Linear.Matrix:det44 from linear-1.19.1.3

Percentage Accurate: 30.1% → 53.7%

Time: 19.2s

Alternatives: 34

Speedup: 5.8×

• 11.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 30.1% accurate, 1.0× speedup

Math

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

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: 53.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_1 := j \cdot x - k \cdot z\\ t_2 := k \cdot y2 - j \cdot y3\\ t_3 := j \cdot t - k \cdot y\\ t_4 := a \cdot b - c \cdot i\\ \mathbf{if}\;y0 \leq -5.9 \cdot 10^{+221}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-1, k \cdot y5, c \cdot x\right)\right)\\ \mathbf{elif}\;y0 \leq -5.8 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{b}\right)\right)\right) + t\_2 \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;y0 \leq 6.2 \cdot 10^{-298}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t\_3, y1 \cdot t\_2\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{elif}\;y0 \leq 4 \cdot 10^{-54}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot t\_3\right) - y1 \cdot t\_1\right)\right)\\ \mathbf{elif}\;y0 \leq 1.16 \cdot 10^{-14}:\\ \;\;\;\;-1 \cdot \left(z \cdot \left(\mathsf{fma}\left(t, t\_4, y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)\\ \mathbf{elif}\;y0 \leq 2.1 \cdot 10^{+189}:\\ \;\;\;\;x \cdot \left(y \cdot t\_4\right) + y1 \cdot \left(y4 \cdot t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(\mathsf{fma}\left(-1, y5 \cdot t\_2, c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot t\_1\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (let* ((t_1 (- (* j x) (* k z)))
       (t_2 (- (* k y2) (* j y3)))
       (t_3 (- (* j t) (* k y)))
       (t_4 (- (* a b) (* c i))))
  (if (<= y0 -5.9e+221)
    (* y0 (* y2 (fma -1.0 (* k y5) (* c x))))
    (if (<= y0 -5.8e-72)
      (+
       (* x (* y (* b (+ a (* -1.0 (/ (* c i) b))))))
       (* t_2 (- (* y4 y1) (* y5 y0))))
      (if (<= y0 6.2e-298)
        (* y4 (- (fma b t_3 (* y1 t_2)) (* c (- (* t y2) (* y y3)))))
        (if (<= y0 4e-54)
          (*
           -1.0
           (*
            i
            (- (fma c (- (* x y) (* t z)) (* y5 t_3)) (* y1 t_1))))
          (if (<= y0 1.16e-14)
            (*
             -1.0
             (*
              z
              (-
               (fma t t_4 (* y3 (- (* c y0) (* a y1))))
               (* k (- (* b y0) (* i y1))))))
            (if (<= y0 2.1e+189)
              (+ (* x (* y t_4)) (* y1 (* y4 t_2)))
              (*
               y0
               (-
                (fma -1.0 (* y5 t_2) (* c (- (* x y2) (* y3 z))))
                (* b t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (j * x) - (k * z);
	double t_2 = (k * y2) - (j * y3);
	double t_3 = (j * t) - (k * y);
	double t_4 = (a * b) - (c * i);
	double tmp;
	if (y0 <= -5.9e+221) {
		tmp = y0 * (y2 * fma(-1.0, (k * y5), (c * x)));
	} else if (y0 <= -5.8e-72) {
		tmp = (x * (y * (b * (a + (-1.0 * ((c * i) / b)))))) + (t_2 * ((y4 * y1) - (y5 * y0)));
	} else if (y0 <= 6.2e-298) {
		tmp = y4 * (fma(b, t_3, (y1 * t_2)) - (c * ((t * y2) - (y * y3))));
	} else if (y0 <= 4e-54) {
		tmp = -1.0 * (i * (fma(c, ((x * y) - (t * z)), (y5 * t_3)) - (y1 * t_1)));
	} else if (y0 <= 1.16e-14) {
		tmp = -1.0 * (z * (fma(t, t_4, (y3 * ((c * y0) - (a * y1)))) - (k * ((b * y0) - (i * y1)))));
	} else if (y0 <= 2.1e+189) {
		tmp = (x * (y * t_4)) + (y1 * (y4 * t_2));
	} else {
		tmp = y0 * (fma(-1.0, (y5 * t_2), (c * ((x * y2) - (y3 * z)))) - (b * 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 * x) - Float64(k * z))
	t_2 = Float64(Float64(k * y2) - Float64(j * y3))
	t_3 = Float64(Float64(j * t) - Float64(k * y))
	t_4 = Float64(Float64(a * b) - Float64(c * i))
	tmp = 0.0
	if (y0 <= -5.9e+221)
		tmp = Float64(y0 * Float64(y2 * fma(-1.0, Float64(k * y5), Float64(c * x))));
	elseif (y0 <= -5.8e-72)
		tmp = Float64(Float64(x * Float64(y * Float64(b * Float64(a + Float64(-1.0 * Float64(Float64(c * i) / b)))))) + Float64(t_2 * Float64(Float64(y4 * y1) - Float64(y5 * y0))));
	elseif (y0 <= 6.2e-298)
		tmp = Float64(y4 * Float64(fma(b, t_3, Float64(y1 * t_2)) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))));
	elseif (y0 <= 4e-54)
		tmp = Float64(-1.0 * Float64(i * Float64(fma(c, Float64(Float64(x * y) - Float64(t * z)), Float64(y5 * t_3)) - Float64(y1 * t_1))));
	elseif (y0 <= 1.16e-14)
		tmp = Float64(-1.0 * Float64(z * Float64(fma(t, t_4, Float64(y3 * Float64(Float64(c * y0) - Float64(a * y1)))) - Float64(k * Float64(Float64(b * y0) - Float64(i * y1))))));
	elseif (y0 <= 2.1e+189)
		tmp = Float64(Float64(x * Float64(y * t_4)) + Float64(y1 * Float64(y4 * t_2)));
	else
		tmp = Float64(y0 * Float64(fma(-1.0, Float64(y5 * t_2), Float64(c * Float64(Float64(x * y2) - Float64(y3 * z)))) - Float64(b * 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 * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -5.9e+221], N[(y0 * N[(y2 * N[(-1.0 * N[(k * y5), $MachinePrecision] + N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5.8e-72], N[(N[(x * N[(y * N[(b * N[(a + N[(-1.0 * N[(N[(c * i), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 6.2e-298], N[(y4 * N[(N[(b * t$95$3 + N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 4e-54], N[(-1.0 * N[(i * N[(N[(c * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1.16e-14], N[(-1.0 * N[(z * N[(N[(t * t$95$4 + 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], If[LessEqual[y0, 2.1e+189], N[(N[(x * N[(y * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(N[(-1.0 * N[(y5 * t$95$2), $MachinePrecision] + N[(c * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y0 < -5.9e221

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-1, k \cdot \color{blue}{y5}, c \cdot x\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-1, k \cdot y5, c \cdot x\right)\right) \]

