Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 29.7% → 52.0%

Time: 21.0s

Alternatives: 26

Speedup: 4.4×

• 88.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (+
  (-
   (+
    (+
     (-
      (* (- (* x y) (* z t)) (- (* a b) (* c i)))
      (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i))))
     (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a))))
    (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i))))
   (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a))))
  (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
}

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, y0, y1, y2, y3, y4, y5)
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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)))
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 y0, double y1, double y2, double y3, double y4, double y5) {
	return (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(Float64(y0 * b) - Float64(y1 * i)))) + Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(y0 * c) - Float64(y1 * a)))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * Float64(Float64(y4 * b) - Float64(y5 * i)))) - Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(y4 * c) - Float64(y5 * a)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * b), $MachinePrecision] - N[(y1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 29.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (+
  (-
   (+
    (+
     (-
      (* (- (* x y) (* z t)) (- (* a b) (* c i)))
      (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i))))
     (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a))))
    (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i))))
   (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a))))
  (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
}

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, y0, y1, y2, y3, y4, y5)
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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)))
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 y0, double y1, double y2, double y3, double y4, double y5) {
	return (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(Float64(y0 * b) - Float64(y1 * i)))) + Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(y0 * c) - Float64(y1 * a)))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * Float64(Float64(y4 * b) - Float64(y5 * i)))) - Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(y4 * c) - Float64(y5 * a)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * b), $MachinePrecision] - N[(y1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 52.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ t_2 := j \cdot t - k \cdot y\\ t_3 := k \cdot y2 - j \cdot y3\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) + t\_3 \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-253}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t\_2, y1 \cdot t\_3\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+52}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot t\_2\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          -1.0
          (*
           z
           (-
            (fma t (- (* a b) (* c i)) (* y3 (- (* c y0) (* a y1))))
            (* k (- (* b y0) (* i y1)))))))
        (t_2 (- (* j t) (* k y)))
        (t_3 (- (* k y2) (* j y3))))
   (if (<= z -2.4e+163)
     t_1
     (if (<= z -9e+49)
       (+ (* t (* y4 (- (* b j) (* c y2)))) (* t_3 (- (* y4 y1) (* y5 y0))))
       (if (<= z -6e-253)
         (* y4 (- (fma b t_2 (* y1 t_3)) (* c (- (* t y2) (* y y3)))))
         (if (<= z 6.4e+52)
           (*
            -1.0
            (*
             i
             (-
              (fma c (- (* x y) (* t z)) (* y5 t_2))
              (* y1 (- (* j x) (* k z))))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -1.0 * (z * (fma(t, ((a * b) - (c * i)), (y3 * ((c * y0) - (a * y1)))) - (k * ((b * y0) - (i * y1)))));
	double t_2 = (j * t) - (k * y);
	double t_3 = (k * y2) - (j * y3);
	double tmp;
	if (z <= -2.4e+163) {
		tmp = t_1;
	} else if (z <= -9e+49) {
		tmp = (t * (y4 * ((b * j) - (c * y2)))) + (t_3 * ((y4 * y1) - (y5 * y0)));
	} else if (z <= -6e-253) {
		tmp = y4 * (fma(b, t_2, (y1 * t_3)) - (c * ((t * y2) - (y * y3))));
	} else if (z <= 6.4e+52) {
		tmp = -1.0 * (i * (fma(c, ((x * y) - (t * z)), (y5 * t_2)) - (y1 * ((j * x) - (k * z)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(-1.0 * Float64(z * Float64(fma(t, Float64(Float64(a * b) - Float64(c * i)), Float64(y3 * Float64(Float64(c * y0) - Float64(a * y1)))) - Float64(k * Float64(Float64(b * y0) - Float64(i * y1))))))
	t_2 = Float64(Float64(j * t) - Float64(k * y))
	t_3 = Float64(Float64(k * y2) - Float64(j * y3))
	tmp = 0.0
	if (z <= -2.4e+163)
		tmp = t_1;
	elseif (z <= -9e+49)
		tmp = Float64(Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2)))) + Float64(t_3 * Float64(Float64(y4 * y1) - Float64(y5 * y0))));
	elseif (z <= -6e-253)
		tmp = Float64(y4 * Float64(fma(b, t_2, Float64(y1 * t_3)) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (z <= 6.4e+52)
		tmp = Float64(-1.0 * Float64(i * Float64(fma(c, Float64(Float64(x * y) - Float64(t * z)), Float64(y5 * t_2)) - Float64(y1 * Float64(Float64(j * x) - Float64(k * z))))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(-1.0 * N[(z * N[(N[(t * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+163], t$95$1, If[LessEqual[z, -9e+49], N[(N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6e-253], N[(y4 * N[(N[(b * t$95$2 + N[(y1 * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+52], N[(-1.0 * N[(i * N[(N[(c * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(y1 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3999999999999999e163 or 6.4e52 < z

   1. Initial program 22.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 55.6%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   if -2.3999999999999999e163 < z < -8.99999999999999965e49

   1. Initial program 27.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. lift--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. lift-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - \color{blue}{y} \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      10. lift-*.f64 35.8

          \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot \color{blue}{y3}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Applied rewrites 35.8%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in t around inf

      \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y4 \cdot \color{blue}{\left(b \cdot j - c \cdot y2\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - \color{blue}{c \cdot y2}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lower--.f64 N/A

         \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot \color{blue}{y2}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 35.1

         \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   7. Applied rewrites 35.1%

      \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if -8.99999999999999965e49 < z < -6.0000000000000004e-253

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

   4. Applied rewrites 38.2%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -6.0000000000000004e-253 < z < 6.4e52

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 37.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 2: 43.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ t_2 := j \cdot t - k \cdot y\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-187}:\\ \;\;\;\;y4 \cdot \left(b \cdot t\_2 - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+52}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot t\_2\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1
         (*
          -1.0
          (*
           z
           (-
            (fma t (- (* a b) (* c i)) (* y3 (- (* c y0) (* a y1))))
            (* k (- (* b y0) (* i y1)))))))
        (t_2 (- (* j t) (* k y))))
   (if (<= z -7.2e+163)
     t_1
     (if (<= z -5.8e-187)
       (+
        (* y4 (- (* b t_2) (* c (- (* t y2) (* y y3)))))
        (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))
       (if (<= z 6.4e+52)
         (*
          -1.0
          (*
           i
           (-
            (fma c (- (* x y) (* t z)) (* y5 t_2))
            (* y1 (- (* j x) (* k z))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = -1.0 * (z * (fma(t, ((a * b) - (c * i)), (y3 * ((c * y0) - (a * y1)))) - (k * ((b * y0) - (i * y1)))));
	double t_2 = (j * t) - (k * y);
	double tmp;
	if (z <= -7.2e+163) {
		tmp = t_1;
	} else if (z <= -5.8e-187) {
		tmp = (y4 * ((b * t_2) - (c * ((t * y2) - (y * y3))))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
	} else if (z <= 6.4e+52) {
		tmp = -1.0 * (i * (fma(c, ((x * y) - (t * z)), (y5 * t_2)) - (y1 * ((j * x) - (k * z)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(-1.0 * Float64(z * Float64(fma(t, Float64(Float64(a * b) - Float64(c * i)), Float64(y3 * Float64(Float64(c * y0) - Float64(a * y1)))) - Float64(k * Float64(Float64(b * y0) - Float64(i * y1))))))
	t_2 = Float64(Float64(j * t) - Float64(k * y))
	tmp = 0.0
	if (z <= -7.2e+163)
		tmp = t_1;
	elseif (z <= -5.8e-187)
		tmp = Float64(Float64(y4 * Float64(Float64(b * t_2) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3))))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0))));
	elseif (z <= 6.4e+52)
		tmp = Float64(-1.0 * Float64(i * Float64(fma(c, Float64(Float64(x * y) - Float64(t * z)), Float64(y5 * t_2)) - Float64(y1 * Float64(Float64(j * x) - Float64(k * z))))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(-1.0 * N[(z * N[(N[(t * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(y3 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(k * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+163], t$95$1, If[LessEqual[z, -5.8e-187], N[(N[(y4 * N[(N[(b * t$95$2), $MachinePrecision] - N[(c * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+52], N[(-1.0 * N[(i * N[(N[(c * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(y1 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.19999999999999955e163 or 6.4e52 < z

   1. Initial program 22.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 55.6%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   if -7.19999999999999955e163 < z < -5.79999999999999977e-187

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. lift--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. lift-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - \color{blue}{y} \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      10. lift-*.f64 37.3

          \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot \color{blue}{y3}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Applied rewrites 37.3%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if -5.79999999999999977e-187 < z < 6.4e52

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 37.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 43.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + t\_1 \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{if}\;t\_2 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(\mathsf{fma}\left(-1, y5 \cdot t\_1, c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* k y2) (* j y3)))
        (t_2
         (+
          (-
           (+
            (+
             (-
              (* (- (* x y) (* z t)) (- (* a b) (* c i)))
              (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i))))
             (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a))))
            (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i))))
           (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a))))
          (* t_1 (- (* y4 y1) (* y5 y0))))))
   (if (<= t_2 INFINITY)
     t_2
     (*
      y0
      (-
       (fma -1.0 (* y5 t_1) (* c (- (* x y2) (* y3 z))))
       (* b (- (* j x) (* k z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (k * y2) - (j * y3);
	double t_2 = (((((((x * y) - (z * t)) * ((a * b) - (c * i))) - (((x * j) - (z * k)) * ((y0 * b) - (y1 * i)))) + (((x * y2) - (z * y3)) * ((y0 * c) - (y1 * a)))) + (((t * j) - (y * k)) * ((y4 * b) - (y5 * i)))) - (((t * y2) - (y * y3)) * ((y4 * c) - (y5 * a)))) + (t_1 * ((y4 * y1) - (y5 * y0)));
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = y0 * (fma(-1.0, (y5 * t_1), (c * ((x * y2) - (y3 * z)))) - (b * ((j * x) - (k * z))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(k * y2) - Float64(j * y3))
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * Float64(Float64(a * b) - Float64(c * i))) - Float64(Float64(Float64(x * j) - Float64(z * k)) * Float64(Float64(y0 * b) - Float64(y1 * i)))) + Float64(Float64(Float64(x * y2) - Float64(z * y3)) * Float64(Float64(y0 * c) - Float64(y1 * a)))) + Float64(Float64(Float64(t * j) - Float64(y * k)) * Float64(Float64(y4 * b) - Float64(y5 * i)))) - Float64(Float64(Float64(t * y2) - Float64(y * y3)) * Float64(Float64(y4 * c) - Float64(y5 * a)))) + Float64(t_1 * Float64(Float64(y4 * y1) - Float64(y5 * y0))))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(y0 * Float64(fma(-1.0, Float64(y5 * t_1), Float64(c * Float64(Float64(x * y2) - Float64(y3 * z)))) - Float64(b * Float64(Float64(j * x) - Float64(k * z)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x * j), $MachinePrecision] - N[(z * k), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * b), $MachinePrecision] - N[(y1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * y2), $MachinePrecision] - N[(z * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y0 * c), $MachinePrecision] - N[(y1 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t * j), $MachinePrecision] - N[(y * k), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * b), $MachinePrecision] - N[(y5 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(y0 * N[(N[(-1.0 * N[(y5 * t$95$1), $MachinePrecision] + N[(c * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (-.f64 (*.f64 a b) (*.f64 c i))) (*.f64 (-.f64 (*.f64 x j) (*.f64 z k)) (-.f64 (*.f64 y0 b) (*.f64 y1 i)))) (*.f64 (-.f64 (*.f64 x y2) (*.f64 z y3)) (-.f64 (*.f64 y0 c) (*.f64 y1 a)))) (*.f64 (-.f64 (*.f64 t j) (*.f64 y k)) (-.f64 (*.f64 y4 b) (*.f64 y5 i)))) (*.f64 (-.f64 (*.f64 t y2) (*.f64 y y3)) (-.f64 (*.f64 y4 c) (*.f64 y5 a)))) (*.f64 (-.f64 (*.f64 k y2) (*.f64 j y3)) (-.f64 (*.f64 y4 y1) (*.f64 y5 y0)))) < +inf.0

   1. Initial program 91.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if +inf.0 < (+.f64 (-.f64 (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z t)) (-.f64 (*.f64 a b) (*.f64 c i))) (*.f64 (-.f64 (*.f64 x j) (*.f64 z k)) (-.f64 (*.f64 y0 b) (*.f64 y1 i)))) (*.f64 (-.f64 (*.f64 x y2) (*.f64 z y3)) (-.f64 (*.f64 y0 c) (*.f64 y1 a)))) (*.f64 (-.f64 (*.f64 t j) (*.f64 y k)) (-.f64 (*.f64 y4 b) (*.f64 y5 i)))) (*.f64 (-.f64 (*.f64 t y2) (*.f64 y y3)) (-.f64 (*.f64 y4 c) (*.f64 y5 a)))) (*.f64 (-.f64 (*.f64 k y2) (*.f64 j y3)) (-.f64 (*.f64 y4 y1) (*.f64 y5 y0))))

