\right)\right) - 4 \cdot i\right)} \]
   3. 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 55.8

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

   4. Applied rewrites 55.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*r* N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-*.f64 56.7

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

   6. Applied rewrites 56.7%

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

Alternative 14: 36.0% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+134}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq 2 \cdot 10^{+108}:\\ \;\;\;\;-4 \cdot \left(a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -4e+134)
   (* c b)
   (if (<= (* b c) 2e+108) (* -4.0 (* a t)) (* c b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double tmp;
	if ((b * c) <= -4e+134) {
		tmp = c * b;
	} else if ((b * c) <= 2e+108) {
		tmp = -4.0 * (a * t);
	} 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) <= (-4d+134)) then
        tmp = c * b
    else if ((b * c) <= 2d+108) then
        tmp = (-4.0d0) * (a * t)
    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) <= -4e+134) {
		tmp = c * b;
	} else if ((b * c) <= 2e+108) {
		tmp = -4.0 * (a * t);
	} else {
		tmp = c * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	tmp = 0
	if (b * c) <= -4e+134:
		tmp = c * b
	elif (b * c) <= 2e+108:
		tmp = -4.0 * (a * t)
	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) <= -4e+134)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= 2e+108)
		tmp = Float64(-4.0 * Float64(a * t));
	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) <= -4e+134)
		tmp = c * b;
	elseif ((b * c) <= 2e+108)
		tmp = -4.0 * (a * t);
	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], -4e+134], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 2e+108], N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -3.99999999999999969e134 or 2.0000000000000001e108 < (*.f64 b c)

   1. Initial program 81.4%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 59.2

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

   4. Applied rewrites 59.2%

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

   if -3.99999999999999969e134 < (*.f64 b c) < 2.0000000000000001e108

   1. Initial program 87.4%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 25.0

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

   4. Applied rewrites 25.0%

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

Alternative 15: 37.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot c \leq -4 \cdot 10^{+134}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;b \cdot c \leq 5 \cdot 10^{+89}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (if (<= (* b c) -4e+134)
   (* c b)
   (if (<= (* b c) 5e+89) (* -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) <= -4e+134) {
		tmp = c * b;
	} else if ((b * c) <= 5e+89) {
		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) <= (-4d+134)) then
        tmp = c * b
    else if ((b * c) <= 5d+89) 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) <= -4e+134) {
		tmp = c * b;
	} else if ((b * c) <= 5e+89) {
		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) <= -4e+134:
		tmp = c * b
	elif (b * c) <= 5e+89:
		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) <= -4e+134)
		tmp = Float64(c * b);
	elseif (Float64(b * c) <= 5e+89)
		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) <= -4e+134)
		tmp = c * b;
	elseif ((b * c) <= 5e+89)
		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], -4e+134], N[(c * b), $MachinePrecision], If[LessEqual[N[(b * c), $MachinePrecision], 5e+89], N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision], N[(c * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b c) < -3.99999999999999969e134 or 4.99999999999999983e89 < (*.f64 b c)

   1. Initial program 81.7%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 57.6

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

   4. Applied rewrites 57.6%

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

   if -3.99999999999999969e134 < (*.f64 b c) < 4.99999999999999983e89

   1. Initial program 87.4%

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

   2. Taylor expanded in j around inf

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

      1. lower-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 26.8

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

   4. Applied rewrites 26.8%

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

Alternative 16: 51.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot b - \left(i \cdot x\right) \cdot 4\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+106}:\\ \;\;\;\;c \cdot b - j \cdot \left(k \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (- (* c b) (* (* i x) 4.0))))
   (if (<= x -9.5e+43)
     t_1
     (if (<= x 3.9e+106) (- (* c b) (* j (* k 27.0))) 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 = (c * b) - ((i * x) * 4.0);
	double tmp;
	if (x <= -9.5e+43) {
		tmp = t_1;
	} else if (x <= 3.9e+106) {
		tmp = (c * b) - (j * (k * 27.0));
	} else {
		tmp = t_1;
	}
	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 = (c * b) - ((i * x) * 4.0d0)
    if (x <= (-9.5d+43)) then
        tmp = t_1
    else if (x <= 3.9d+106) then
        tmp = (c * b) - (j * (k * 27.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = (c * b) - ((i * x) * 4.0);
	double tmp;
	if (x <= -9.5e+43) {
		tmp = t_1;
	} else if (x <= 3.9e+106) {
		tmp = (c * b) - (j * (k * 27.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = (c * b) - ((i * x) * 4.0)
	tmp = 0
	if x <= -9.5e+43:
		tmp = t_1
	elif x <= 3.9e+106:
		tmp = (c * b) - (j * (k * 27.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(c * b) - Float64(Float64(i * x) * 4.0))
	tmp = 0.0
	if (x <= -9.5e+43)
		tmp = t_1;
	elseif (x <= 3.9e+106)
		tmp = Float64(Float64(c * b) - Float64(j * Float64(k * 27.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = (c * b) - ((i * x) * 4.0);
	tmp = 0.0;
	if (x <= -9.5e+43)
		tmp = t_1;
	elseif (x <= 3.9e+106)
		tmp = (c * b) - (j * (k * 27.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(c * b), $MachinePrecision] - N[(N[(i * x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.5e+43], t$95$1, If[LessEqual[x, 3.9e+106], N[(N[(c * b), $MachinePrecision] - N[(j * N[(k * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000004e43 or 3.89999999999999968e106 < x

   1. Initial program 73.6%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{b \cdot c - \left(4 \cdot \left(a \cdot t\right) + \left(4 \cdot \left(i \cdot x\right) + 27 \cdot \left(j \cdot k\right)\right)\right)} \]
   3. 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 65.1

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

   4. Applied rewrites 65.1%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-*.f64 48.9

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

   7. Applied rewrites 48.9%

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

   if -9.5000000000000004e43 < x < 3.89999999999999968e106

   1. Initial program 92.8%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 52.4

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

   4. Applied rewrites 52.4%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 52.4

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

   6. Applied rewrites 52.4%

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

Alternative 17: 24.2% 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 85.5%

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

2. Taylor expanded in b around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 24.2

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

4. Applied rewrites 24.2%

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

Developer Target 1: 89.1% 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 2025093 
(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)))