      5. lower-*.f64 26.5%

         \[\leadsto y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-1, k \cdot y5, c \cdot x\right)\right) \]

   7. Applied rewrites 26.5%

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-1, k \cdot y5, c \cdot x\right)\right)} \]

   if -5.9e221 < y0 < -5.8e-72

   1. Initial program 30.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.2%

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

   7. Applied rewrites 42.2%

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

   8. Taylor expanded in b around inf

      \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + \color{blue}{-1 \cdot \frac{c \cdot i}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \color{blue}{\frac{c \cdot i}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{\color{blue}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{b}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{b}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 42.5%

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{b}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   10. Applied rewrites 42.5%

       \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + \color{blue}{-1 \cdot \frac{c \cdot i}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   if -5.8e-72 < y0 < 6.2000000000000003e-298

   1. Initial program 30.1%

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

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   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 37.1%

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

   if 6.2000000000000003e-298 < y0 < 4.0000000000000001e-54

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in i around -inf

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

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

   7. Applied rewrites 37.4%

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

   if 4.0000000000000001e-54 < y0 < 1.1600000000000001e-14

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(\left(t \cdot \left(a \cdot b - c \cdot i\right) + y3 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - k \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\right)} \]
   6. 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

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

   7. Applied rewrites 36.6%

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

   if 1.1600000000000001e-14 < y0 < 2.0999999999999999e189

   1. Initial program 30.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.2%

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

   7. Applied rewrites 42.2%

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

   8. Taylor expanded in y0 around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 37.4%

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

   10. Applied rewrites 37.4%

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

   if 2.0999999999999999e189 < y0

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

      \[\leadsto \color{blue}{y0 \cdot \left(\mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - b \cdot \left(j \cdot x - k \cdot z\right)\right)} \]
3. Recombined 7 regimes into one program.
4. Add Preprocessing

Alternative 2: 45.7% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (let* ((t_1 (- (* t y2) (* y y3)))
       (t_2 (- (* k y2) (* j y3)))
       (t_3
        (+
         (-
          (+
           (+
            (-
             (* (- (* 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_1 (- (* y4 c) (* y5 a))))
         (* t_2 (- (* y4 y1) (* y5 y0))))))
  (if (<= t_3 INFINITY)
    t_3
    (* y4 (- (fma b (- (* j t) (* k y)) (* y1 t_2)) (* c 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 = (t * y2) - (y * y3);
	double t_2 = (k * y2) - (j * y3);
	double t_3 = (((((((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_1 * ((y4 * c) - (y5 * a)))) + (t_2 * ((y4 * y1) - (y5 * y0)));
	double tmp;
	if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = y4 * (fma(b, ((j * t) - (k * y)), (y1 * t_2)) - (c * 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(t * y2) - Float64(y * y3))
	t_2 = Float64(Float64(k * y2) - Float64(j * y3))
	t_3 = 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(t_1 * Float64(Float64(y4 * c) - Float64(y5 * a)))) + Float64(t_2 * Float64(Float64(y4 * y1) - Float64(y5 * y0))))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(y4 * Float64(fma(b, Float64(Float64(j * t) - Float64(k * y)), Float64(y1 * t_2)) - Float64(c * 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[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = 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[(t$95$1 * N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(y4 * N[(N[(b * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$1), $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 30.1%

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

   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 30.1%

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

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   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 37.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 44.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)\\ t_2 := t \cdot y2 - y \cdot y3\\ \mathbf{if}\;j \leq -9.4 \cdot 10^{+247}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.28 \cdot 10^{-266}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot t\_2\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{+160}:\\ \;\;\;\;c \cdot \left(\mathsf{fma}\left(-1, i \cdot \left(x \cdot y - t \cdot z\right), y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (let* ((t_1
        (*
         j
         (-
          (fma
           -1.0
           (* y3 (- (* y1 y4) (* y0 y5)))
           (* t (- (* b y4) (* i y5))))
          (* x (- (* b y0) (* i y1))))))
       (t_2 (- (* t y2) (* y y3))))
  (if (<= j -9.4e+247)
    (* j (* x (- (* i y1) (* b y0))))
    (if (<= j -6.5e+33)
      t_1
      (if (<= j -1.28e-266)
        (*
         y4
         (-
          (fma b (- (* j t) (* k y)) (* y1 (- (* k y2) (* j y3))))
          (* c t_2)))
        (if (<= j 5.6e+160)
          (*
           c
           (-
            (fma
             -1.0
             (* i (- (* x y) (* t z)))
             (* y0 (- (* x y2) (* y3 z))))
            (* y4 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 = j * (fma(-1.0, (y3 * ((y1 * y4) - (y0 * y5))), (t * ((b * y4) - (i * y5)))) - (x * ((b * y0) - (i * y1))));
	double t_2 = (t * y2) - (y * y3);
	double tmp;
	if (j <= -9.4e+247) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (j <= -6.5e+33) {
		tmp = t_1;
	} else if (j <= -1.28e-266) {
		tmp = y4 * (fma(b, ((j * t) - (k * y)), (y1 * ((k * y2) - (j * y3)))) - (c * t_2));
	} else if (j <= 5.6e+160) {
		tmp = c * (fma(-1.0, (i * ((x * y) - (t * z))), (y0 * ((x * y2) - (y3 * z)))) - (y4 * 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(j * Float64(fma(-1.0, Float64(y3 * Float64(Float64(y1 * y4) - Float64(y0 * y5))), Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))) - Float64(x * Float64(Float64(b * y0) - Float64(i * y1)))))
	t_2 = Float64(Float64(t * y2) - Float64(y * y3))
	tmp = 0.0
	if (j <= -9.4e+247)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (j <= -6.5e+33)
		tmp = t_1;
	elseif (j <= -1.28e-266)
		tmp = Float64(y4 * Float64(fma(b, Float64(Float64(j * t) - Float64(k * y)), Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) - Float64(c * t_2)));
	elseif (j <= 5.6e+160)
		tmp = Float64(c * Float64(fma(-1.0, Float64(i * Float64(Float64(x * y) - Float64(t * z))), Float64(y0 * Float64(Float64(x * y2) - Float64(y3 * z)))) - Float64(y4 * t_2)));
	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[(j * N[(N[(-1.0 * N[(y3 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.4e+247], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.5e+33], t$95$1, If[LessEqual[j, -1.28e-266], N[(y4 * N[(N[(b * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.6e+160], N[(c * N[(N[(-1.0 * N[(i * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -9.4000000000000005e247

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

      4. lower-*.f64 27.1%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

   7. Applied rewrites 27.1%

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

   if -9.4000000000000005e247 < j < -6.4999999999999999e33 or 5.5999999999999999e160 < j

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   if -6.4999999999999999e33 < j < -1.2799999999999999e-266