   1. Initial program 0.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - \color{blue}{b \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 33.1%

      \[\leadsto \color{blue}{y0 \cdot \left(\mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 43.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-123}:\\ \;\;\;\;t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \left(\mathsf{fma}\left(y, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+52}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+181}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* b (* -1.0 (* z (- (* a t) (* k y0)))))))
   (if (<= z -3.8e+215)
     t_1
     (if (<= z -1.8e-123)
       (+
        (* t (* y4 (- (* b j) (* c y2))))
        (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))
       (if (<= z -8.2e-293)
         (*
          x
          (-
           (fma y (- (* a b) (* c i)) (* y2 (- (* c y0) (* a y1))))
           (* j (- (* b y0) (* i y1)))))
         (if (<= z 6.4e+52)
           (*
            -1.0
            (*
             i
             (- (fma c (* x y) (* y5 (- (* j t) (* k y)))) (* j (* x y1)))))
           (if (<= z 1.65e+181)
             t_1
             (* c (* z (fma -1.0 (* y0 y3) (* i 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = b * (-1.0 * (z * ((a * t) - (k * y0))));
	double tmp;
	if (z <= -3.8e+215) {
		tmp = t_1;
	} else if (z <= -1.8e-123) {
		tmp = (t * (y4 * ((b * j) - (c * y2)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
	} else if (z <= -8.2e-293) {
		tmp = x * (fma(y, ((a * b) - (c * i)), (y2 * ((c * y0) - (a * y1)))) - (j * ((b * y0) - (i * y1))));
	} else if (z <= 6.4e+52) {
		tmp = -1.0 * (i * (fma(c, (x * y), (y5 * ((j * t) - (k * y)))) - (j * (x * y1))));
	} else if (z <= 1.65e+181) {
		tmp = t_1;
	} else {
		tmp = c * (z * fma(-1.0, (y0 * y3), (i * t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(b * Float64(-1.0 * Float64(z * Float64(Float64(a * t) - Float64(k * y0)))))
	tmp = 0.0
	if (z <= -3.8e+215)
		tmp = t_1;
	elseif (z <= -1.8e-123)
		tmp = Float64(Float64(t * Float64(y4 * Float64(Float64(b * j) - Float64(c * y2)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0))));
	elseif (z <= -8.2e-293)
		tmp = Float64(x * Float64(fma(y, Float64(Float64(a * b) - Float64(c * i)), Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1)))) - Float64(j * Float64(Float64(b * y0) - Float64(i * y1)))));
	elseif (z <= 6.4e+52)
		tmp = Float64(-1.0 * Float64(i * Float64(fma(c, Float64(x * y), Float64(y5 * Float64(Float64(j * t) - Float64(k * y)))) - Float64(j * Float64(x * y1)))));
	elseif (z <= 1.65e+181)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(z * fma(-1.0, Float64(y0 * y3), Float64(i * t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(b * N[(-1.0 * N[(z * N[(N[(a * t), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+215], t$95$1, If[LessEqual[z, -1.8e-123], N[(N[(t * N[(y4 * N[(N[(b * j), $MachinePrecision] - N[(c * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.2e-293], N[(x * N[(N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+52], N[(-1.0 * N[(i * N[(N[(c * N[(x * y), $MachinePrecision] + N[(y5 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+181], t$95$1, N[(c * N[(z * N[(-1.0 * N[(y0 * y3), $MachinePrecision] + N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.79999999999999968e215 or 6.4e52 < z < 1.65000000000000008e181

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.6%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in z around -inf

      \[\leadsto b \cdot \left(-1 \cdot \color{blue}{\left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \color{blue}{\left(a \cdot t - k \cdot y0\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - \color{blue}{k \cdot y0}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot \color{blue}{y0}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right) \]

      5. lower-*.f64 39.6

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right) \]

   7. Applied rewrites 39.6%

      \[\leadsto b \cdot \left(-1 \cdot \color{blue}{\left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)}\right) \]

   if -3.79999999999999968e215 < z < -1.7999999999999998e-123

   1. Initial program 29.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. lift--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. lift-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - \color{blue}{y} \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      10. lift-*.f64 35.0

          \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot \color{blue}{y3}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Applied rewrites 35.0%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in t around inf

      \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y4 \cdot \color{blue}{\left(b \cdot j - c \cdot y2\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - \color{blue}{c \cdot y2}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lower--.f64 N/A

         \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot \color{blue}{y2}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 34.9

         \[\leadsto t \cdot \left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   7. Applied rewrites 34.9%

      \[\leadsto t \cdot \color{blue}{\left(y4 \cdot \left(b \cdot j - c \cdot y2\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if -1.7999999999999998e-123 < z < -8.19999999999999975e-293

   1. Initial program 34.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto x \cdot \left(\left(y \cdot \left(a \cdot b - c \cdot i\right) + y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{j \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 41.2%

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{fma}\left(y, a \cdot b - c \cdot i, y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - j \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   if -8.19999999999999975e-293 < z < 6.4e52

   1. Initial program 34.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 37.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \color{blue}{\left(x \cdot y1\right)}\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(\color{blue}{x} \cdot y1\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      4. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot \color{blue}{y1}\right)\right)\right) \]

      9. lower-*.f64 36.0

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

   7. Applied rewrites 36.0%

      \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]

   if 1.65000000000000008e181 < z

   1. Initial program 24.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 53.0%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in c around -inf

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + \color{blue}{i \cdot t}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot \color{blue}{y3}, i \cdot t\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right) \]

      5. lower-*.f64 41.6

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right) \]

   7. Applied rewrites 41.6%

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 5: 42.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot t - k \cdot y\\ t_2 := -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot t\_1\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\\ t_3 := k \cdot y2 - j \cdot y3\\ t_4 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;i \leq -310000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{-181}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t\_1, y1 \cdot t\_3\right) - c \cdot t\_4\right)\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{+26}:\\ \;\;\;\;-1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, t\_1, y0 \cdot t\_3\right) - a \cdot t\_4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* j t) (* k y)))
        (t_2
         (*
          -1.0
          (*
           i
           (-
            (fma c (- (* x y) (* t z)) (* y5 t_1))
            (* y1 (- (* j x) (* k z)))))))
        (t_3 (- (* k y2) (* j y3)))
        (t_4 (- (* t y2) (* y y3))))
   (if (<= i -310000000.0)
     t_2
     (if (<= i 4.1e-181)
       (* y4 (- (fma b t_1 (* y1 t_3)) (* c t_4)))
       (if (<= i 4.5e+26)
         (* -1.0 (* y5 (- (fma i t_1 (* y0 t_3)) (* a t_4))))
         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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * t) - (k * y);
	double t_2 = -1.0 * (i * (fma(c, ((x * y) - (t * z)), (y5 * t_1)) - (y1 * ((j * x) - (k * z)))));
	double t_3 = (k * y2) - (j * y3);
	double t_4 = (t * y2) - (y * y3);
	double tmp;
	if (i <= -310000000.0) {
		tmp = t_2;
	} else if (i <= 4.1e-181) {
		tmp = y4 * (fma(b, t_1, (y1 * t_3)) - (c * t_4));
	} else if (i <= 4.5e+26) {
		tmp = -1.0 * (y5 * (fma(i, t_1, (y0 * t_3)) - (a * t_4)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * t) - Float64(k * y))
	t_2 = Float64(-1.0 * Float64(i * Float64(fma(c, Float64(Float64(x * y) - Float64(t * z)), Float64(y5 * t_1)) - Float64(y1 * Float64(Float64(j * x) - Float64(k * z))))))
	t_3 = Float64(Float64(k * y2) - Float64(j * y3))
	t_4 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (i <= -310000000.0)
		tmp = t_2;
	elseif (i <= 4.1e-181)
		tmp = Float64(y4 * Float64(fma(b, t_1, Float64(y1 * t_3)) - Float64(c * t_4)));
	elseif (i <= 4.5e+26)
		tmp = Float64(-1.0 * Float64(y5 * Float64(fma(i, t_1, Float64(y0 * t_3)) - Float64(a * t_4))));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 * N[(i * N[(N[(c * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(y1 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -310000000.0], t$95$2, If[LessEqual[i, 4.1e-181], N[(y4 * N[(N[(b * t$95$1 + N[(y1 * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.5e+26], N[(-1.0 * N[(y5 * N[(N[(i * t$95$1 + N[(y0 * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(a * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.1e8 or 4.49999999999999978e26 < i

   1. Initial program 25.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 49.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   if -3.1e8 < i < 4.1000000000000001e-181

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

   4. Applied rewrites 39.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if 4.1000000000000001e-181 < i < 4.49999999999999978e26

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{a \cdot \left(t \cdot y2 - y \cdot y3\right)}\right)\right) \]

   4. Applied rewrites 36.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 38.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot t - k \cdot y\\ t_2 := -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot t\_1\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\\ \mathbf{if}\;i \leq -310000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 4.7 \cdot 10^{-133}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t\_1, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq 480000:\\ \;\;\;\;b \cdot \left(y4 \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* j t) (* k y)))
        (t_2
         (*
          -1.0
          (*
           i
           (-
            (fma c (- (* x y) (* t z)) (* y5 t_1))
            (* y1 (- (* j x) (* k z))))))))
   (if (<= i -310000000.0)
     t_2
     (if (<= i 4.7e-133)
       (*
        y4
        (-
         (fma b t_1 (* y1 (- (* k y2) (* j y3))))
         (* c (- (* t y2) (* y y3)))))
       (if (<= i 480000.0) (* b (* y4 t_1)) 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * t) - (k * y);
	double t_2 = -1.0 * (i * (fma(c, ((x * y) - (t * z)), (y5 * t_1)) - (y1 * ((j * x) - (k * z)))));
	double tmp;
	if (i <= -310000000.0) {
		tmp = t_2;
	} else if (i <= 4.7e-133) {
		tmp = y4 * (fma(b, t_1, (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	} else if (i <= 480000.0) {
		tmp = b * (y4 * t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * t) - Float64(k * y))
	t_2 = Float64(-1.0 * Float64(i * Float64(fma(c, Float64(Float64(x * y) - Float64(t * z)), Float64(y5 * t_1)) - Float64(y1 * Float64(Float64(j * x) - Float64(k * z))))))
	tmp = 0.0
	if (i <= -310000000.0)
		tmp = t_2;
	elseif (i <= 4.7e-133)
		tmp = Float64(y4 * Float64(fma(b, t_1, Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (i <= 480000.0)
		tmp = Float64(b * Float64(y4 * t_1));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 * N[(i * N[(N[(c * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(y1 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -310000000.0], t$95$2, If[LessEqual[i, 4.7e-133], N[(y4 * N[(N[(b * t$95$1 + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 480000.0], N[(b * N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.1e8 or 4.8e5 < i

   1. Initial program 25.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 48.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   if -3.1e8 < i < 4.70000000000000003e-133

   1. Initial program 33.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

   4. Applied rewrites 39.6%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if 4.70000000000000003e-133 < i < 4.8e5

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 38.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in y4 around inf

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot \color{blue}{y}\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) \]

      4. lift-*.f64 27.0

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - \color{blue}{k \cdot y}\right)\right) \]

   7. Applied rewrites 27.0%

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 38.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot t - k \cdot y\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+82}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-253}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t\_1, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+52}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot t\_1\right) - j \cdot \left(x \cdot y1\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+181}:\\ \;\;\;\;b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* j t) (* k y))))
   (if (<= z -3.2e+82)
     (* -1.0 (* i (- (* -1.0 (* k (* y y5))) (* y1 (- (* j x) (* k z))))))
     (if (<= z -6e-253)
       (*
        y4
        (-
         (fma b t_1 (* y1 (- (* k y2) (* j y3))))
         (* c (- (* t y2) (* y y3)))))
       (if (<= z 6.4e+52)
         (* -1.0 (* i (- (fma c (* x y) (* y5 t_1)) (* j (* x y1)))))
         (if (<= z 1.65e+181)
           (* b (* -1.0 (* z (- (* a t) (* k y0)))))
           (* c (* z (fma -1.0 (* y0 y3) (* i 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * t) - (k * y);
	double tmp;
	if (z <= -3.2e+82) {
		tmp = -1.0 * (i * ((-1.0 * (k * (y * y5))) - (y1 * ((j * x) - (k * z)))));
	} else if (z <= -6e-253) {
		tmp = y4 * (fma(b, t_1, (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	} else if (z <= 6.4e+52) {
		tmp = -1.0 * (i * (fma(c, (x * y), (y5 * t_1)) - (j * (x * y1))));
	} else if (z <= 1.65e+181) {
		tmp = b * (-1.0 * (z * ((a * t) - (k * y0))));
	} else {
		tmp = c * (z * fma(-1.0, (y0 * y3), (i * t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * t) - Float64(k * y))
	tmp = 0.0
	if (z <= -3.2e+82)
		tmp = Float64(-1.0 * Float64(i * Float64(Float64(-1.0 * Float64(k * Float64(y * y5))) - Float64(y1 * Float64(Float64(j * x) - Float64(k * z))))));
	elseif (z <= -6e-253)
		tmp = Float64(y4 * Float64(fma(b, t_1, Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (z <= 6.4e+52)
		tmp = Float64(-1.0 * Float64(i * Float64(fma(c, Float64(x * y), Float64(y5 * t_1)) - Float64(j * Float64(x * y1)))));
	elseif (z <= 1.65e+181)
		tmp = Float64(b * Float64(-1.0 * Float64(z * Float64(Float64(a * t) - Float64(k * y0)))));
	else
		tmp = Float64(c * Float64(z * fma(-1.0, Float64(y0 * y3), Float64(i * t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+82], N[(-1.0 * N[(i * N[(N[(-1.0 * N[(k * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y1 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6e-253], N[(y4 * N[(N[(b * t$95$1 + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+52], N[(-1.0 * N[(i * N[(N[(c * N[(x * y), $MachinePrecision] + N[(y5 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+181], N[(b * N[(-1.0 * N[(z * N[(N[(a * t), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(z * N[(-1.0 * N[(y0 * y3), $MachinePrecision] + N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.19999999999999975e82

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 36.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in k around inf

      \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - \color{blue}{y1} \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. lower-*.f64 35.2

         \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   7. Applied rewrites 35.2%

      \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - \color{blue}{y1} \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   if -3.19999999999999975e82 < z < -6.0000000000000004e-253

   1. Initial program 33.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

   4. Applied rewrites 38.4%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if -6.0000000000000004e-253 < z < 6.4e52

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 37.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \color{blue}{\left(x \cdot y1\right)}\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(\color{blue}{x} \cdot y1\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      4. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot \color{blue}{y1}\right)\right)\right) \]

      9. lower-*.f64 35.8

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

   7. Applied rewrites 35.8%

      \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]

   if 6.4e52 < z < 1.65000000000000008e181

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in z around -inf

      \[\leadsto b \cdot \left(-1 \cdot \color{blue}{\left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \color{blue}{\left(a \cdot t - k \cdot y0\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - \color{blue}{k \cdot y0}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot \color{blue}{y0}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right) \]

      5. lower-*.f64 32.8

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right) \]

   7. Applied rewrites 32.8%

      \[\leadsto b \cdot \left(-1 \cdot \color{blue}{\left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)}\right) \]

   if 1.65000000000000008e181 < z

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 59.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in c around -inf

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + \color{blue}{i \cdot t}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot \color{blue}{y3}, i \cdot t\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right) \]

      5. lower-*.f64 45.4

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right) \]