   1. Initial program 30.1%

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

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   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 37.1%

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

   if -1.2799999999999999e-266 < j < 5.5999999999999999e160

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \color{blue}{\left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto c \cdot \left(\left(-1 \cdot \left(i \cdot \left(x \cdot y - t \cdot z\right)\right) + y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - \color{blue}{y4 \cdot \left(t \cdot y2 - y \cdot y3\right)}\right) \]

   7. Applied rewrites 37.2%

      \[\leadsto \color{blue}{c \cdot \left(\mathsf{fma}\left(-1, i \cdot \left(x \cdot y - t \cdot z\right), y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) - y4 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 43.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} t_1 := y1 \cdot y4 - y0 \cdot y5\\ t_2 := c \cdot y4 - a \cdot y5\\ t_3 := j \cdot t - k \cdot y\\ t_4 := y4 \cdot \left(\mathsf{fma}\left(b, t\_3, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ t_5 := c \cdot y0 - a \cdot y1\\ \mathbf{if}\;y4 \leq -3 \cdot 10^{+27}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y4 \leq -1.12 \cdot 10^{-190}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(k, t\_1, x \cdot t\_5\right) - t \cdot t\_2\right)\\ \mathbf{elif}\;y4 \leq 6 \cdot 10^{-102}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot t\_3\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 98000000000000:\\ \;\;\;\;-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, t\_1, z \cdot t\_5\right) - y \cdot t\_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (let* ((t_1 (- (* y1 y4) (* y0 y5)))
       (t_2 (- (* c y4) (* a y5)))
       (t_3 (- (* j t) (* k y)))
       (t_4
        (*
         y4
         (-
          (fma b t_3 (* y1 (- (* k y2) (* j y3))))
          (* c (- (* t y2) (* y y3))))))
       (t_5 (- (* c y0) (* a y1))))
  (if (<= y4 -3e+27)
    t_4
    (if (<= y4 -1.12e-190)
      (* y2 (- (fma k t_1 (* x t_5)) (* t t_2)))
      (if (<= y4 6e-102)
        (*
         -1.0
         (*
          i
          (-
           (fma c (- (* x y) (* t z)) (* y5 t_3))
           (* y1 (- (* j x) (* k z))))))
        (if (<= y4 98000000000000.0)
          (* -1.0 (* y3 (- (fma j t_1 (* z t_5)) (* y t_2))))
          t_4))))))

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 = (y1 * y4) - (y0 * y5);
	double t_2 = (c * y4) - (a * y5);
	double t_3 = (j * t) - (k * y);
	double t_4 = y4 * (fma(b, t_3, (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	double t_5 = (c * y0) - (a * y1);
	double tmp;
	if (y4 <= -3e+27) {
		tmp = t_4;
	} else if (y4 <= -1.12e-190) {
		tmp = y2 * (fma(k, t_1, (x * t_5)) - (t * t_2));
	} else if (y4 <= 6e-102) {
		tmp = -1.0 * (i * (fma(c, ((x * y) - (t * z)), (y5 * t_3)) - (y1 * ((j * x) - (k * z)))));
	} else if (y4 <= 98000000000000.0) {
		tmp = -1.0 * (y3 * (fma(j, t_1, (z * t_5)) - (y * t_2)));
	} else {
		tmp = t_4;
	}
	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(y1 * y4) - Float64(y0 * y5))
	t_2 = Float64(Float64(c * y4) - Float64(a * y5))
	t_3 = Float64(Float64(j * t) - Float64(k * y))
	t_4 = Float64(y4 * Float64(fma(b, t_3, Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))))
	t_5 = Float64(Float64(c * y0) - Float64(a * y1))
	tmp = 0.0
	if (y4 <= -3e+27)
		tmp = t_4;
	elseif (y4 <= -1.12e-190)
		tmp = Float64(y2 * Float64(fma(k, t_1, Float64(x * t_5)) - Float64(t * t_2)));
	elseif (y4 <= 6e-102)
		tmp = Float64(-1.0 * Float64(i * Float64(fma(c, Float64(Float64(x * y) - Float64(t * z)), Float64(y5 * t_3)) - Float64(y1 * Float64(Float64(j * x) - Float64(k * z))))));
	elseif (y4 <= 98000000000000.0)
		tmp = Float64(-1.0 * Float64(y3 * Float64(fma(j, t_1, Float64(z * t_5)) - Float64(y * t_2))));
	else
		tmp = t_4;
	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[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y4 * N[(N[(b * t$95$3 + 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]}, Block[{t$95$5 = N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -3e+27], t$95$4, If[LessEqual[y4, -1.12e-190], N[(y2 * N[(N[(k * t$95$1 + N[(x * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(t * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6e-102], N[(-1.0 * N[(i * N[(N[(c * N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(y5 * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(y1 * N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 98000000000000.0], N[(-1.0 * N[(y3 * N[(N[(j * t$95$1 + N[(z * t$95$5), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y4 < -2.9999999999999998e27 or 9.8e13 < y4

   1. Initial program 30.1%

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

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   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 37.1%

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

   if -2.9999999999999998e27 < y4 < -1.12e-190

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if -1.12e-190 < y4 < 6e-102

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in i around -inf

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

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

   7. Applied rewrites 37.4%

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

   if 6e-102 < y4 < 9.8e13

   1. Initial program 30.1%

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

   2. Taylor expanded in y3 around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]

      2. lower-*.f64 N/A

         \[\leadsto -1 \cdot \left(y3 \cdot \color{blue}{\left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)}\right) \]

      3. lower--.f64 N/A

         \[\leadsto -1 \cdot \left(y3 \cdot \left(\left(j \cdot \left(y1 \cdot y4 - y0 \cdot y5\right) + z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - \color{blue}{y \cdot \left(c \cdot y4 - a \cdot y5\right)}\right)\right) \]

   4. Applied rewrites 37.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y3 \cdot \left(\mathsf{fma}\left(j, y1 \cdot y4 - y0 \cdot y5, z \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - y \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 5: 42.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := t \cdot y2 - y \cdot y3\\ t_2 := t\_1 \cdot \left(y4 \cdot c - y5 \cdot a\right)\\ t_3 := j \cdot t - k \cdot y\\ t_4 := k \cdot y2 - j \cdot y3\\ t_5 := t\_4 \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ t_6 := j \cdot x - k \cdot z\\ t_7 := x \cdot y - t \cdot z\\ t_8 := a \cdot b - c \cdot i\\ t_9 := \left(\left(\left(\left(\left(x \cdot y - z \cdot t\right) \cdot t\_8 - \left(x \cdot j - z \cdot k\right) \cdot \left(y0 \cdot b - y1 \cdot i\right)\right) + \left(x \cdot y2 - z \cdot y3\right) \cdot \left(y0 \cdot c - y1 \cdot a\right)\right) + \left(t \cdot j - y \cdot k\right) \cdot \left(y4 \cdot b - y5 \cdot i\right)\right) - t\_2\right) + t\_5\\ \mathbf{if}\;t\_9 \leq 2 \cdot 10^{+231}:\\ \;\;\;\;\mathsf{fma}\left(-1, i \cdot \left(y5 \cdot t\_3\right), \mathsf{fma}\left(-1, y0 \cdot \left(y5 \cdot t\_4\right), \mathsf{fma}\left(t\_8, t\_7, \left(c \cdot y0 - a \cdot y1\right) \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) - \mathsf{fma}\left(-1, a \cdot \left(y5 \cdot t\_1\right), \left(b \cdot y0 - i \cdot y1\right) \cdot t\_6\right)\\ \mathbf{elif}\;t\_9 \leq \infty:\\ \;\;\;\;\left(b \cdot \left(\mathsf{fma}\left(a, t\_7, y4 \cdot t\_3\right) - y0 \cdot t\_6\right) - t\_2\right) + t\_5\\ \mathbf{else}:\\ \;\;\;\;y4 \cdot \left(\mathsf{fma}\left(b, t\_3, y1 \cdot t\_4\right) - c \cdot t\_1\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (let* ((t_1 (- (* t y2) (* y y3)))
       (t_2 (* t_1 (- (* y4 c) (* y5 a))))
       (t_3 (- (* j t) (* k y)))
       (t_4 (- (* k y2) (* j y3)))
       (t_5 (* t_4 (- (* y4 y1) (* y5 y0))))
       (t_6 (- (* j x) (* k z)))
       (t_7 (- (* x y) (* t z)))
       (t_8 (- (* a b) (* c i)))
       (t_9
        (+
         (-
          (+
           (+
            (-
             (* (- (* x y) (* z t)) t_8)
             (* (- (* 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_2)
         t_5)))
  (if (<= t_9 2e+231)
    (-
     (fma
      -1.0
      (* i (* y5 t_3))
      (fma
       -1.0
       (* y0 (* y5 t_4))
       (fma t_8 t_7 (* (- (* c y0) (* a y1)) (- (* x y2) (* y3 z))))))
     (fma -1.0 (* a (* y5 t_1)) (* (- (* b y0) (* i y1)) t_6)))
    (if (<= t_9 INFINITY)
      (+ (- (* b (- (fma a t_7 (* y4 t_3)) (* y0 t_6))) t_2) t_5)
      (* y4 (- (fma b t_3 (* y1 t_4)) (* c 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 = (t * y2) - (y * y3);
	double t_2 = t_1 * ((y4 * c) - (y5 * a));
	double t_3 = (j * t) - (k * y);
	double t_4 = (k * y2) - (j * y3);
	double t_5 = t_4 * ((y4 * y1) - (y5 * y0));
	double t_6 = (j * x) - (k * z);
	double t_7 = (x * y) - (t * z);
	double t_8 = (a * b) - (c * i);
	double t_9 = (((((((x * y) - (z * t)) * t_8) - (((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_2) + t_5;
	double tmp;
	if (t_9 <= 2e+231) {
		tmp = fma(-1.0, (i * (y5 * t_3)), fma(-1.0, (y0 * (y5 * t_4)), fma(t_8, t_7, (((c * y0) - (a * y1)) * ((x * y2) - (y3 * z)))))) - fma(-1.0, (a * (y5 * t_1)), (((b * y0) - (i * y1)) * t_6));
	} else if (t_9 <= ((double) INFINITY)) {
		tmp = ((b * (fma(a, t_7, (y4 * t_3)) - (y0 * t_6))) - t_2) + t_5;
	} else {
		tmp = y4 * (fma(b, t_3, (y1 * t_4)) - (c * 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(t * y2) - Float64(y * y3))
	t_2 = Float64(t_1 * Float64(Float64(y4 * c) - Float64(y5 * a)))
	t_3 = Float64(Float64(j * t) - Float64(k * y))
	t_4 = Float64(Float64(k * y2) - Float64(j * y3))
	t_5 = Float64(t_4 * Float64(Float64(y4 * y1) - Float64(y5 * y0)))
	t_6 = Float64(Float64(j * x) - Float64(k * z))
	t_7 = Float64(Float64(x * y) - Float64(t * z))
	t_8 = Float64(Float64(a * b) - Float64(c * i))
	t_9 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) - Float64(z * t)) * t_8) - 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)))) - t_2) + t_5)
	tmp = 0.0
	if (t_9 <= 2e+231)
		tmp = Float64(fma(-1.0, Float64(i * Float64(y5 * t_3)), fma(-1.0, Float64(y0 * Float64(y5 * t_4)), fma(t_8, t_7, Float64(Float64(Float64(c * y0) - Float64(a * y1)) * Float64(Float64(x * y2) - Float64(y3 * z)))))) - fma(-1.0, Float64(a * Float64(y5 * t_1)), Float64(Float64(Float64(b * y0) - Float64(i * y1)) * t_6)));
	elseif (t_9 <= Inf)
		tmp = Float64(Float64(Float64(b * Float64(fma(a, t_7, Float64(y4 * t_3)) - Float64(y0 * t_6))) - t_2) + t_5);
	else
		tmp = Float64(y4 * Float64(fma(b, t_3, Float64(y1 * t_4)) - Float64(c * 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[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[(N[(y4 * c), $MachinePrecision] - N[(y5 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(j * x), $MachinePrecision] - N[(k * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$9 = N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] * t$95$8), $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] - t$95$2), $MachinePrecision] + t$95$5), $MachinePrecision]}, If[LessEqual[t$95$9, 2e+231], N[(N[(-1.0 * N[(i * N[(y5 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(-1.0 * N[(y0 * N[(y5 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(t$95$8 * t$95$7 + N[(N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision] * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-1.0 * N[(a * N[(y5 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * y0), $MachinePrecision] - N[(i * y1), $MachinePrecision]), $MachinePrecision] * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$9, Infinity], N[(N[(N[(b * N[(N[(a * t$95$7 + N[(y4 * t$95$3), $MachinePrecision]), $MachinePrecision] - N[(y0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] + t$95$5), $MachinePrecision], N[(y4 * N[(N[(b * t$95$3 + N[(y1 * t$95$4), $MachinePrecision]), $MachinePrecision] - N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 3 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)))) < 2.0000000000000001e231

   1. Initial program 30.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.2%

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

   7. Applied rewrites 42.2%

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

   8. Taylor expanded in b around inf

      \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + \color{blue}{-1 \cdot \frac{c \cdot i}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \color{blue}{\frac{c \cdot i}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{\color{blue}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{b}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{b}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 42.5%

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{b}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   10. Applied rewrites 42.5%

       \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + \color{blue}{-1 \cdot \frac{c \cdot i}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   11. Taylor expanded in y4 around 0