   7. Applied rewrites 45.4%

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 8: 37.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot t - k \cdot y\\ \mathbf{if}\;i \leq -1.02 \cdot 10^{-38}:\\ \;\;\;\;-1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{-201}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-287}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right)\right)\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-200}:\\ \;\;\;\;b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(y4 \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot y1, y5 \cdot t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* j t) (* k y))))
   (if (<= i -1.02e-38)
     (* -1.0 (* y1 (* i (- (* k z) (* j x)))))
     (if (<= i -8.5e-201)
       (+
        (* y4 (* c (* y y3)))
        (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))
       (if (<= i -1.25e-287)
         (* -1.0 (* i (* c (- (* x y) (* t z)))))
         (if (<= i 5e-200)
           (* b (* x (- (* a y) (* j y0))))
           (if (<= i 1.1e+79)
             (* b (* y4 t_1))
             (* -1.0 (* i (fma x (- (* c y) (* j y1)) (* y5 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * t) - (k * y);
	double tmp;
	if (i <= -1.02e-38) {
		tmp = -1.0 * (y1 * (i * ((k * z) - (j * x))));
	} else if (i <= -8.5e-201) {
		tmp = (y4 * (c * (y * y3))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
	} else if (i <= -1.25e-287) {
		tmp = -1.0 * (i * (c * ((x * y) - (t * z))));
	} else if (i <= 5e-200) {
		tmp = b * (x * ((a * y) - (j * y0)));
	} else if (i <= 1.1e+79) {
		tmp = b * (y4 * t_1);
	} else {
		tmp = -1.0 * (i * fma(x, ((c * y) - (j * y1)), (y5 * t_1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * t) - Float64(k * y))
	tmp = 0.0
	if (i <= -1.02e-38)
		tmp = Float64(-1.0 * Float64(y1 * Float64(i * Float64(Float64(k * z) - Float64(j * x)))));
	elseif (i <= -8.5e-201)
		tmp = Float64(Float64(y4 * Float64(c * Float64(y * y3))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0))));
	elseif (i <= -1.25e-287)
		tmp = Float64(-1.0 * Float64(i * Float64(c * Float64(Float64(x * y) - Float64(t * z)))));
	elseif (i <= 5e-200)
		tmp = Float64(b * Float64(x * Float64(Float64(a * y) - Float64(j * y0))));
	elseif (i <= 1.1e+79)
		tmp = Float64(b * Float64(y4 * t_1));
	else
		tmp = Float64(-1.0 * Float64(i * fma(x, Float64(Float64(c * y) - Float64(j * y1)), Float64(y5 * t_1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.02e-38], N[(-1.0 * N[(y1 * N[(i * N[(N[(k * z), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -8.5e-201], N[(N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.25e-287], N[(-1.0 * N[(i * N[(c * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5e-200], N[(b * N[(x * N[(N[(a * y), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.1e+79], N[(b * N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(i * N[(x * N[(N[(c * y), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -1.01999999999999998e-38

   1. Initial program 25.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 46.5%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y1 around inf

      \[\leadsto -1 \cdot \left(y1 \cdot \color{blue}{\left(i \cdot \left(k \cdot z - j \cdot x\right) + \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right) + \color{blue}{\frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}}\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - \color{blue}{j \cdot x}, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot \color{blue}{x}, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      6. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

   7. Applied rewrites 47.6%

      \[\leadsto -1 \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)}\right) \]

   8. Taylor expanded in y1 around inf

      \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - \color{blue}{j \cdot x}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot \color{blue}{x}\right)\right)\right) \]

      2. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right)\right)\right) \]

      4. lift-*.f64 36.5

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right)\right)\right) \]

   10. Applied rewrites 36.5%

       \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - \color{blue}{j \cdot x}\right)\right)\right) \]

   if -1.01999999999999998e-38 < i < -8.5000000000000007e-201

   1. Initial program 33.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. lift--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. lift-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - \color{blue}{y} \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      10. lift-*.f64 37.7

          \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot \color{blue}{y3}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Applied rewrites 37.7%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y3 around inf

      \[\leadsto y4 \cdot \left(c \cdot \color{blue}{\left(y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot \color{blue}{y3}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lift-*.f64 37.2

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   7. Applied rewrites 37.2%

      \[\leadsto y4 \cdot \left(c \cdot \color{blue}{\left(y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if -8.5000000000000007e-201 < i < -1.25000000000000006e-287

   1. Initial program 32.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 24.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in c around inf

      \[\leadsto -1 \cdot \left(i \cdot \left(c \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - \color{blue}{t \cdot z}\right)\right)\right) \]

      2. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot \color{blue}{z}\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right)\right)\right) \]

      4. lift-*.f64 18.1

         \[\leadsto -1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right)\right)\right) \]

   7. Applied rewrites 18.1%

      \[\leadsto -1 \cdot \left(i \cdot \left(c \cdot \color{blue}{\left(x \cdot y - t \cdot z\right)}\right)\right) \]

   if -1.25000000000000006e-287 < i < 4.99999999999999991e-200

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 39.0%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 27.6

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 27.6%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   if 4.99999999999999991e-200 < i < 1.0999999999999999e79

   1. Initial program 34.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 38.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in y4 around inf

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot \color{blue}{y}\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) \]

      4. lift-*.f64 28.3

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - \color{blue}{k \cdot y}\right)\right) \]

   7. Applied rewrites 28.3%

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]

   if 1.0999999999999999e79 < i

   1. Initial program 24.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 53.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \color{blue}{\left(x \cdot y1\right)}\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(\color{blue}{x} \cdot y1\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      4. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot \color{blue}{y1}\right)\right)\right) \]

      9. lower-*.f64 45.3

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

   7. Applied rewrites 45.3%

      \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto -1 \cdot \left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right) + y5 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right)\right) \]
   9. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot \color{blue}{y1}, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot y1, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot y1, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot y1, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]

      5. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot y1, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot y1, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot y1, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]

      8. lift-*.f64 48.1

         \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot y1, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]

   10. Applied rewrites 48.1%

       \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - \color{blue}{j \cdot y1}, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 9: 36.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+82}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-187}:\\ \;\;\;\;y4 \cdot \left(-1 \cdot \left(c \cdot \left(t \cdot y2\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+52}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+181}:\\ \;\;\;\;b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -3.9e+82)
   (* -1.0 (* i (- (* -1.0 (* k (* y y5))) (* y1 (- (* j x) (* k z))))))
   (if (<= z -2.8e-187)
     (+
      (* y4 (* -1.0 (* c (* t y2))))
      (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))
     (if (<= z 6.4e+52)
       (*
        -1.0
        (* i (- (fma c (* x y) (* y5 (- (* j t) (* k y)))) (* j (* x y1)))))
       (if (<= z 1.65e+181)
         (* b (* -1.0 (* z (- (* a t) (* k y0)))))
         (* c (* z (fma -1.0 (* y0 y3) (* i 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -3.9e+82) {
		tmp = -1.0 * (i * ((-1.0 * (k * (y * y5))) - (y1 * ((j * x) - (k * z)))));
	} else if (z <= -2.8e-187) {
		tmp = (y4 * (-1.0 * (c * (t * y2)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
	} else if (z <= 6.4e+52) {
		tmp = -1.0 * (i * (fma(c, (x * y), (y5 * ((j * t) - (k * y)))) - (j * (x * y1))));
	} else if (z <= 1.65e+181) {
		tmp = b * (-1.0 * (z * ((a * t) - (k * y0))));
	} else {
		tmp = c * (z * fma(-1.0, (y0 * y3), (i * t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (z <= -3.9e+82)
		tmp = Float64(-1.0 * Float64(i * Float64(Float64(-1.0 * Float64(k * Float64(y * y5))) - Float64(y1 * Float64(Float64(j * x) - Float64(k * z))))));
	elseif (z <= -2.8e-187)
		tmp = Float64(Float64(y4 * Float64(-1.0 * Float64(c * Float64(t * y2)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0))));
	elseif (z <= 6.4e+52)
		tmp = Float64(-1.0 * Float64(i * Float64(fma(c, Float64(x * y), Float64(y5 * Float64(Float64(j * t) - Float64(k * y)))) - Float64(j * Float64(x * y1)))));
	elseif (z <= 1.65e+181)
		tmp = Float64(b * Float64(-1.0 * Float64(z * Float64(Float64(a * t) - Float64(k * y0)))));
	else
		tmp = Float64(c * Float64(z * fma(-1.0, Float64(y0 * y3), Float64(i * t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[z, -3.9e+82], N[(-1.0 * N[(i * N[(N[(-1.0 * N[(k * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y1 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-187], N[(N[(y4 * N[(-1.0 * N[(c * N[(t * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+52], N[(-1.0 * N[(i * N[(N[(c * N[(x * y), $MachinePrecision] + N[(y5 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+181], N[(b * N[(-1.0 * N[(z * N[(N[(a * t), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(z * N[(-1.0 * N[(y0 * y3), $MachinePrecision] + N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.89999999999999976e82

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 36.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in k around inf

      \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - \color{blue}{y1} \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. lower-*.f64 35.2

         \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   7. Applied rewrites 35.2%

      \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - \color{blue}{y1} \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   if -3.89999999999999976e82 < z < -2.8e-187

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. lift--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. lift-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - \color{blue}{y} \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      10. lift-*.f64 38.1

          \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot \color{blue}{y3}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Applied rewrites 38.1%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y2 around inf

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(c \cdot \left(t \cdot y2\right)\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(c \cdot \color{blue}{\left(t \cdot y2\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(-1 \cdot \left(c \cdot \left(t \cdot \color{blue}{y2}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lift-*.f64 36.2

         \[\leadsto y4 \cdot \left(-1 \cdot \left(c \cdot \left(t \cdot y2\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   7. Applied rewrites 36.2%

      \[\leadsto y4 \cdot \left(-1 \cdot \color{blue}{\left(c \cdot \left(t \cdot y2\right)\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if -2.8e-187 < z < 6.4e52

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 37.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \color{blue}{\left(x \cdot y1\right)}\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(\color{blue}{x} \cdot y1\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      4. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot \color{blue}{y1}\right)\right)\right) \]

      9. lower-*.f64 36.3

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

   7. Applied rewrites 36.3%

      \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]

   if 6.4e52 < z < 1.65000000000000008e181

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in z around -inf

      \[\leadsto b \cdot \left(-1 \cdot \color{blue}{\left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \color{blue}{\left(a \cdot t - k \cdot y0\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - \color{blue}{k \cdot y0}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot \color{blue}{y0}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right) \]

      5. lower-*.f64 32.8

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right) \]

   7. Applied rewrites 32.8%

      \[\leadsto b \cdot \left(-1 \cdot \color{blue}{\left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)}\right) \]

   if 1.65000000000000008e181 < z

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 59.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in c around -inf

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + \color{blue}{i \cdot t}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot \color{blue}{y3}, i \cdot t\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right) \]

      5. lower-*.f64 45.4

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right) \]

   7. Applied rewrites 45.4%

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 10: 36.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+82}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-187}:\\ \;\;\;\;-1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+52}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+181}:\\ \;\;\;\;b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -3.9e+82)
   (* -1.0 (* i (- (* -1.0 (* k (* y y5))) (* y1 (- (* j x) (* k z))))))
   (if (<= z -2.8e-187)
     (+
      (* -1.0 (* c (* t (* y2 y4))))
      (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))
     (if (<= z 6.4e+52)
       (*
        -1.0
        (* i (- (fma c (* x y) (* y5 (- (* j t) (* k y)))) (* j (* x y1)))))
       (if (<= z 1.65e+181)
         (* b (* -1.0 (* z (- (* a t) (* k y0)))))
         (* c (* z (fma -1.0 (* y0 y3) (* i 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -3.9e+82) {
		tmp = -1.0 * (i * ((-1.0 * (k * (y * y5))) - (y1 * ((j * x) - (k * z)))));
	} else if (z <= -2.8e-187) {
		tmp = (-1.0 * (c * (t * (y2 * y4)))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
	} else if (z <= 6.4e+52) {
		tmp = -1.0 * (i * (fma(c, (x * y), (y5 * ((j * t) - (k * y)))) - (j * (x * y1))));
	} else if (z <= 1.65e+181) {
		tmp = b * (-1.0 * (z * ((a * t) - (k * y0))));
	} else {
		tmp = c * (z * fma(-1.0, (y0 * y3), (i * t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (z <= -3.9e+82)
		tmp = Float64(-1.0 * Float64(i * Float64(Float64(-1.0 * Float64(k * Float64(y * y5))) - Float64(y1 * Float64(Float64(j * x) - Float64(k * z))))));
	elseif (z <= -2.8e-187)
		tmp = Float64(Float64(-1.0 * Float64(c * Float64(t * Float64(y2 * y4)))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0))));
	elseif (z <= 6.4e+52)
		tmp = Float64(-1.0 * Float64(i * Float64(fma(c, Float64(x * y), Float64(y5 * Float64(Float64(j * t) - Float64(k * y)))) - Float64(j * Float64(x * y1)))));
	elseif (z <= 1.65e+181)
		tmp = Float64(b * Float64(-1.0 * Float64(z * Float64(Float64(a * t) - Float64(k * y0)))));
	else
		tmp = Float64(c * Float64(z * fma(-1.0, Float64(y0 * y3), Float64(i * t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[z, -3.9e+82], N[(-1.0 * N[(i * N[(N[(-1.0 * N[(k * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y1 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-187], N[(N[(-1.0 * N[(c * N[(t * N[(y2 * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+52], N[(-1.0 * N[(i * N[(N[(c * N[(x * y), $MachinePrecision] + N[(y5 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+181], N[(b * N[(-1.0 * N[(z * N[(N[(a * t), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(z * N[(-1.0 * N[(y0 * y3), $MachinePrecision] + N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.89999999999999976e82

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 36.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in k around inf

      \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - \color{blue}{y1} \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. lower-*.f64 35.2

         \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   7. Applied rewrites 35.2%

      \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - \color{blue}{y1} \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   if -3.89999999999999976e82 < z < -2.8e-187

   1. Initial program 33.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. lift--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. lift-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - \color{blue}{y} \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      10. lift-*.f64 38.1

          \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot \color{blue}{y3}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Applied rewrites 38.1%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y2 around inf

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(t \cdot \left(y2 \cdot y4\right)\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(c \cdot \left(t \cdot \color{blue}{\left(y2 \cdot y4\right)}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot \color{blue}{y4}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower-*.f64 34.5

         \[\leadsto -1 \cdot \left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   7. Applied rewrites 34.5%

      \[\leadsto -1 \cdot \color{blue}{\left(c \cdot \left(t \cdot \left(y2 \cdot y4\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if -2.8e-187 < z < 6.4e52

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 37.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \color{blue}{\left(x \cdot y1\right)}\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(\color{blue}{x} \cdot y1\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      4. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot \color{blue}{y1}\right)\right)\right) \]

      9. lower-*.f64 36.3

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

   7. Applied rewrites 36.3%

      \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]

   if 6.4e52 < z < 1.65000000000000008e181

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in z around -inf

      \[\leadsto b \cdot \left(-1 \cdot \color{blue}{\left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \color{blue}{\left(a \cdot t - k \cdot y0\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - \color{blue}{k \cdot y0}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot \color{blue}{y0}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right) \]

      5. lower-*.f64 32.8

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right) \]