       \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right)\right) + \left(-1 \cdot \left(y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) + \left(\left(a \cdot b - c \cdot i\right) \cdot \left(x \cdot y - t \cdot z\right) + \left(c \cdot y0 - a \cdot y1\right) \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) - \left(-1 \cdot \left(a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\right) + \left(b \cdot y0 - i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   13. Applied rewrites 29.4%

       \[\leadsto \color{blue}{\mathsf{fma}\left(-1, i \cdot \left(y5 \cdot \left(j \cdot t - k \cdot y\right)\right), \mathsf{fma}\left(-1, y0 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right), \mathsf{fma}\left(a \cdot b - c \cdot i, x \cdot y - t \cdot z, \left(c \cdot y0 - a \cdot y1\right) \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\right)\right) - \mathsf{fma}\left(-1, a \cdot \left(y5 \cdot \left(t \cdot y2 - y \cdot y3\right)\right), \left(b \cdot y0 - i \cdot y1\right) \cdot \left(j \cdot x - k \cdot z\right)\right)} \]

   if 2.0000000000000001e231 < (+.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 30.1%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 33.2%

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

   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 30.1%

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

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   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 37.1%

      \[\leadsto \color{blue}{y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 41.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} t_1 := y4 \cdot y1 - y5 \cdot y0\\ t_2 := k \cdot y2 - j \cdot y3\\ \mathbf{if}\;y0 \leq -4.7 \cdot 10^{+221}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-1, k \cdot y5, c \cdot x\right)\right)\\ \mathbf{elif}\;y0 \leq -4.7 \cdot 10^{+69}:\\ \;\;\;\;y \cdot \left(-1 \cdot \left(y4 \cdot \left(b \cdot k - c \cdot y3\right)\right)\right) + t\_2 \cdot t\_1\\ \mathbf{elif}\;y0 \leq -3.9 \cdot 10^{-174}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y2 \cdot k - y3 \cdot j, \left(i \cdot y\right) \cdot \left(y5 \cdot k - c \cdot x\right)\right)\\ \mathbf{elif}\;y0 \leq 0.052:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 2.35 \cdot 10^{+189}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) + y1 \cdot \left(y4 \cdot t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \mathsf{fma}\left(-1, y5 \cdot t\_2, c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (let* ((t_1 (- (* y4 y1) (* y5 y0))) (t_2 (- (* k y2) (* j y3))))
  (if (<= y0 -4.7e+221)
    (* y0 (* y2 (fma -1.0 (* k y5) (* c x))))
    (if (<= y0 -4.7e+69)
      (+ (* y (* -1.0 (* y4 (- (* b k) (* c y3))))) (* t_2 t_1))
      (if (<= y0 -3.9e-174)
        (fma
         t_1
         (- (* y2 k) (* y3 j))
         (* (* i y) (- (* y5 k) (* c x))))
        (if (<= y0 0.052)
          (*
           y2
           (-
            (fma
             k
             (- (* y1 y4) (* y0 y5))
             (* x (- (* c y0) (* a y1))))
            (* t (- (* c y4) (* a y5)))))
          (if (<= y0 2.35e+189)
            (+ (* x (* y (- (* a b) (* c i)))) (* y1 (* y4 t_2)))
            (*
             y0
             (fma -1.0 (* y5 t_2) (* c (- (* x y2) (* y3 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 = (y4 * y1) - (y5 * y0);
	double t_2 = (k * y2) - (j * y3);
	double tmp;
	if (y0 <= -4.7e+221) {
		tmp = y0 * (y2 * fma(-1.0, (k * y5), (c * x)));
	} else if (y0 <= -4.7e+69) {
		tmp = (y * (-1.0 * (y4 * ((b * k) - (c * y3))))) + (t_2 * t_1);
	} else if (y0 <= -3.9e-174) {
		tmp = fma(t_1, ((y2 * k) - (y3 * j)), ((i * y) * ((y5 * k) - (c * x))));
	} else if (y0 <= 0.052) {
		tmp = y2 * (fma(k, ((y1 * y4) - (y0 * y5)), (x * ((c * y0) - (a * y1)))) - (t * ((c * y4) - (a * y5))));
	} else if (y0 <= 2.35e+189) {
		tmp = (x * (y * ((a * b) - (c * i)))) + (y1 * (y4 * t_2));
	} else {
		tmp = y0 * fma(-1.0, (y5 * t_2), (c * ((x * y2) - (y3 * 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(y4 * y1) - Float64(y5 * y0))
	t_2 = Float64(Float64(k * y2) - Float64(j * y3))
	tmp = 0.0
	if (y0 <= -4.7e+221)
		tmp = Float64(y0 * Float64(y2 * fma(-1.0, Float64(k * y5), Float64(c * x))));
	elseif (y0 <= -4.7e+69)
		tmp = Float64(Float64(y * Float64(-1.0 * Float64(y4 * Float64(Float64(b * k) - Float64(c * y3))))) + Float64(t_2 * t_1));
	elseif (y0 <= -3.9e-174)
		tmp = fma(t_1, Float64(Float64(y2 * k) - Float64(y3 * j)), Float64(Float64(i * y) * Float64(Float64(y5 * k) - Float64(c * x))));
	elseif (y0 <= 0.052)
		tmp = Float64(y2 * Float64(fma(k, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) - Float64(t * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (y0 <= 2.35e+189)
		tmp = Float64(Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i)))) + Float64(y1 * Float64(y4 * t_2)));
	else
		tmp = Float64(y0 * fma(-1.0, Float64(y5 * t_2), Float64(c * Float64(Float64(x * y2) - Float64(y3 * 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[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y0, -4.7e+221], N[(y0 * N[(y2 * N[(-1.0 * N[(k * y5), $MachinePrecision] + N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -4.7e+69], N[(N[(y * N[(-1.0 * N[(y4 * N[(N[(b * k), $MachinePrecision] - N[(c * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -3.9e-174], N[(t$95$1 * N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] + N[(N[(i * y), $MachinePrecision] * N[(N[(y5 * k), $MachinePrecision] - N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 0.052], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.35e+189], N[(N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(y4 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(-1.0 * N[(y5 * t$95$2), $MachinePrecision] + N[(c * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y0 < -4.7000000000000001e221

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-1, k \cdot \color{blue}{y5}, c \cdot x\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-1, k \cdot y5, c \cdot x\right)\right) \]

      5. lower-*.f64 26.5%

         \[\leadsto y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-1, k \cdot y5, c \cdot x\right)\right) \]

   7. Applied rewrites 26.5%

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-1, k \cdot y5, c \cdot x\right)\right)} \]

   if -4.7000000000000001e221 < y0 < -4.7e69

   1. Initial program 30.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in y4 around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 34.9%

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

   7. Applied rewrites 34.9%

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

   if -4.7e69 < y0 < -3.8999999999999999e-174

   1. Initial program 30.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot \color{blue}{x}, k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 38.2%

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   7. Applied rewrites 38.2%

      \[\leadsto i \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)} \]

   9. Applied rewrites 38.7%

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

   if -3.8999999999999999e-174 < y0 < 0.051999999999999998

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if 0.051999999999999998 < y0 < 2.35e189

   1. Initial program 30.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.2%

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

   7. Applied rewrites 42.2%

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

   8. Taylor expanded in y0 around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 37.4%

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

   10. Applied rewrites 37.4%

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

   if 2.35e189 < y0

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in b around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      9. lower-*.f64 33.8%

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   7. Applied rewrites 33.8%

      \[\leadsto y0 \cdot \mathsf{fma}\left(-1, \color{blue}{y5 \cdot \left(k \cdot y2 - j \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 7: 41.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} t_1 := j \cdot t - k \cdot y\\ t_2 := y4 \cdot \left(\mathsf{fma}\left(b, t\_1, y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y4 \leq -3 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq -1.12 \cdot 10^{-190}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 1.6 \cdot 10^{-102}:\\ \;\;\;\;-1 \cdot \left(i \cdot \left(\mathsf{fma}\left(c, x \cdot y - t \cdot z, y5 \cdot t\_1\right) - y1 \cdot \left(j \cdot x - k \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

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
        (*
         y4
         (-
          (fma b t_1 (* y1 (- (* k y2) (* j y3))))
          (* c (- (* t y2) (* y y3)))))))
  (if (<= y4 -3e+27)
    t_2
    (if (<= y4 -1.12e-190)
      (*
       y2
       (-
        (fma k (- (* y1 y4) (* y0 y5)) (* x (- (* c y0) (* a y1))))
        (* t (- (* c y4) (* a y5)))))
      (if (<= y4 1.6e-102)
        (*
         -1.0
         (*
          i
          (-
           (fma c (- (* x y) (* t z)) (* y5 t_1))
           (* y1 (- (* j x) (* k z))))))
        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 = y4 * (fma(b, t_1, (y1 * ((k * y2) - (j * y3)))) - (c * ((t * y2) - (y * y3))));
	double tmp;
	if (y4 <= -3e+27) {
		tmp = t_2;
	} else if (y4 <= -1.12e-190) {
		tmp = y2 * (fma(k, ((y1 * y4) - (y0 * y5)), (x * ((c * y0) - (a * y1)))) - (t * ((c * y4) - (a * y5))));
	} else if (y4 <= 1.6e-102) {
		tmp = -1.0 * (i * (fma(c, ((x * y) - (t * z)), (y5 * t_1)) - (y1 * ((j * x) - (k * z)))));
	} 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(y4 * Float64(fma(b, t_1, Float64(y1 * Float64(Float64(k * y2) - Float64(j * y3)))) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))))
	tmp = 0.0
	if (y4 <= -3e+27)
		tmp = t_2;
	elseif (y4 <= -1.12e-190)
		tmp = Float64(y2 * Float64(fma(k, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) - Float64(t * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (y4 <= 1.6e-102)
		tmp = 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))))));
	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[(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[y4, -3e+27], t$95$2, If[LessEqual[y4, -1.12e-190], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.6e-102], 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], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -2.9999999999999998e27 or 1.5999999999999999e-102 < y4

   1. Initial program 30.1%

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

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   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 37.1%

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

   if -2.9999999999999998e27 < y4 < -1.12e-190

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if -1.12e-190 < y4 < 1.5999999999999999e-102

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in i around -inf

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

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

   7. Applied rewrites 37.4%

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

Alternative 8: 39.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ t_2 := y4 \cdot \left(\mathsf{fma}\left(b, j \cdot t - k \cdot y, y1 \cdot t\_1\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)\\ \mathbf{if}\;y4 \leq -3 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y4 \leq 9 \cdot 10^{-282}:\\ \;\;\;\;y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;y4 \leq 1.02 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b\right)\right) + t\_1 \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

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
        (*
         y4
         (-
          (fma b (- (* j t) (* k y)) (* y1 t_1))
          (* c (- (* t y2) (* y y3)))))))
  (if (<= y4 -3e+27)
    t_2
    (if (<= y4 9e-282)
      (*
       y2
       (-
        (fma k (- (* y1 y4) (* y0 y5)) (* x (- (* c y0) (* a y1))))
        (* t (- (* c y4) (* a y5)))))
      (if (<= y4 1.02e-201)
        (+ (* x (* y (* a b))) (* t_1 (- (* y4 y1) (* y5 y0))))
        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 = (k * y2) - (j * y3);
	double t_2 = y4 * (fma(b, ((j * t) - (k * y)), (y1 * t_1)) - (c * ((t * y2) - (y * y3))));
	double tmp;
	if (y4 <= -3e+27) {
		tmp = t_2;
	} else if (y4 <= 9e-282) {
		tmp = y2 * (fma(k, ((y1 * y4) - (y0 * y5)), (x * ((c * y0) - (a * y1)))) - (t * ((c * y4) - (a * y5))));
	} else if (y4 <= 1.02e-201) {
		tmp = (x * (y * (a * b))) + (t_1 * ((y4 * y1) - (y5 * y0)));
	} 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(k * y2) - Float64(j * y3))
	t_2 = Float64(y4 * Float64(fma(b, Float64(Float64(j * t) - Float64(k * y)), Float64(y1 * t_1)) - Float64(c * Float64(Float64(t * y2) - Float64(y * y3)))))
	tmp = 0.0
	if (y4 <= -3e+27)
		tmp = t_2;
	elseif (y4 <= 9e-282)
		tmp = Float64(y2 * Float64(fma(k, Float64(Float64(y1 * y4) - Float64(y0 * y5)), Float64(x * Float64(Float64(c * y0) - Float64(a * y1)))) - Float64(t * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (y4 <= 1.02e-201)
		tmp = Float64(Float64(x * Float64(y * Float64(a * b))) + Float64(t_1 * Float64(Float64(y4 * y1) - Float64(y5 * y0))));
	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[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y4 * N[(N[(b * N[(N[(j * t), $MachinePrecision] - N[(k * y), $MachinePrecision]), $MachinePrecision] + N[(y1 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(t * y2), $MachinePrecision] - N[(y * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y4, -3e+27], t$95$2, If[LessEqual[y4, 9e-282], N[(y2 * N[(N[(k * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 1.02e-201], N[(N[(x * N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -2.9999999999999998e27 or 1.02e-201 < y4

   1. Initial program 30.1%

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

   2. Taylor expanded in y4 around inf

      \[\leadsto \color{blue}{y4 \cdot \left(\left(b \cdot \left(j \cdot t - k \cdot y\right) + y1 \cdot \left(k \cdot y2 - j \cdot y3\right)\right) - c \cdot \left(t \cdot y2 - y \cdot y3\right)\right)} \]
   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 37.1%