   7. Applied rewrites 32.8%

      \[\leadsto b \cdot \left(-1 \cdot \color{blue}{\left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)}\right) \]

   if 1.65000000000000008e181 < z

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 59.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in c around -inf

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + \color{blue}{i \cdot t}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot \color{blue}{y3}, i \cdot t\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right) \]

      5. lower-*.f64 45.4

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right) \]

   7. Applied rewrites 45.4%

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 11: 36.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot t - k \cdot y\\ t_2 := k \cdot z - j \cdot x\\ \mathbf{if}\;i \leq -1.6 \cdot 10^{-38}:\\ \;\;\;\;-1 \cdot \left(y1 \cdot \left(i \cdot t\_2\right)\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-180}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t\_1, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq 2.25 \cdot 10^{-70}:\\ \;\;\;\;b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot t\_1\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, t\_2, \frac{i \cdot \mathsf{fma}\left(-1, k \cdot \left(y \cdot y5\right), c \cdot \left(x \cdot y\right)\right)}{y1}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* j t) (* k y))) (t_2 (- (* k z) (* j x))))
   (if (<= i -1.6e-38)
     (* -1.0 (* y1 (* i t_2)))
     (if (<= i 1.1e-180)
       (*
        y4
        (-
         (fma b t_1 (* y1 (- (* k y2) (* j y3))))
         (* c (- (* t y2) (* y y3)))))
       (if (<= i 2.25e-70)
         (*
          b
          (-
           (fma a (- (* x y) (* t z)) (* y4 t_1))
           (* y0 (- (* j x) (* k z)))))
         (*
          -1.0
          (*
           y1
           (fma
            i
            t_2
            (/ (* i (fma -1.0 (* k (* y y5)) (* c (* x y)))) y1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * t) - (k * y);
	double t_2 = (k * z) - (j * x);
	double tmp;
	if (i <= -1.6e-38) {
		tmp = -1.0 * (y1 * (i * t_2));
	} else if (i <= 1.1e-180) {
		tmp = y4 * (fma(b, t_1, (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	} else if (i <= 2.25e-70) {
		tmp = b * (fma(a, ((x * y) - (t * z)), (y4 * t_1)) - (y0 * ((j * x) - (k * z))));
	} else {
		tmp = -1.0 * (y1 * fma(i, t_2, ((i * fma(-1.0, (k * (y * y5)), (c * (x * y)))) / y1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * t) - Float64(k * y))
	t_2 = Float64(Float64(k * z) - Float64(j * x))
	tmp = 0.0
	if (i <= -1.6e-38)
		tmp = Float64(-1.0 * Float64(y1 * Float64(i * t_2)));
	elseif (i <= 1.1e-180)
		tmp = Float64(y4 * Float64(fma(b, t_1, Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (i <= 2.25e-70)
		tmp = Float64(b * Float64(fma(a, Float64(Float64(x * y) - Float64(t * z)), Float64(y4 * t_1)) - Float64(y0 * Float64(Float64(j * x) - Float64(k * z)))));
	else
		tmp = Float64(-1.0 * Float64(y1 * fma(i, t_2, Float64(Float64(i * fma(-1.0, Float64(k * Float64(y * y5)), Float64(c * Float64(x * y)))) / y1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * z), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.6e-38], N[(-1.0 * N[(y1 * N[(i * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.1e-180], N[(y4 * N[(N[(b * t$95$1 + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.25e-70], N[(b * N[(N[(a * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(y0 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(y1 * N[(i * t$95$2 + N[(N[(i * N[(-1.0 * N[(k * N[(y * y5), $MachinePrecision]), $MachinePrecision] + N[(c * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.59999999999999989e-38

   1. Initial program 25.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 46.5%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y1 around inf

      \[\leadsto -1 \cdot \left(y1 \cdot \color{blue}{\left(i \cdot \left(k \cdot z - j \cdot x\right) + \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right) + \color{blue}{\frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}}\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - \color{blue}{j \cdot x}, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot \color{blue}{x}, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      6. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

   7. Applied rewrites 47.6%

      \[\leadsto -1 \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)}\right) \]

   8. Taylor expanded in y1 around inf

      \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - \color{blue}{j \cdot x}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot \color{blue}{x}\right)\right)\right) \]

      2. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right)\right)\right) \]

      4. lift-*.f64 36.5

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right)\right)\right) \]

   10. Applied rewrites 36.5%

       \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - \color{blue}{j \cdot x}\right)\right)\right) \]

   if -1.59999999999999989e-38 < i < 1.10000000000000007e-180

   1. Initial program 33.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

   4. Applied rewrites 39.3%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   if 1.10000000000000007e-180 < i < 2.25000000000000011e-70

   1. Initial program 31.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 36.5%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 2.25000000000000011e-70 < i

   1. Initial program 28.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 45.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y1 around inf

      \[\leadsto -1 \cdot \left(y1 \cdot \color{blue}{\left(i \cdot \left(k \cdot z - j \cdot x\right) + \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right) + \color{blue}{\frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}}\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - \color{blue}{j \cdot x}, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot \color{blue}{x}, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      6. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

   7. Applied rewrites 45.1%

      \[\leadsto -1 \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)}\right) \]

   8. Taylor expanded in t around 0

      \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) + c \cdot \left(x \cdot y\right)\right)}{y1}\right)\right) \]
   9. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \mathsf{fma}\left(-1, k \cdot \left(y \cdot y5\right), c \cdot \left(x \cdot y\right)\right)}{y1}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \mathsf{fma}\left(-1, k \cdot \left(y \cdot y5\right), c \cdot \left(x \cdot y\right)\right)}{y1}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \mathsf{fma}\left(-1, k \cdot \left(y \cdot y5\right), c \cdot \left(x \cdot y\right)\right)}{y1}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \mathsf{fma}\left(-1, k \cdot \left(y \cdot y5\right), c \cdot \left(x \cdot y\right)\right)}{y1}\right)\right) \]

      5. lift-*.f64 39.5

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \mathsf{fma}\left(-1, k \cdot \left(y \cdot y5\right), c \cdot \left(x \cdot y\right)\right)}{y1}\right)\right) \]

   10. Applied rewrites 39.5%

       \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \mathsf{fma}\left(-1, k \cdot \left(y \cdot y5\right), c \cdot \left(x \cdot y\right)\right)}{y1}\right)\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 12: 34.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+71}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-167}:\\ \;\;\;\;y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+52}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+181}:\\ \;\;\;\;b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= z -1.4e+71)
   (* -1.0 (* i (- (* -1.0 (* k (* y y5))) (* y1 (- (* j x) (* k z))))))
   (if (<= z -3.9e-167)
     (+
      (* y4 (* c (* y y3)))
      (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))
     (if (<= z 6.4e+52)
       (*
        -1.0
        (* i (- (fma c (* x y) (* y5 (- (* j t) (* k y)))) (* j (* x y1)))))
       (if (<= z 1.65e+181)
         (* b (* -1.0 (* z (- (* a t) (* k y0)))))
         (* c (* z (fma -1.0 (* y0 y3) (* i 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (z <= -1.4e+71) {
		tmp = -1.0 * (i * ((-1.0 * (k * (y * y5))) - (y1 * ((j * x) - (k * z)))));
	} else if (z <= -3.9e-167) {
		tmp = (y4 * (c * (y * y3))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
	} else if (z <= 6.4e+52) {
		tmp = -1.0 * (i * (fma(c, (x * y), (y5 * ((j * t) - (k * y)))) - (j * (x * y1))));
	} else if (z <= 1.65e+181) {
		tmp = b * (-1.0 * (z * ((a * t) - (k * y0))));
	} else {
		tmp = c * (z * fma(-1.0, (y0 * y3), (i * t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (z <= -1.4e+71)
		tmp = Float64(-1.0 * Float64(i * Float64(Float64(-1.0 * Float64(k * Float64(y * y5))) - Float64(y1 * Float64(Float64(j * x) - Float64(k * z))))));
	elseif (z <= -3.9e-167)
		tmp = Float64(Float64(y4 * Float64(c * Float64(y * y3))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0))));
	elseif (z <= 6.4e+52)
		tmp = Float64(-1.0 * Float64(i * Float64(fma(c, Float64(x * y), Float64(y5 * Float64(Float64(j * t) - Float64(k * y)))) - Float64(j * Float64(x * y1)))));
	elseif (z <= 1.65e+181)
		tmp = Float64(b * Float64(-1.0 * Float64(z * Float64(Float64(a * t) - Float64(k * y0)))));
	else
		tmp = Float64(c * Float64(z * fma(-1.0, Float64(y0 * y3), Float64(i * t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[z, -1.4e+71], N[(-1.0 * N[(i * N[(N[(-1.0 * N[(k * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y1 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.9e-167], N[(N[(y4 * N[(c * N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+52], N[(-1.0 * N[(i * N[(N[(c * N[(x * y), $MachinePrecision] + N[(y5 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+181], N[(b * N[(-1.0 * N[(z * N[(N[(a * t), $MachinePrecision] - N[(k * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(z * N[(-1.0 * N[(y0 * y3), $MachinePrecision] + N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.40000000000000001e71

   1. Initial program 23.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 36.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in k around inf

      \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - \color{blue}{y1} \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

      3. lower-*.f64 35.0

         \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   7. Applied rewrites 35.0%

      \[\leadsto -1 \cdot \left(i \cdot \left(-1 \cdot \left(k \cdot \left(y \cdot y5\right)\right) - \color{blue}{y1} \cdot \left(j \cdot x - k \cdot z\right)\right)\right) \]

   if -1.40000000000000001e71 < z < -3.89999999999999984e-167

   1. Initial program 32.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \color{blue}{\left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{c \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - \color{blue}{c} \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      7. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      8. lift--.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      9. lift-*.f64 N/A

         \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - \color{blue}{y} \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      10. lift-*.f64 37.2

          \[\leadsto y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot \color{blue}{y3}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y4 \cdot \left(b \cdot \left(j \cdot t - k \cdot y\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y3 around inf

      \[\leadsto y4 \cdot \left(c \cdot \color{blue}{\left(y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot \color{blue}{y3}\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lift-*.f64 36.7

         \[\leadsto y4 \cdot \left(c \cdot \left(y \cdot y3\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   7. Applied rewrites 36.7%

      \[\leadsto y4 \cdot \left(c \cdot \color{blue}{\left(y \cdot y3\right)}\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if -3.89999999999999984e-167 < z < 6.4e52

   1. Initial program 34.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 37.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \color{blue}{\left(x \cdot y1\right)}\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(\color{blue}{x} \cdot y1\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      4. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot \color{blue}{y1}\right)\right)\right) \]

      9. lower-*.f64 36.2

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

   7. Applied rewrites 36.2%

      \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]

   if 6.4e52 < z < 1.65000000000000008e181

   1. Initial program 26.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in z around -inf

      \[\leadsto b \cdot \left(-1 \cdot \color{blue}{\left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \color{blue}{\left(a \cdot t - k \cdot y0\right)}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - \color{blue}{k \cdot y0}\right)\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot \color{blue}{y0}\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right) \]

      5. lower-*.f64 32.8

         \[\leadsto b \cdot \left(-1 \cdot \left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)\right) \]

   7. Applied rewrites 32.8%

      \[\leadsto b \cdot \left(-1 \cdot \color{blue}{\left(z \cdot \left(a \cdot t - k \cdot y0\right)\right)}\right) \]

   if 1.65000000000000008e181 < z

   1. Initial program 20.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 59.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in c around -inf

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot y3\right) + i \cdot t\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \left(-1 \cdot \left(y0 \cdot y3\right) + \color{blue}{i \cdot t}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot \color{blue}{y3}, i \cdot t\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right) \]

      5. lower-*.f64 45.4

         \[\leadsto c \cdot \left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right) \]

   7. Applied rewrites 45.4%

      \[\leadsto c \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-1, y0 \cdot y3, i \cdot t\right)\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 13: 34.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot t - k \cdot y\\ \mathbf{if}\;i \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;-1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\\ \mathbf{elif}\;i \leq -5.4 \cdot 10^{-288}:\\ \;\;\;\;a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-200}:\\ \;\;\;\;b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(y4 \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot y1, y5 \cdot t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (- (* j t) (* k y))))
   (if (<= i -5.8e+19)
     (* -1.0 (* y1 (* i (- (* k z) (* j x)))))
     (if (<= i -5.4e-288)
       (* a (* z (fma -1.0 (* b t) (* y1 y3))))
       (if (<= i 5e-200)
         (* b (* x (- (* a y) (* j y0))))
         (if (<= i 1.1e+79)
           (* b (* y4 t_1))
           (* -1.0 (* i (fma x (- (* c y) (* j y1)) (* y5 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * t) - (k * y);
	double tmp;
	if (i <= -5.8e+19) {
		tmp = -1.0 * (y1 * (i * ((k * z) - (j * x))));
	} else if (i <= -5.4e-288) {
		tmp = a * (z * fma(-1.0, (b * t), (y1 * y3)));
	} else if (i <= 5e-200) {
		tmp = b * (x * ((a * y) - (j * y0)));
	} else if (i <= 1.1e+79) {
		tmp = b * (y4 * t_1);
	} else {
		tmp = -1.0 * (i * fma(x, ((c * y) - (j * y1)), (y5 * t_1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(Float64(j * t) - Float64(k * y))
	tmp = 0.0
	if (i <= -5.8e+19)
		tmp = Float64(-1.0 * Float64(y1 * Float64(i * Float64(Float64(k * z) - Float64(j * x)))));
	elseif (i <= -5.4e-288)
		tmp = Float64(a * Float64(z * fma(-1.0, Float64(b * t), Float64(y1 * y3))));
	elseif (i <= 5e-200)
		tmp = Float64(b * Float64(x * Float64(Float64(a * y) - Float64(j * y0))));
	elseif (i <= 1.1e+79)
		tmp = Float64(b * Float64(y4 * t_1));
	else
		tmp = Float64(-1.0 * Float64(i * fma(x, Float64(Float64(c * y) - Float64(j * y1)), Float64(y5 * t_1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.8e+19], N[(-1.0 * N[(y1 * N[(i * N[(N[(k * z), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.4e-288], N[(a * N[(z * N[(-1.0 * N[(b * t), $MachinePrecision] + N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5e-200], N[(b * N[(x * N[(N[(a * y), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.1e+79], N[(b * N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(i * N[(x * N[(N[(c * y), $MachinePrecision] - N[(j * y1), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -5.8e19

   1. Initial program 24.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 49.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y1 around inf

      \[\leadsto -1 \cdot \left(y1 \cdot \color{blue}{\left(i \cdot \left(k \cdot z - j \cdot x\right) + \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right) + \color{blue}{\frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}}\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - \color{blue}{j \cdot x}, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot \color{blue}{x}, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      6. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

   7. Applied rewrites 49.7%

      \[\leadsto -1 \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)}\right) \]

   8. Taylor expanded in y1 around inf

      \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - \color{blue}{j \cdot x}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot \color{blue}{x}\right)\right)\right) \]

      2. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right)\right)\right) \]

      4. lift-*.f64 39.5

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right)\right)\right) \]

   10. Applied rewrites 39.5%

       \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - \color{blue}{j \cdot x}\right)\right)\right) \]

   if -5.8e19 < i < -5.4000000000000002e-288

   1. Initial program 33.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 37.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + \color{blue}{y1 \cdot y3}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot \color{blue}{t}, y1 \cdot y3\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right) \]

      5. lower-*.f64 28.0

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right) \]

   7. Applied rewrites 28.0%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right)} \]

   if -5.4000000000000002e-288 < i < 4.99999999999999991e-200

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 27.6

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 27.6%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   if 4.99999999999999991e-200 < i < 1.0999999999999999e79

   1. Initial program 34.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 38.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in y4 around inf

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot \color{blue}{y}\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) \]

      4. lift-*.f64 28.3

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - \color{blue}{k \cdot y}\right)\right) \]

   7. Applied rewrites 28.3%

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]

   if 1.0999999999999999e79 < i

   1. Initial program 24.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 53.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \color{blue}{\left(x \cdot y1\right)}\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(\color{blue}{x} \cdot y1\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      4. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot \color{blue}{y1}\right)\right)\right) \]

      9. lower-*.f64 45.3

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

   7. Applied rewrites 45.3%

      \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto -1 \cdot \left(i \cdot \left(x \cdot \left(c \cdot y - j \cdot y1\right) + y5 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right)\right) \]
   9. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot \color{blue}{y1}, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot y1, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot y1, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot y1, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]

      5. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot y1, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot y1, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot y1, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]

      8. lift-*.f64 48.1

         \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - j \cdot y1, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]

   10. Applied rewrites 48.1%

       \[\leadsto -1 \cdot \left(i \cdot \mathsf{fma}\left(x, c \cdot y - \color{blue}{j \cdot y1}, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 14: 32.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.8 \cdot 10^{+19}:\\ \;\;\;\;-1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right)\right)\right)\\ \mathbf{elif}\;i \leq -5.4 \cdot 10^{-288}:\\ \;\;\;\;a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-200}:\\ \;\;\;\;b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 480000:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= i -5.8e+19)
   (* -1.0 (* y1 (* i (- (* k z) (* j x)))))
   (if (<= i -5.4e-288)
     (* a (* z (fma -1.0 (* b t) (* y1 y3))))
     (if (<= i 5e-200)
       (* b (* x (- (* a y) (* j y0))))
       (if (<= i 480000.0)
         (* b (* y4 (- (* j t) (* k y))))
         (* i (* y (fma -1.0 (* c x) (* k y5)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (i <= -5.8e+19) {
		tmp = -1.0 * (y1 * (i * ((k * z) - (j * x))));
	} else if (i <= -5.4e-288) {
		tmp = a * (z * fma(-1.0, (b * t), (y1 * y3)));
	} else if (i <= 5e-200) {
		tmp = b * (x * ((a * y) - (j * y0)));
	} else if (i <= 480000.0) {
		tmp = b * (y4 * ((j * t) - (k * y)));
	} else {
		tmp = i * (y * fma(-1.0, (c * x), (k * y5)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (i <= -5.8e+19)
		tmp = Float64(-1.0 * Float64(y1 * Float64(i * Float64(Float64(k * z) - Float64(j * x)))));
	elseif (i <= -5.4e-288)
		tmp = Float64(a * Float64(z * fma(-1.0, Float64(b * t), Float64(y1 * y3))));
	elseif (i <= 5e-200)
		tmp = Float64(b * Float64(x * Float64(Float64(a * y) - Float64(j * y0))));
	elseif (i <= 480000.0)
		tmp = Float64(b * Float64(y4 * Float64(Float64(j * t) - Float64(k * y))));
	else
		tmp = Float64(i * Float64(y * fma(-1.0, Float64(c * x), Float64(k * y5))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[i, -5.8e+19], N[(-1.0 * N[(y1 * N[(i * N[(N[(k * z), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.4e-288], N[(a * N[(z * N[(-1.0 * N[(b * t), $MachinePrecision] + N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5e-200], N[(b * N[(x * N[(N[(a * y), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 480000.0], N[(b * N[(y4 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * N[(-1.0 * N[(c * x), $MachinePrecision] + N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -5.8e19

   1. Initial program 24.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 49.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y1 around inf

      \[\leadsto -1 \cdot \left(y1 \cdot \color{blue}{\left(i \cdot \left(k \cdot z - j \cdot x\right) + \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right) + \color{blue}{\frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}}\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - \color{blue}{j \cdot x}, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot \color{blue}{x}, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

      6. lower-/.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)\right) \]

   7. Applied rewrites 49.7%

      \[\leadsto -1 \cdot \left(y1 \cdot \color{blue}{\mathsf{fma}\left(i, k \cdot z - j \cdot x, \frac{i \cdot \mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right)}{y1}\right)}\right) \]

   8. Taylor expanded in y1 around inf

      \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - \color{blue}{j \cdot x}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot \color{blue}{x}\right)\right)\right) \]

      2. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right)\right)\right) \]

      4. lift-*.f64 39.5

         \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - j \cdot x\right)\right)\right) \]

   10. Applied rewrites 39.5%

       \[\leadsto -1 \cdot \left(y1 \cdot \left(i \cdot \left(k \cdot z - \color{blue}{j \cdot x}\right)\right)\right) \]

   if -5.8e19 < i < -5.4000000000000002e-288

   1. Initial program 33.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 37.5%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + \color{blue}{y1 \cdot y3}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot \color{blue}{t}, y1 \cdot y3\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right) \]

      5. lower-*.f64 28.0

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right) \]

   7. Applied rewrites 28.0%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right)} \]

   if -5.4000000000000002e-288 < i < 4.99999999999999991e-200

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 27.6

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 27.6%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   if 4.99999999999999991e-200 < i < 4.8e5

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 38.6%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in y4 around inf

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot \color{blue}{y}\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) \]

      4. lift-*.f64 28.9

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - \color{blue}{k \cdot y}\right)\right) \]

   7. Applied rewrites 28.9%

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]

   if 4.8e5 < i

   1. Initial program 26.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 49.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y around -inf

      \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + \color{blue}{k \cdot y5}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot \color{blue}{x}, k \cdot y5\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) \]

      5. lower-*.f64 33.0

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) \]

   7. Applied rewrites 33.0%

      \[\leadsto i \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 15: 32.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right)\\ \mathbf{if}\;i \leq -5.7 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -4.6 \cdot 10^{-55}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{elif}\;i \leq -5 \cdot 10^{-153}:\\ \;\;\;\;a \cdot \left(b \cdot \left(x \cdot y - t \cdot z\right)\right)\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-200}:\\ \;\;\;\;b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 480000:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y (fma -1.0 (* c x) (* k y5))))))
   (if (<= i -5.7e+59)
     t_1
     (if (<= i -4.6e-55)
       (* y0 (* c (- (* x y2) (* y3 z))))
       (if (<= i -5e-153)
         (* a (* b (- (* x y) (* t z))))
         (if (<= i -1.5e-283)
           (* x (* y0 (- (* c y2) (* b j))))
           (if (<= i 5e-200)
             (* b (* x (- (* a y) (* j y0))))
             (if (<= i 480000.0) (* b (* y4 (- (* j t) (* k y)))) 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y * fma(-1.0, (c * x), (k * y5)));
	double tmp;
	if (i <= -5.7e+59) {
		tmp = t_1;
	} else if (i <= -4.6e-55) {
		tmp = y0 * (c * ((x * y2) - (y3 * z)));
	} else if (i <= -5e-153) {
		tmp = a * (b * ((x * y) - (t * z)));
	} else if (i <= -1.5e-283) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (i <= 5e-200) {
		tmp = b * (x * ((a * y) - (j * y0)));
	} else if (i <= 480000.0) {
		tmp = b * (y4 * ((j * t) - (k * y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(y * fma(-1.0, Float64(c * x), Float64(k * y5))))
	tmp = 0.0
	if (i <= -5.7e+59)
		tmp = t_1;
	elseif (i <= -4.6e-55)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(y3 * z))));
	elseif (i <= -5e-153)
		tmp = Float64(a * Float64(b * Float64(Float64(x * y) - Float64(t * z))));
	elseif (i <= -1.5e-283)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (i <= 5e-200)
		tmp = Float64(b * Float64(x * Float64(Float64(a * y) - Float64(j * y0))));
	elseif (i <= 480000.0)
		tmp = Float64(b * Float64(y4 * Float64(Float64(j * t) - Float64(k * y))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(y * N[(-1.0 * N[(c * x), $MachinePrecision] + N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.7e+59], t$95$1, If[LessEqual[i, -4.6e-55], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5e-153], N[(a * N[(b * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.5e-283], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5e-200], N[(b * N[(x * N[(N[(a * y), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 480000.0], N[(b * N[(y4 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -5.7000000000000001e59 or 4.8e5 < i

   1. Initial program 25.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 50.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y around -inf

      \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + \color{blue}{k \cdot y5}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot \color{blue}{x}, k \cdot y5\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) \]

      5. lower-*.f64 33.8

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) \]

   7. Applied rewrites 33.8%

      \[\leadsto i \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right)} \]

   if -5.7000000000000001e59 < i < -4.60000000000000023e-55

   1. Initial program 31.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - \color{blue}{b \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in c around inf

      \[\leadsto y0 \cdot \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right) \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      4. lift-*.f64 28.2

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right)\right) \]

   7. Applied rewrites 28.2%

      \[\leadsto y0 \cdot \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right) \]

   if -4.60000000000000023e-55 < i < -5.00000000000000033e-153

   1. Initial program 32.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 37.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 26.7

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

   7. Applied rewrites 26.7%

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

   if -5.00000000000000033e-153 < i < -1.49999999999999998e-283

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - \color{blue}{b \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 38.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y0 \cdot \color{blue}{\left(c \cdot y2 - b \cdot j\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y0 \cdot \left(c \cdot y2 - \color{blue}{b \cdot j}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot \color{blue}{j}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right) \]

      5. lower-*.f64 27.4

         \[\leadsto x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right) \]

   7. Applied rewrites 27.4%

      \[\leadsto x \cdot \color{blue}{\left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)} \]

   if -1.49999999999999998e-283 < i < 4.99999999999999991e-200

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 38.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 27.8

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 27.8%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   if 4.99999999999999991e-200 < i < 4.8e5

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 38.6%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in y4 around inf

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot \color{blue}{y}\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) \]

      4. lift-*.f64 28.9

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - \color{blue}{k \cdot y}\right)\right) \]

   7. Applied rewrites 28.9%

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 16: 32.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right)\\ \mathbf{if}\;i \leq -6.4 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -5.4 \cdot 10^{-288}:\\ \;\;\;\;a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-200}:\\ \;\;\;\;b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right)\\ \mathbf{elif}\;i \leq 480000:\\ \;\;\;\;b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* y (fma -1.0 (* c x) (* k y5))))))
   (if (<= i -6.4e+29)
     t_1
     (if (<= i -5.4e-288)
       (* a (* z (fma -1.0 (* b t) (* y1 y3))))
       (if (<= i 5e-200)
         (* b (* x (- (* a y) (* j y0))))
         (if (<= i 480000.0) (* b (* y4 (- (* j t) (* k y)))) 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (y * fma(-1.0, (c * x), (k * y5)));
	double tmp;
	if (i <= -6.4e+29) {
		tmp = t_1;
	} else if (i <= -5.4e-288) {
		tmp = a * (z * fma(-1.0, (b * t), (y1 * y3)));
	} else if (i <= 5e-200) {
		tmp = b * (x * ((a * y) - (j * y0)));
	} else if (i <= 480000.0) {
		tmp = b * (y4 * ((j * t) - (k * y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(y * fma(-1.0, Float64(c * x), Float64(k * y5))))
	tmp = 0.0
	if (i <= -6.4e+29)
		tmp = t_1;
	elseif (i <= -5.4e-288)
		tmp = Float64(a * Float64(z * fma(-1.0, Float64(b * t), Float64(y1 * y3))));
	elseif (i <= 5e-200)
		tmp = Float64(b * Float64(x * Float64(Float64(a * y) - Float64(j * y0))));
	elseif (i <= 480000.0)
		tmp = Float64(b * Float64(y4 * Float64(Float64(j * t) - Float64(k * y))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(y * N[(-1.0 * N[(c * x), $MachinePrecision] + N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -6.4e+29], t$95$1, If[LessEqual[i, -5.4e-288], N[(a * N[(z * N[(-1.0 * N[(b * t), $MachinePrecision] + N[(y1 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5e-200], N[(b * N[(x * N[(N[(a * y), $MachinePrecision] - N[(j * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 480000.0], N[(b * N[(y4 * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -6.39999999999999973e29 or 4.8e5 < i

   1. Initial program 25.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 49.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y around -inf

      \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + \color{blue}{k \cdot y5}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot \color{blue}{x}, k \cdot y5\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) \]

      5. lower-*.f64 33.3

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) \]

   7. Applied rewrites 33.3%

      \[\leadsto i \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right)} \]

   if -6.39999999999999973e29 < i < -5.4000000000000002e-288

   1. Initial program 33.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 37.8%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot t\right) + y1 \cdot y3\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \left(-1 \cdot \left(b \cdot t\right) + \color{blue}{y1 \cdot y3}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot \color{blue}{t}, y1 \cdot y3\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right) \]

      5. lower-*.f64 27.9

         \[\leadsto a \cdot \left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right) \]

   7. Applied rewrites 27.9%

      \[\leadsto a \cdot \color{blue}{\left(z \cdot \mathsf{fma}\left(-1, b \cdot t, y1 \cdot y3\right)\right)} \]

   if -5.4000000000000002e-288 < i < 4.99999999999999991e-200

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 39.1%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - \color{blue}{j \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

      4. lower-*.f64 27.6

         \[\leadsto b \cdot \left(x \cdot \left(a \cdot y - j \cdot y0\right)\right) \]

   7. Applied rewrites 27.6%

      \[\leadsto b \cdot \left(x \cdot \color{blue}{\left(a \cdot y - j \cdot y0\right)}\right) \]

   if 4.99999999999999991e-200 < i < 4.8e5

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 38.6%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in y4 around inf