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

   if -2.9999999999999998e27 < y4 < 9.0000000000000002e-282

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   if 9.0000000000000002e-282 < y4 < 1.02e-201

   1. Initial program 30.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.2%

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

   7. Applied rewrites 42.2%

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

   8. Taylor expanded in b around inf

      \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + \color{blue}{-1 \cdot \frac{c \cdot i}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \color{blue}{\frac{c \cdot i}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{\color{blue}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{b}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{b}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 42.5%

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{b}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   10. Applied rewrites 42.5%

       \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + \color{blue}{-1 \cdot \frac{c \cdot i}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   11. Taylor expanded in a around inf

       \[\leadsto x \cdot \left(y \cdot \left(a \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   12. Step-by-step derivation

       1. lower-*.f64 39.7%

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

   13. Applied rewrites 39.7%

       \[\leadsto x \cdot \left(y \cdot \left(a \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 39.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;j \leq -7.4 \cdot 10^{+247}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{-34}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-137}:\\ \;\;\;\;\mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2 \cdot k - y3 \cdot j, \left(i \cdot y\right) \cdot \left(y5 \cdot k - c \cdot x\right)\right)\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{-215}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 6.1 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) + y1 \cdot \left(y4 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y5 \cdot \left(y3 + -1 \cdot \frac{b \cdot x}{y5}\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (if (<= j -7.4e+247)
  (* j (* x (- (* i y1) (* b y0))))
  (if (<= j -2.8e-34)
    (*
     j
     (fma
      -1.0
      (* y3 (- (* y1 y4) (* y0 y5)))
      (* t (- (* b y4) (* i y5)))))
    (if (<= j -6.6e-137)
      (fma
       (- (* y4 y1) (* y5 y0))
       (- (* y2 k) (* y3 j))
       (* (* i y) (- (* y5 k) (* c x))))
      (if (<= j 9.2e-215)
        (* y2 (* t (- (* a y5) (* c y4))))
        (if (<= j 6.1e+80)
          (+
           (* x (* y (- (* a b) (* c i))))
           (* y1 (* y4 (- (* k y2) (* j y3)))))
          (* y0 (* j (* y5 (+ y3 (* -1.0 (/ (* b x) 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 (j <= -7.4e+247) {
		tmp = j * (x * ((i * y1) - (b * y0)));
	} else if (j <= -2.8e-34) {
		tmp = j * fma(-1.0, (y3 * ((y1 * y4) - (y0 * y5))), (t * ((b * y4) - (i * y5))));
	} else if (j <= -6.6e-137) {
		tmp = fma(((y4 * y1) - (y5 * y0)), ((y2 * k) - (y3 * j)), ((i * y) * ((y5 * k) - (c * x))));
	} else if (j <= 9.2e-215) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (j <= 6.1e+80) {
		tmp = (x * (y * ((a * b) - (c * i)))) + (y1 * (y4 * ((k * y2) - (j * y3))));
	} else {
		tmp = y0 * (j * (y5 * (y3 + (-1.0 * ((b * x) / 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 (j <= -7.4e+247)
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	elseif (j <= -2.8e-34)
		tmp = Float64(j * fma(-1.0, Float64(y3 * Float64(Float64(y1 * y4) - Float64(y0 * y5))), Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))));
	elseif (j <= -6.6e-137)
		tmp = fma(Float64(Float64(y4 * y1) - Float64(y5 * y0)), Float64(Float64(y2 * k) - Float64(y3 * j)), Float64(Float64(i * y) * Float64(Float64(y5 * k) - Float64(c * x))));
	elseif (j <= 9.2e-215)
		tmp = Float64(y2 * Float64(t * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (j <= 6.1e+80)
		tmp = Float64(Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i)))) + Float64(y1 * Float64(y4 * Float64(Float64(k * y2) - Float64(j * y3)))));
	else
		tmp = Float64(y0 * Float64(j * Float64(y5 * Float64(y3 + Float64(-1.0 * Float64(Float64(b * x) / 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[j, -7.4e+247], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.8e-34], N[(j * N[(-1.0 * N[(y3 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.6e-137], N[(N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] + N[(N[(i * y), $MachinePrecision] * N[(N[(y5 * k), $MachinePrecision] - N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.2e-215], N[(y2 * N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.1e+80], N[(N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(y4 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(j * N[(y5 * N[(y3 + N[(-1.0 * N[(N[(b * x), $MachinePrecision] / y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -7.3999999999999996e247

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

      4. lower-*.f64 27.1%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

   7. Applied rewrites 27.1%

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

   if -7.3999999999999996e247 < j < -2.8e-34

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}, t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - \color{blue}{y0 \cdot y5}\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot \color{blue}{y5}\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      9. lower-*.f64 33.9%

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

   7. Applied rewrites 33.9%

      \[\leadsto j \cdot \mathsf{fma}\left(-1, \color{blue}{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}, t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

   if -2.8e-34 < j < -6.6000000000000004e-137

   1. Initial program 30.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot \color{blue}{x}, k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 38.2%

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   7. Applied rewrites 38.2%

      \[\leadsto i \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)} \]

   9. Applied rewrites 38.7%

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

   if -6.6000000000000004e-137 < j < 9.1999999999999996e-215

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\left(a \cdot y5 - c \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \left(a \cdot y5 - \color{blue}{c \cdot y4}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot \color{blue}{y4}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right) \]

      4. lower-*.f64 27.5%

         \[\leadsto y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right) \]

   7. Applied rewrites 27.5%

      \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\left(a \cdot y5 - c \cdot y4\right)}\right) \]

   if 9.1999999999999996e-215 < j < 6.0999999999999998e80

   1. Initial program 30.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.2%

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

   7. Applied rewrites 42.2%

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

   8. Taylor expanded in y0 around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 37.4%

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

   10. Applied rewrites 37.4%

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

   if 6.0999999999999998e80 < j

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - \color{blue}{b \cdot x}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot \color{blue}{x}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

      4. lower-*.f64 26.2%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   8. Taylor expanded in y5 around inf

      \[\leadsto y0 \cdot \left(j \cdot \left(y5 \cdot \left(y3 + \color{blue}{-1 \cdot \frac{b \cdot x}{y5}}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y5 \cdot \left(y3 + -1 \cdot \frac{b \cdot x}{y5}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y5 \cdot \left(y3 + -1 \cdot \frac{b \cdot x}{y5}\right)\right)\right) \]

      5. lower-*.f64 28.3%

         \[\leadsto y0 \cdot \left(j \cdot \left(y5 \cdot \left(y3 + -1 \cdot \frac{b \cdot x}{y5}\right)\right)\right) \]