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot \color{blue}{y}\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - k \cdot y\right)\right) \]

      4. lift-*.f64 28.9

         \[\leadsto b \cdot \left(y4 \cdot \left(j \cdot t - \color{blue}{k \cdot y}\right)\right) \]

   7. Applied rewrites 28.9%

      \[\leadsto b \cdot \left(y4 \cdot \color{blue}{\left(j \cdot t - k \cdot y\right)}\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 17: 32.0% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -2.3 \cdot 10^{-32}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)\\ \mathbf{elif}\;y5 \leq 9 \cdot 10^{-94}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y5 \leq 2.4 \cdot 10^{-5}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 9 \cdot 10^{+110}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(y5 \cdot \mathsf{fma}\left(-1, y0 \cdot y2, i \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -2.3e-32)
   (* y3 (* y5 (- (* j y0) (* a y))))
   (if (<= y5 9e-94)
     (* y1 (* z (- (* a y3) (* i k))))
     (if (<= y5 2.4e-5)
       (* b (* j (- (* t y4) (* x y0))))
       (if (<= y5 9e+110)
         (* i (* y1 (- (* j x) (* k z))))
         (* k (* y5 (fma -1.0 (* y0 y2) (* i y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -2.3e-32) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (y5 <= 9e-94) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y5 <= 2.4e-5) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y5 <= 9e+110) {
		tmp = i * (y1 * ((j * x) - (k * z)));
	} else {
		tmp = k * (y5 * fma(-1.0, (y0 * y2), (i * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -2.3e-32)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(a * y))));
	elseif (y5 <= 9e-94)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (y5 <= 2.4e-5)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y5 <= 9e+110)
		tmp = Float64(i * Float64(y1 * Float64(Float64(j * x) - Float64(k * z))));
	else
		tmp = Float64(k * Float64(y5 * fma(-1.0, Float64(y0 * y2), Float64(i * y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -2.3e-32], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 9e-94], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.4e-5], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 9e+110], N[(i * N[(y1 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(k * N[(y5 * N[(-1.0 * N[(y0 * y2), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -2.3000000000000001e-32

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{a \cdot \left(t \cdot y2 - y \cdot y3\right)}\right)\right) \]

   4. Applied rewrites 45.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf

      \[\leadsto y3 \cdot \color{blue}{\left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \color{blue}{\left(j \cdot y0 - a \cdot y\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - \color{blue}{a \cdot y}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot \color{blue}{y}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

      5. lower-*.f64 35.3

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

   7. Applied rewrites 35.3%

      \[\leadsto y3 \cdot \color{blue}{\left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]

   if -2.3000000000000001e-32 < y5 < 9.0000000000000004e-94

   1. Initial program 34.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 40.7%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in y1 around -inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - \color{blue}{i \cdot k}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot \color{blue}{k}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

      5. lower-*.f64 28.0

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

   7. Applied rewrites 28.0%

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   if 9.0000000000000004e-94 < y5 < 2.4000000000000001e-5

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around inf

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4 - x \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - \color{blue}{x \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      4. lower-*.f64 27.1

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 27.1%

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4 - x \cdot y0\right)}\right) \]

   if 2.4000000000000001e-5 < y5 < 9.0000000000000005e110

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 35.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y1 around -inf

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      2. lift--.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot \color{blue}{z}\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. lift-*.f64 28.2

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - \color{blue}{k \cdot z}\right)\right) \]

   7. Applied rewrites 28.2%

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 9.0000000000000005e110 < y5

   1. Initial program 23.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{a \cdot \left(t \cdot y2 - y \cdot y3\right)}\right)\right) \]

   4. Applied rewrites 56.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   5. Taylor expanded in k around -inf

      \[\leadsto k \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto k \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(y0 \cdot y2\right) + i \cdot y\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto k \cdot \left(y5 \cdot \left(-1 \cdot \left(y0 \cdot y2\right) + \color{blue}{i \cdot y}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto k \cdot \left(y5 \cdot \mathsf{fma}\left(-1, y0 \cdot \color{blue}{y2}, i \cdot y\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto k \cdot \left(y5 \cdot \mathsf{fma}\left(-1, y0 \cdot y2, i \cdot y\right)\right) \]

      5. lower-*.f64 43.1

         \[\leadsto k \cdot \left(y5 \cdot \mathsf{fma}\left(-1, y0 \cdot y2, i \cdot y\right)\right) \]

   7. Applied rewrites 43.1%

      \[\leadsto k \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(-1, y0 \cdot y2, i \cdot y\right)\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 18: 30.8% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y1 \leq -8 \cdot 10^{+167}:\\ \;\;\;\;i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -1.45 \cdot 10^{-278}:\\ \;\;\;\;j \cdot \left(y5 \cdot \mathsf{fma}\left(-1, i \cdot t, y0 \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 9.5 \cdot 10^{+43}:\\ \;\;\;\;i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 8.8 \cdot 10^{+225}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y1 -8e+167)
   (* i (* z (- (* c t) (* k y1))))
   (if (<= y1 -1.45e-278)
     (* j (* y5 (fma -1.0 (* i t) (* y0 y3))))
     (if (<= y1 9.5e+43)
       (* i (* y (fma -1.0 (* c x) (* k y5))))
       (if (<= y1 8.8e+225)
         (* i (* y1 (- (* j x) (* k z))))
         (* y1 (* z (- (* a y3) (* i 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y1 <= -8e+167) {
		tmp = i * (z * ((c * t) - (k * y1)));
	} else if (y1 <= -1.45e-278) {
		tmp = j * (y5 * fma(-1.0, (i * t), (y0 * y3)));
	} else if (y1 <= 9.5e+43) {
		tmp = i * (y * fma(-1.0, (c * x), (k * y5)));
	} else if (y1 <= 8.8e+225) {
		tmp = i * (y1 * ((j * x) - (k * z)));
	} else {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y1 <= -8e+167)
		tmp = Float64(i * Float64(z * Float64(Float64(c * t) - Float64(k * y1))));
	elseif (y1 <= -1.45e-278)
		tmp = Float64(j * Float64(y5 * fma(-1.0, Float64(i * t), Float64(y0 * y3))));
	elseif (y1 <= 9.5e+43)
		tmp = Float64(i * Float64(y * fma(-1.0, Float64(c * x), Float64(k * y5))));
	elseif (y1 <= 8.8e+225)
		tmp = Float64(i * Float64(y1 * Float64(Float64(j * x) - Float64(k * z))));
	else
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y1, -8e+167], N[(i * N[(z * N[(N[(c * t), $MachinePrecision] - N[(k * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -1.45e-278], N[(j * N[(y5 * N[(-1.0 * N[(i * t), $MachinePrecision] + N[(y0 * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 9.5e+43], N[(i * N[(y * N[(-1.0 * N[(c * x), $MachinePrecision] + N[(k * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 8.8e+225], N[(i * N[(y1 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y1 < -8.0000000000000003e167

   1. Initial program 24.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 39.9%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in i around -inf

      \[\leadsto i \cdot \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \color{blue}{\left(c \cdot t - k \cdot y1\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \left(c \cdot t - \color{blue}{k \cdot y1}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \left(c \cdot t - k \cdot \color{blue}{y1}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right) \]

      5. lower-*.f64 39.5

         \[\leadsto i \cdot \left(z \cdot \left(c \cdot t - k \cdot y1\right)\right) \]

   7. Applied rewrites 39.5%

      \[\leadsto i \cdot \color{blue}{\left(z \cdot \left(c \cdot t - k \cdot y1\right)\right)} \]

   if -8.0000000000000003e167 < y1 < -1.45e-278

   1. Initial program 30.9%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{a \cdot \left(t \cdot y2 - y \cdot y3\right)}\right)\right) \]

   4. Applied rewrites 36.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   5. Taylor expanded in j around -inf

      \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \left(y5 \cdot \color{blue}{\left(-1 \cdot \left(i \cdot t\right) + y0 \cdot y3\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \left(y5 \cdot \left(-1 \cdot \left(i \cdot t\right) + \color{blue}{y0 \cdot y3}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \left(y5 \cdot \mathsf{fma}\left(-1, i \cdot \color{blue}{t}, y0 \cdot y3\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \left(y5 \cdot \mathsf{fma}\left(-1, i \cdot t, y0 \cdot y3\right)\right) \]

      5. lower-*.f64 27.6

         \[\leadsto j \cdot \left(y5 \cdot \mathsf{fma}\left(-1, i \cdot t, y0 \cdot y3\right)\right) \]

   7. Applied rewrites 27.6%

      \[\leadsto j \cdot \color{blue}{\left(y5 \cdot \mathsf{fma}\left(-1, i \cdot t, y0 \cdot y3\right)\right)} \]

   if -1.45e-278 < y1 < 9.5000000000000004e43

   1. Initial program 33.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 35.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y around -inf

      \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(-1 \cdot \left(c \cdot x\right) + k \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \left(-1 \cdot \left(c \cdot x\right) + \color{blue}{k \cdot y5}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot \color{blue}{x}, k \cdot y5\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) \]

      5. lower-*.f64 25.0

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) \]

   7. Applied rewrites 25.0%

      \[\leadsto i \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right)} \]

   if 9.5000000000000004e43 < y1 < 8.80000000000000055e225

   1. Initial program 26.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 38.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y1 around -inf

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      2. lift--.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot \color{blue}{z}\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. lift-*.f64 37.0

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - \color{blue}{k \cdot z}\right)\right) \]

   7. Applied rewrites 37.0%

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 8.80000000000000055e225 < y1

   1. Initial program 20.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 38.1%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in y1 around -inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - \color{blue}{i \cdot k}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot \color{blue}{k}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

      5. lower-*.f64 46.3

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

   7. Applied rewrites 46.3%

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 19: 30.6% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -2.3 \cdot 10^{-32}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)\\ \mathbf{elif}\;y5 \leq 9 \cdot 10^{-94}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{elif}\;y5 \leq 2.4 \cdot 10^{-5}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{elif}\;y5 \leq 2.3 \cdot 10^{+111}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -2.3e-32)
   (* y3 (* y5 (- (* j y0) (* a y))))
   (if (<= y5 9e-94)
     (* y1 (* z (- (* a y3) (* i k))))
     (if (<= y5 2.4e-5)
       (* b (* j (- (* t y4) (* x y0))))
       (if (<= y5 2.3e+111)
         (* i (* y1 (- (* j x) (* k z))))
         (* a (* y5 (- (* t y2) (* y y3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -2.3e-32) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (y5 <= 9e-94) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y5 <= 2.4e-5) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y5 <= 2.3e+111) {
		tmp = i * (y1 * ((j * x) - (k * z)));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	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, y0, y1, y2, y3, y4, y5)
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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-2.3d-32)) then
        tmp = y3 * (y5 * ((j * y0) - (a * y)))
    else if (y5 <= 9d-94) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else if (y5 <= 2.4d-5) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else if (y5 <= 2.3d+111) then
        tmp = i * (y1 * ((j * x) - (k * z)))
    else
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -2.3e-32) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (y5 <= 9e-94) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else if (y5 <= 2.4e-5) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else if (y5 <= 2.3e+111) {
		tmp = i * (y1 * ((j * x) - (k * z)));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -2.3e-32:
		tmp = y3 * (y5 * ((j * y0) - (a * y)))
	elif y5 <= 9e-94:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	elif y5 <= 2.4e-5:
		tmp = b * (j * ((t * y4) - (x * y0)))
	elif y5 <= 2.3e+111:
		tmp = i * (y1 * ((j * x) - (k * z)))
	else:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -2.3e-32)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(a * y))));
	elseif (y5 <= 9e-94)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	elseif (y5 <= 2.4e-5)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	elseif (y5 <= 2.3e+111)
		tmp = Float64(i * Float64(y1 * Float64(Float64(j * x) - Float64(k * z))));
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -2.3e-32)
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	elseif (y5 <= 9e-94)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	elseif (y5 <= 2.4e-5)
		tmp = b * (j * ((t * y4) - (x * y0)));
	elseif (y5 <= 2.3e+111)
		tmp = i * (y1 * ((j * x) - (k * z)));
	else
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -2.3e-32], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 9e-94], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.4e-5], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 2.3e+111], N[(i * N[(y1 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y5 < -2.3000000000000001e-32

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{a \cdot \left(t \cdot y2 - y \cdot y3\right)}\right)\right) \]

   4. Applied rewrites 45.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf

      \[\leadsto y3 \cdot \color{blue}{\left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \color{blue}{\left(j \cdot y0 - a \cdot y\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - \color{blue}{a \cdot y}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot \color{blue}{y}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

      5. lower-*.f64 35.3

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

   7. Applied rewrites 35.3%

      \[\leadsto y3 \cdot \color{blue}{\left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]

   if -2.3000000000000001e-32 < y5 < 9.0000000000000004e-94

   1. Initial program 34.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 40.7%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in y1 around -inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - \color{blue}{i \cdot k}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot \color{blue}{k}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

      5. lower-*.f64 28.0

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

   7. Applied rewrites 28.0%

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   if 9.0000000000000004e-94 < y5 < 2.4000000000000001e-5

   1. Initial program 34.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(\left(a \cdot \left(x \cdot y - t \cdot z\right) + y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y0 \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 35.7%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(a, x \cdot y - t \cdot z, y4 \cdot \left(j \cdot t - k \cdot y\right)\right) - y0 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in j around inf

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4 - x \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - \color{blue}{x \cdot y0}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot \color{blue}{y0}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      4. lower-*.f64 27.1

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 27.1%

      \[\leadsto b \cdot \left(j \cdot \color{blue}{\left(t \cdot y4 - x \cdot y0\right)}\right) \]

   if 2.4000000000000001e-5 < y5 < 2.30000000000000002e111

   1. Initial program 29.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 35.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y1 around -inf

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      2. lift--.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot \color{blue}{z}\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. lift-*.f64 28.2

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - \color{blue}{k \cdot z}\right)\right) \]

   7. Applied rewrites 28.2%

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 2.30000000000000002e111 < y5

   1. Initial program 23.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{a \cdot \left(t \cdot y2 - y \cdot y3\right)}\right)\right) \]

   4. Applied rewrites 56.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

      3. lift--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot \color{blue}{y3}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. lift-*.f64 44.6

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Applied rewrites 44.6%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 20: 30.6% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)\\ t_2 := i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\\ \mathbf{if}\;y1 \leq -4.2 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -3.5 \cdot 10^{-76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y1 \leq 4.4 \cdot 10^{+57}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y1 \leq 1.05 \cdot 10^{+226}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y1 (* y3 z)))) (t_2 (* i (* y1 (- (* j x) (* k z))))))
   (if (<= y1 -4.2e+77)
     t_1
     (if (<= y1 -3.5e-76)
       t_2
       (if (<= y1 4.4e+57)
         (* a (* y5 (- (* t y2) (* y y3))))
         (if (<= y1 1.05e+226) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * (y3 * z));
	double t_2 = i * (y1 * ((j * x) - (k * z)));
	double tmp;
	if (y1 <= -4.2e+77) {
		tmp = t_1;
	} else if (y1 <= -3.5e-76) {
		tmp = t_2;
	} else if (y1 <= 4.4e+57) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 1.05e+226) {
		tmp = t_2;
	} 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, y0, y1, y2, y3, y4, y5)
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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y1 * (y3 * z))
    t_2 = i * (y1 * ((j * x) - (k * z)))
    if (y1 <= (-4.2d+77)) then
        tmp = t_1
    else if (y1 <= (-3.5d-76)) then
        tmp = t_2
    else if (y1 <= 4.4d+57) then
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    else if (y1 <= 1.05d+226) then
        tmp = t_2
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * (y3 * z));
	double t_2 = i * (y1 * ((j * x) - (k * z)));
	double tmp;
	if (y1 <= -4.2e+77) {
		tmp = t_1;
	} else if (y1 <= -3.5e-76) {
		tmp = t_2;
	} else if (y1 <= 4.4e+57) {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	} else if (y1 <= 1.05e+226) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y1 * (y3 * z))
	t_2 = i * (y1 * ((j * x) - (k * z)))
	tmp = 0
	if y1 <= -4.2e+77:
		tmp = t_1
	elif y1 <= -3.5e-76:
		tmp = t_2
	elif y1 <= 4.4e+57:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	elif y1 <= 1.05e+226:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y1 * Float64(y3 * z)))
	t_2 = Float64(i * Float64(y1 * Float64(Float64(j * x) - Float64(k * z))))
	tmp = 0.0
	if (y1 <= -4.2e+77)
		tmp = t_1;
	elseif (y1 <= -3.5e-76)
		tmp = t_2;
	elseif (y1 <= 4.4e+57)
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	elseif (y1 <= 1.05e+226)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y1 * (y3 * z));
	t_2 = i * (y1 * ((j * x) - (k * z)));
	tmp = 0.0;
	if (y1 <= -4.2e+77)
		tmp = t_1;
	elseif (y1 <= -3.5e-76)
		tmp = t_2;
	elseif (y1 <= 4.4e+57)
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	elseif (y1 <= 1.05e+226)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y1 * N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y1 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -4.2e+77], t$95$1, If[LessEqual[y1, -3.5e-76], t$95$2, If[LessEqual[y1, 4.4e+57], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1.05e+226], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -4.1999999999999997e77 or 1.04999999999999997e226 < y1

   1. Initial program 24.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 39.3%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in y1 around -inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - \color{blue}{i \cdot k}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot \color{blue}{k}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

      5. lower-*.f64 39.5

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

   7. Applied rewrites 39.5%

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   8. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot \color{blue}{z}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]

      3. lower-*.f64 29.4

         \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]

   10. Applied rewrites 29.4%

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]

   if -4.1999999999999997e77 < y1 < -3.49999999999999997e-76 or 4.4000000000000001e57 < y1 < 1.04999999999999997e226

   1. Initial program 28.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 38.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y1 around -inf

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      2. lift--.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot \color{blue}{z}\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. lift-*.f64 30.2

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - \color{blue}{k \cdot z}\right)\right) \]

   7. Applied rewrites 30.2%

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if -3.49999999999999997e-76 < y1 < 4.4000000000000001e57

   1. Initial program 32.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{a \cdot \left(t \cdot y2 - y \cdot y3\right)}\right)\right) \]

   4. Applied rewrites 37.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

      3. lift--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot \color{blue}{y3}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. lift-*.f64 28.0

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Applied rewrites 28.0%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 29.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y5 \leq -2.3 \cdot 10^{-32}:\\ \;\;\;\;y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)\\ \mathbf{elif}\;y5 \leq 1.2 \cdot 10^{+112}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y5 -2.3e-32)
   (* y3 (* y5 (- (* j y0) (* a y))))
   (if (<= y5 1.2e+112)
     (* y1 (* z (- (* a y3) (* i k))))
     (* a (* y5 (- (* t y2) (* y y3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -2.3e-32) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (y5 <= 1.2e+112) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	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, y0, y1, y2, y3, y4, y5)
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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y5 <= (-2.3d-32)) then
        tmp = y3 * (y5 * ((j * y0) - (a * y)))
    else if (y5 <= 1.2d+112) then
        tmp = y1 * (z * ((a * y3) - (i * k)))
    else
        tmp = a * (y5 * ((t * y2) - (y * y3)))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y5 <= -2.3e-32) {
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	} else if (y5 <= 1.2e+112) {
		tmp = y1 * (z * ((a * y3) - (i * k)));
	} else {
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y5 <= -2.3e-32:
		tmp = y3 * (y5 * ((j * y0) - (a * y)))
	elif y5 <= 1.2e+112:
		tmp = y1 * (z * ((a * y3) - (i * k)))
	else:
		tmp = a * (y5 * ((t * y2) - (y * y3)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y5 <= -2.3e-32)
		tmp = Float64(y3 * Float64(y5 * Float64(Float64(j * y0) - Float64(a * y))));
	elseif (y5 <= 1.2e+112)
		tmp = Float64(y1 * Float64(z * Float64(Float64(a * y3) - Float64(i * k))));
	else
		tmp = Float64(a * Float64(y5 * Float64(Float64(t * y2) - Float64(y * y3))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y5 <= -2.3e-32)
		tmp = y3 * (y5 * ((j * y0) - (a * y)));
	elseif (y5 <= 1.2e+112)
		tmp = y1 * (z * ((a * y3) - (i * k)));
	else
		tmp = a * (y5 * ((t * y2) - (y * y3)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y5, -2.3e-32], N[(y3 * N[(y5 * N[(N[(j * y0), $MachinePrecision] - N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y5, 1.2e+112], N[(y1 * N[(z * N[(N[(a * y3), $MachinePrecision] - N[(i * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(y5 * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y5 < -2.3000000000000001e-32

   1. Initial program 25.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{a \cdot \left(t \cdot y2 - y \cdot y3\right)}\right)\right) \]

   4. Applied rewrites 45.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   5. Taylor expanded in y3 around -inf

      \[\leadsto y3 \cdot \color{blue}{\left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \color{blue}{\left(j \cdot y0 - a \cdot y\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - \color{blue}{a \cdot y}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot \color{blue}{y}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

      5. lower-*.f64 35.3

         \[\leadsto y3 \cdot \left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right) \]

   7. Applied rewrites 35.3%

      \[\leadsto y3 \cdot \color{blue}{\left(y5 \cdot \left(j \cdot y0 - a \cdot y\right)\right)} \]

   if -2.3000000000000001e-32 < y5 < 1.2e112

   1. Initial program 33.8%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 40.0%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in y1 around -inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - \color{blue}{i \cdot k}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot \color{blue}{k}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

      5. lower-*.f64 27.9

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

   7. Applied rewrites 27.9%

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   if 1.2e112 < y5

   1. Initial program 23.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{a \cdot \left(t \cdot y2 - y \cdot y3\right)}\right)\right) \]

   4. Applied rewrites 56.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

      3. lift--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot \color{blue}{y3}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. lift-*.f64 44.7

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Applied rewrites 44.7%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 22: 28.9% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(k \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-102}:\\ \;\;\;\;i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+80}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* i (* k (- (* y y5) (* y1 z))))))
   (if (<= y -1.12e+136)
     t_1
     (if (<= y 5e-102)
       (* i (* y1 (- (* j x) (* k z))))
       (if (<= y 2.3e+80) (* y0 (* c (* x y2))) 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (k * ((y * y5) - (y1 * z)));
	double tmp;
	if (y <= -1.12e+136) {
		tmp = t_1;
	} else if (y <= 5e-102) {
		tmp = i * (y1 * ((j * x) - (k * z)));
	} else if (y <= 2.3e+80) {
		tmp = y0 * (c * (x * y2));
	} 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, y0, y1, y2, y3, y4, y5)
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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (k * ((y * y5) - (y1 * z)))
    if (y <= (-1.12d+136)) then
        tmp = t_1
    else if (y <= 5d-102) then
        tmp = i * (y1 * ((j * x) - (k * z)))
    else if (y <= 2.3d+80) then
        tmp = y0 * (c * (x * y2))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = i * (k * ((y * y5) - (y1 * z)));
	double tmp;
	if (y <= -1.12e+136) {
		tmp = t_1;
	} else if (y <= 5e-102) {
		tmp = i * (y1 * ((j * x) - (k * z)));
	} else if (y <= 2.3e+80) {
		tmp = y0 * (c * (x * y2));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = i * (k * ((y * y5) - (y1 * z)))
	tmp = 0
	if y <= -1.12e+136:
		tmp = t_1
	elif y <= 5e-102:
		tmp = i * (y1 * ((j * x) - (k * z)))
	elif y <= 2.3e+80:
		tmp = y0 * (c * (x * y2))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(i * Float64(k * Float64(Float64(y * y5) - Float64(y1 * z))))
	tmp = 0.0
	if (y <= -1.12e+136)
		tmp = t_1;
	elseif (y <= 5e-102)
		tmp = Float64(i * Float64(y1 * Float64(Float64(j * x) - Float64(k * z))));
	elseif (y <= 2.3e+80)
		tmp = Float64(y0 * Float64(c * Float64(x * y2)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = i * (k * ((y * y5) - (y1 * z)));
	tmp = 0.0;
	if (y <= -1.12e+136)
		tmp = t_1;
	elseif (y <= 5e-102)
		tmp = i * (y1 * ((j * x) - (k * z)));
	elseif (y <= 2.3e+80)
		tmp = y0 * (c * (x * y2));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(i * N[(k * N[(N[(y * y5), $MachinePrecision] - N[(y1 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e+136], t$95$1, If[LessEqual[y, 5e-102], N[(i * N[(y1 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+80], N[(y0 * N[(c * N[(x * y2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.12000000000000001e136 or 2.30000000000000004e80 < y

   1. Initial program 23.0%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 37.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in k around -inf

      \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \left(k \cdot \left(y \cdot y5 - \color{blue}{y1 \cdot z}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto i \cdot \left(k \cdot \left(y \cdot y5 - y1 \cdot \color{blue}{z}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto i \cdot \left(k \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      5. lower-*.f64 36.4

         \[\leadsto i \cdot \left(k \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

   7. Applied rewrites 36.4%

      \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   if -1.12000000000000001e136 < y < 5.00000000000000026e-102

   1. Initial program 33.4%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in y1 around -inf

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \color{blue}{\left(j \cdot x - k \cdot z\right)}\right) \]

      2. lift--.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot \color{blue}{z}\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right) \]

      5. lift-*.f64 27.8

         \[\leadsto i \cdot \left(y1 \cdot \left(j \cdot x - \color{blue}{k \cdot z}\right)\right) \]

   7. Applied rewrites 27.8%

      \[\leadsto i \cdot \color{blue}{\left(y1 \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 5.00000000000000026e-102 < y < 2.30000000000000004e80

   1. Initial program 31.3%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y0 around inf

      \[\leadsto \color{blue}{y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \color{blue}{\left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(\left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) + c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - \color{blue}{b \cdot \left(j \cdot x - k \cdot z\right)}\right) \]

   4. Applied rewrites 36.7%

      \[\leadsto \color{blue}{y0 \cdot \left(\mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   5. Taylor expanded in c around inf

      \[\leadsto y0 \cdot \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right) \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      4. lift-*.f64 26.0

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right)\right) \]

   7. Applied rewrites 26.0%

      \[\leadsto y0 \cdot \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 16.5

         \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right) \]

   10. Applied rewrites 16.5%

       \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 23: 25.8% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y3 \leq -2 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)\\ \mathbf{elif}\;y3 \leq 4.8 \cdot 10^{-151}:\\ \;\;\;\;i \cdot \left(k \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)\\ \mathbf{elif}\;y3 \leq 1.05 \cdot 10^{+80}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y1 \cdot \left(z \cdot \left(a \cdot y3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (if (<= y3 -2e+72)
   (* a (* y1 (* y3 z)))
   (if (<= y3 4.8e-151)
     (* i (* k (- (* y y5) (* y1 z))))
     (if (<= y3 1.05e+80)
       (* -1.0 (* i (* c (* x y))))
       (* y1 (* z (* a y3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -2e+72) {
		tmp = a * (y1 * (y3 * z));
	} else if (y3 <= 4.8e-151) {
		tmp = i * (k * ((y * y5) - (y1 * z)));
	} else if (y3 <= 1.05e+80) {
		tmp = -1.0 * (i * (c * (x * y)));
	} else {
		tmp = y1 * (z * (a * y3));
	}
	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, y0, y1, y2, y3, y4, y5)
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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: tmp
    if (y3 <= (-2d+72)) then
        tmp = a * (y1 * (y3 * z))
    else if (y3 <= 4.8d-151) then
        tmp = i * (k * ((y * y5) - (y1 * z)))
    else if (y3 <= 1.05d+80) then
        tmp = (-1.0d0) * (i * (c * (x * y)))
    else
        tmp = y1 * (z * (a * y3))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (y3 <= -2e+72) {
		tmp = a * (y1 * (y3 * z));
	} else if (y3 <= 4.8e-151) {
		tmp = i * (k * ((y * y5) - (y1 * z)));
	} else if (y3 <= 1.05e+80) {
		tmp = -1.0 * (i * (c * (x * y)));
	} else {
		tmp = y1 * (z * (a * y3));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y3 <= -2e+72:
		tmp = a * (y1 * (y3 * z))
	elif y3 <= 4.8e-151:
		tmp = i * (k * ((y * y5) - (y1 * z)))
	elif y3 <= 1.05e+80:
		tmp = -1.0 * (i * (c * (x * y)))
	else:
		tmp = y1 * (z * (a * y3))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0
	if (y3 <= -2e+72)
		tmp = Float64(a * Float64(y1 * Float64(y3 * z)));
	elseif (y3 <= 4.8e-151)
		tmp = Float64(i * Float64(k * Float64(Float64(y * y5) - Float64(y1 * z))));
	elseif (y3 <= 1.05e+80)
		tmp = Float64(-1.0 * Float64(i * Float64(c * Float64(x * y))));
	else
		tmp = Float64(y1 * Float64(z * Float64(a * y3)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = 0.0;
	if (y3 <= -2e+72)
		tmp = a * (y1 * (y3 * z));
	elseif (y3 <= 4.8e-151)
		tmp = i * (k * ((y * y5) - (y1 * z)));
	elseif (y3 <= 1.05e+80)
		tmp = -1.0 * (i * (c * (x * y)));
	else
		tmp = y1 * (z * (a * y3));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[y3, -2e+72], N[(a * N[(y1 * N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 4.8e-151], N[(i * N[(k * N[(N[(y * y5), $MachinePrecision] - N[(y1 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y3, 1.05e+80], N[(-1.0 * N[(i * N[(c * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y1 * N[(z * N[(a * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y3 < -1.99999999999999989e72

   1. Initial program 24.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 40.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in y1 around -inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - \color{blue}{i \cdot k}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot \color{blue}{k}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

      5. lower-*.f64 33.5

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

   7. Applied rewrites 33.5%

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   8. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot \color{blue}{z}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]

      3. lower-*.f64 29.7

         \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]

   10. Applied rewrites 29.7%

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]

   if -1.99999999999999989e72 < y3 < 4.8e-151

   1. Initial program 33.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 39.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in k around -inf

      \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto i \cdot \left(k \cdot \color{blue}{\left(y \cdot y5 - y1 \cdot z\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto i \cdot \left(k \cdot \left(y \cdot y5 - \color{blue}{y1 \cdot z}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto i \cdot \left(k \cdot \left(y \cdot y5 - y1 \cdot \color{blue}{z}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto i \cdot \left(k \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

      5. lower-*.f64 26.6

         \[\leadsto i \cdot \left(k \cdot \left(y \cdot y5 - y1 \cdot z\right)\right) \]

   7. Applied rewrites 26.6%

      \[\leadsto i \cdot \color{blue}{\left(k \cdot \left(y \cdot y5 - y1 \cdot z\right)\right)} \]

   if 4.8e-151 < y3 < 1.05000000000000001e80

   1. Initial program 31.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 38.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \color{blue}{\left(x \cdot y1\right)}\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(\color{blue}{x} \cdot y1\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      4. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot \color{blue}{y1}\right)\right)\right) \]

      9. lower-*.f64 35.5

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

   7. Applied rewrites 35.5%

      \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]

   8. Taylor expanded in c around inf

      \[\leadsto -1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot \color{blue}{y}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y\right)\right)\right) \]

      2. lift-*.f64 16.3

         \[\leadsto -1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y\right)\right)\right) \]

   10. Applied rewrites 16.3%

       \[\leadsto -1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot \color{blue}{y}\right)\right)\right) \]

   if 1.05000000000000001e80 < y3

   1. Initial program 24.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 41.2%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in y1 around -inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - \color{blue}{i \cdot k}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot \color{blue}{k}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

      5. lower-*.f64 33.9

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

   7. Applied rewrites 33.9%

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   8. Taylor expanded in a around inf

      \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 29.7

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3\right)\right) \]

   10. Applied rewrites 29.7%

       \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3\right)\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 24: 21.9% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)\\ \mathbf{if}\;y1 \leq -0.0023:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq -2.15 \cdot 10^{-107}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;y1 \leq 9.2 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y1 (* y3 z)))))
   (if (<= y1 -0.0023)
     t_1
     (if (<= y1 -2.15e-107)
       (* -1.0 (* i (* c (* x y))))
       (if (<= y1 9.2e+72) (* a (* t (* y2 y5))) 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * (y3 * z));
	double tmp;
	if (y1 <= -0.0023) {
		tmp = t_1;
	} else if (y1 <= -2.15e-107) {
		tmp = -1.0 * (i * (c * (x * y)));
	} else if (y1 <= 9.2e+72) {
		tmp = a * (t * (y2 * y5));
	} 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, y0, y1, y2, y3, y4, y5)
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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y1 * (y3 * z))
    if (y1 <= (-0.0023d0)) then
        tmp = t_1
    else if (y1 <= (-2.15d-107)) then
        tmp = (-1.0d0) * (i * (c * (x * y)))
    else if (y1 <= 9.2d+72) then
        tmp = a * (t * (y2 * y5))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * (y3 * z));
	double tmp;
	if (y1 <= -0.0023) {
		tmp = t_1;
	} else if (y1 <= -2.15e-107) {
		tmp = -1.0 * (i * (c * (x * y)));
	} else if (y1 <= 9.2e+72) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y1 * (y3 * z))
	tmp = 0
	if y1 <= -0.0023:
		tmp = t_1
	elif y1 <= -2.15e-107:
		tmp = -1.0 * (i * (c * (x * y)))
	elif y1 <= 9.2e+72:
		tmp = a * (t * (y2 * y5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y1 * Float64(y3 * z)))
	tmp = 0.0
	if (y1 <= -0.0023)
		tmp = t_1;
	elseif (y1 <= -2.15e-107)
		tmp = Float64(-1.0 * Float64(i * Float64(c * Float64(x * y))));
	elseif (y1 <= 9.2e+72)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y1 * (y3 * z));
	tmp = 0.0;
	if (y1 <= -0.0023)
		tmp = t_1;
	elseif (y1 <= -2.15e-107)
		tmp = -1.0 * (i * (c * (x * y)));
	elseif (y1 <= 9.2e+72)
		tmp = a * (t * (y2 * y5));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y1 * N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -0.0023], t$95$1, If[LessEqual[y1, -2.15e-107], N[(-1.0 * N[(i * N[(c * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 9.2e+72], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -0.0023 or 9.199999999999999e72 < y1

   1. Initial program 25.7%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 38.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in y1 around -inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - \color{blue}{i \cdot k}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot \color{blue}{k}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

      5. lower-*.f64 35.3

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

   7. Applied rewrites 35.3%

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   8. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot \color{blue}{z}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]

      3. lower-*.f64 26.0

         \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]

   10. Applied rewrites 26.0%

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]

   if -0.0023 < y1 < -2.1499999999999999e-107

   1. Initial program 34.1%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in i around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y - t \cdot z\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{y1 \cdot \left(j \cdot x - k \cdot z\right)}\right)\right) \]

   4. Applied rewrites 38.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\left(c \cdot \left(x \cdot y\right) + y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \color{blue}{\left(x \cdot y1\right)}\right)\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(\color{blue}{x} \cdot y1\right)\right)\right) \]

      3. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      4. lift--.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      5. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      6. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot \color{blue}{y1}\right)\right)\right) \]

      9. lower-*.f64 35.5

         \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - j \cdot \left(x \cdot y1\right)\right)\right) \]

   7. Applied rewrites 35.5%

      \[\leadsto -1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y, y5 \cdot \left(j \cdot t - k \cdot y\right)\right) - \color{blue}{j \cdot \left(x \cdot y1\right)}\right)\right) \]

   8. Taylor expanded in c around inf

      \[\leadsto -1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot \color{blue}{y}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y\right)\right)\right) \]

      2. lift-*.f64 18.9

         \[\leadsto -1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot y\right)\right)\right) \]

   10. Applied rewrites 18.9%

       \[\leadsto -1 \cdot \left(i \cdot \left(c \cdot \left(x \cdot \color{blue}{y}\right)\right)\right) \]

   if -2.1499999999999999e-107 < y1 < 9.199999999999999e72

   1. Initial program 32.6%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{a \cdot \left(t \cdot y2 - y \cdot y3\right)}\right)\right) \]

   4. Applied rewrites 37.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

      3. lift--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot \color{blue}{y3}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. lift-*.f64 28.1

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Applied rewrites 28.1%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   8. Taylor expanded in y around 0

      \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot \color{blue}{y5}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]

      2. lower-*.f64 18.6

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]

   10. Applied rewrites 18.6%

       \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot \color{blue}{y5}\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 25: 21.9% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right)\\ \mathbf{if}\;y1 \leq -5.5 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 9.2 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (let* ((t_1 (* a (* y1 (* y3 z)))))
   (if (<= y1 -5.5e+75) t_1 (if (<= y1 9.2e+72) (* a (* t (* y2 y5))) 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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * (y3 * z));
	double tmp;
	if (y1 <= -5.5e+75) {
		tmp = t_1;
	} else if (y1 <= 9.2e+72) {
		tmp = a * (t * (y2 * y5));
	} 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, y0, y1, y2, y3, y4, y5)
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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y1 * (y3 * z))
    if (y1 <= (-5.5d+75)) then
        tmp = t_1
    else if (y1 <= 9.2d+72) then
        tmp = a * (t * (y2 * y5))
    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 y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = a * (y1 * (y3 * z));
	double tmp;
	if (y1 <= -5.5e+75) {
		tmp = t_1;
	} else if (y1 <= 9.2e+72) {
		tmp = a * (t * (y2 * y5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	t_1 = a * (y1 * (y3 * z))
	tmp = 0
	if y1 <= -5.5e+75:
		tmp = t_1
	elif y1 <= 9.2e+72:
		tmp = a * (t * (y2 * y5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = Float64(a * Float64(y1 * Float64(y3 * z)))
	tmp = 0.0
	if (y1 <= -5.5e+75)
		tmp = t_1;
	elseif (y1 <= 9.2e+72)
		tmp = Float64(a * Float64(t * Float64(y2 * y5)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	t_1 = a * (y1 * (y3 * z));
	tmp = 0.0;
	if (y1 <= -5.5e+75)
		tmp = t_1;
	elseif (y1 <= 9.2e+72)
		tmp = a * (t * (y2 * y5));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := Block[{t$95$1 = N[(a * N[(y1 * N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -5.5e+75], t$95$1, If[LessEqual[y1, 9.2e+72], N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y1 < -5.5000000000000001e75 or 9.199999999999999e72 < y1

   1. Initial program 25.2%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{k \cdot \left(b \cdot y0 - i \cdot y1\right)}\right)\right) \]

   4. Applied rewrites 38.8%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, a \cdot b - c \cdot i, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]

   5. Taylor expanded in y1 around -inf

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \color{blue}{\left(a \cdot y3 - i \cdot k\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - \color{blue}{i \cdot k}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot \color{blue}{k}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

      5. lower-*.f64 37.1

         \[\leadsto y1 \cdot \left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right) \]

   7. Applied rewrites 37.1%

      \[\leadsto y1 \cdot \color{blue}{\left(z \cdot \left(a \cdot y3 - i \cdot k\right)\right)} \]

   8. Taylor expanded in a around inf

      \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot \color{blue}{z}\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]

      3. lower-*.f64 27.9

         \[\leadsto a \cdot \left(y1 \cdot \left(y3 \cdot z\right)\right) \]

   10. Applied rewrites 27.9%

       \[\leadsto a \cdot \left(y1 \cdot \color{blue}{\left(y3 \cdot z\right)}\right) \]

   if -5.5000000000000001e75 < y1 < 9.199999999999999e72

   1. Initial program 32.5%

      \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   2. Taylor expanded in y5 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{a \cdot \left(t \cdot y2 - y \cdot y3\right)}\right)\right) \]

   4. Applied rewrites 37.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   5. Taylor expanded in a around -inf

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

      3. lift--.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot \color{blue}{y3}\right)\right) \]

      4. lift-*.f64 N/A

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

      5. lift-*.f64 28.0

         \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   7. Applied rewrites 28.0%

      \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

   8. Taylor expanded in y around 0

      \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot \color{blue}{y5}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]

      2. lower-*.f64 18.2

         \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]

   10. Applied rewrites 18.2%

       \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot \color{blue}{y5}\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 26: 17.5% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
 :precision binary64
 (* a (* t (* y2 y5))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (t * (y2 * y5));
}

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, y0, y1, y2, y3, y4, y5)
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), intent (in) :: y0
    real(8), intent (in) :: y1
    real(8), intent (in) :: y2
    real(8), intent (in) :: y3
    real(8), intent (in) :: y4
    real(8), intent (in) :: y5
    code = a * (t * (y2 * y5))
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 y0, double y1, double y2, double y3, double y4, double y5) {
	return a * (t * (y2 * y5));
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	return a * (t * (y2 * y5))

Julia

function code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	return Float64(a * Float64(t * Float64(y2 * y5)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5)
	tmp = a * (t * (y2 * y5));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(a * N[(t * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 29.7%

   \[\left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot \left(a \cdot b - c \cdot i\right) - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - \left(t \cdot y2 - y \cdot y3\right) \cdot \left(y4 \cdot c - y5 \cdot a\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

2. Taylor expanded in y5 around -inf

   \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto -1 \cdot \color{blue}{\left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

   2. lower-*.f64 N/A

      \[\leadsto -1 \cdot \left(y5 \cdot \color{blue}{\left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)}\right) \]

   3. lower--.f64 N/A

      \[\leadsto -1 \cdot \left(y5 \cdot \left(\left(i \cdot \left(j \cdot t - k \cdot y\right) + y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - \color{blue}{a \cdot \left(t \cdot y2 - y \cdot y3\right)}\right)\right) \]

4. Applied rewrites 36.2%

   \[\leadsto \color{blue}{-1 \cdot \left(y5 \cdot \left(\mathsf{fma}\left(i, j \cdot t - k \cdot y, y0 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - a \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right)} \]

5. Taylor expanded in a around -inf

   \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
6. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto a \cdot \left(y5 \cdot \color{blue}{\left(t \cdot y2 - y \cdot y3\right)}\right) \]

   2. lower-*.f64 N/A

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - \color{blue}{y \cdot y3}\right)\right) \]

   3. lift--.f64 N/A

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot \color{blue}{y3}\right)\right) \]

   4. lift-*.f64 N/A

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

   5. lift-*.f64 26.9

      \[\leadsto a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right) \]

7. Applied rewrites 26.9%

   \[\leadsto a \cdot \color{blue}{\left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

8. Taylor expanded in y around 0

   \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot \color{blue}{y5}\right)\right) \]
9. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]

   2. lower-*.f64 17.5

      \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot y5\right)\right) \]

10. Applied rewrites 17.5%

    \[\leadsto a \cdot \left(t \cdot \left(y2 \cdot \color{blue}{y5}\right)\right) \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025119 
(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :name "Linear.Matrix:det44 from linear-1.19.1.3"
  :precision binary64
  (+ (- (+ (+ (- (* (- (* x y) (* z t)) (- (* a b) (* c i))) (* (- (* x j) (* z k)) (- (* y0 b) (* y1 i)))) (* (- (* x y2) (* z y3)) (- (* y0 c) (* y1 a)))) (* (- (* t j) (* y k)) (- (* y4 b) (* y5 i)))) (* (- (* t y2) (* y y3)) (- (* y4 c) (* y5 a)))) (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0)))))