   10. Applied rewrites 28.3%

       \[\leadsto y0 \cdot \left(j \cdot \left(y5 \cdot \left(y3 + \color{blue}{-1 \cdot \frac{b \cdot x}{y5}}\right)\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 10: 38.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-80}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-147}:\\ \;\;\;\;y0 \cdot \mathsf{fma}\left(-1, y5 \cdot t\_1, c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) + t\_1 \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

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))))
  (if (<= x -3.9e+115)
    (* x (* y2 (- (* c y0) (* a y1))))
    (if (<= x -8.2e-80)
      (*
       j
       (fma
        -1.0
        (* y3 (- (* y1 y4) (* y0 y5)))
        (* t (- (* b y4) (* i y5)))))
      (if (<= x -3.4e-147)
        (* y0 (fma -1.0 (* y5 t_1) (* c (- (* x y2) (* y3 z)))))
        (if (<= x 3.2e+138)
          (+
           (* x (* y (- (* a b) (* c i))))
           (* t_1 (- (* y4 y1) (* y5 y0))))
          (* j (* x (- (* i y1) (* b 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) {
	double t_1 = (k * y2) - (j * y3);
	double tmp;
	if (x <= -3.9e+115) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (x <= -8.2e-80) {
		tmp = j * fma(-1.0, (y3 * ((y1 * y4) - (y0 * y5))), (t * ((b * y4) - (i * y5))));
	} else if (x <= -3.4e-147) {
		tmp = y0 * fma(-1.0, (y5 * t_1), (c * ((x * y2) - (y3 * z))));
	} else if (x <= 3.2e+138) {
		tmp = (x * (y * ((a * b) - (c * i)))) + (t_1 * ((y4 * y1) - (y5 * y0)));
	} else {
		tmp = j * (x * ((i * y1) - (b * y0)));
	}
	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))
	tmp = 0.0
	if (x <= -3.9e+115)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (x <= -8.2e-80)
		tmp = Float64(j * fma(-1.0, Float64(y3 * Float64(Float64(y1 * y4) - Float64(y0 * y5))), Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))));
	elseif (x <= -3.4e-147)
		tmp = Float64(y0 * fma(-1.0, Float64(y5 * t_1), Float64(c * Float64(Float64(x * y2) - Float64(y3 * z)))));
	elseif (x <= 3.2e+138)
		tmp = Float64(Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i)))) + Float64(t_1 * Float64(Float64(y4 * y1) - Float64(y5 * y0))));
	else
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	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]}, If[LessEqual[x, -3.9e+115], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.2e-80], N[(j * N[(-1.0 * N[(y3 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.4e-147], N[(y0 * N[(-1.0 * N[(y5 * t$95$1), $MachinePrecision] + N[(c * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+138], N[(N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.9000000000000001e115

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

      5. lower-*.f64 26.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

   7. Applied rewrites 26.9%

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

   if -3.9000000000000001e115 < x < -8.1999999999999999e-80

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}, t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - \color{blue}{y0 \cdot y5}\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot \color{blue}{y5}\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      9. lower-*.f64 33.9%

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

   7. Applied rewrites 33.9%

      \[\leadsto j \cdot \mathsf{fma}\left(-1, \color{blue}{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}, t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

   if -8.1999999999999999e-80 < x < -3.4e-147

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in b around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      9. lower-*.f64 33.8%

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   7. Applied rewrites 33.8%

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

   if -3.4e-147 < x < 3.2000000000000001e138

   1. Initial program 30.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.2%

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

   7. Applied rewrites 42.2%

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

   if 3.2000000000000001e138 < x

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

      4. lower-*.f64 27.1%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

   7. Applied rewrites 27.1%

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 11: 37.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} t_1 := y4 \cdot y1 - y5 \cdot y0\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-92}:\\ \;\;\;\;y2 \cdot \left(-1 \cdot \left(k \cdot \left(y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-156}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \left(a \cdot \left(b \cdot y\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot t\_1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+70}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y2 \cdot k - y3 \cdot j, i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (let* ((t_1 (- (* y4 y1) (* y5 y0))))
  (if (<= x -1.55e+74)
    (* x (* y2 (- (* c y0) (* a y1))))
    (if (<= x -5.3e-92)
      (* y2 (- (* -1.0 (* k (* y0 y5))) (* t (- (* c y4) (* a y5)))))
      (if (<= x -9e-156)
        (* x (* y0 (- (* c y2) (* b j))))
        (if (<= x 1.6e-281)
          (+ (* x (* a (* b y))) (* (- (* k y2) (* j y3)) t_1))
          (if (<= x 4.8e+70)
            (fma t_1 (- (* y2 k) (* y3 j)) (* i (* k (* y y5))))
            (* j (* x (* y0 (- (/ (* i y1) y0) b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double t_1 = (y4 * y1) - (y5 * y0);
	double tmp;
	if (x <= -1.55e+74) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (x <= -5.3e-92) {
		tmp = y2 * ((-1.0 * (k * (y0 * y5))) - (t * ((c * y4) - (a * y5))));
	} else if (x <= -9e-156) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (x <= 1.6e-281) {
		tmp = (x * (a * (b * y))) + (((k * y2) - (j * y3)) * t_1);
	} else if (x <= 4.8e+70) {
		tmp = fma(t_1, ((y2 * k) - (y3 * j)), (i * (k * (y * y5))));
	} else {
		tmp = j * (x * (y0 * (((i * y1) / y0) - b)));
	}
	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(y4 * y1) - Float64(y5 * y0))
	tmp = 0.0
	if (x <= -1.55e+74)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (x <= -5.3e-92)
		tmp = Float64(y2 * Float64(Float64(-1.0 * Float64(k * Float64(y0 * y5))) - Float64(t * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (x <= -9e-156)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (x <= 1.6e-281)
		tmp = Float64(Float64(x * Float64(a * Float64(b * y))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * t_1));
	elseif (x <= 4.8e+70)
		tmp = fma(t_1, Float64(Float64(y2 * k) - Float64(y3 * j)), Float64(i * Float64(k * Float64(y * y5))));
	else
		tmp = Float64(j * Float64(x * Float64(y0 * Float64(Float64(Float64(i * y1) / y0) - b))));
	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[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.55e+74], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.3e-92], N[(y2 * N[(N[(-1.0 * N[(k * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9e-156], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e-281], N[(N[(x * N[(a * N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+70], N[(t$95$1 * N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] + N[(i * N[(k * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(x * N[(y0 * N[(N[(N[(i * y1), $MachinePrecision] / y0), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.5500000000000001e74

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

      5. lower-*.f64 26.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

   7. Applied rewrites 26.9%

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

   if -1.5500000000000001e74 < x < -5.3000000000000003e-92

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in y5 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(-1 \cdot \left(k \cdot \left(y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(-1 \cdot \left(k \cdot \left(y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. lower-*.f64 31.6%

         \[\leadsto y2 \cdot \left(-1 \cdot \left(k \cdot \left(y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   7. Applied rewrites 31.6%

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

   if -5.3000000000000003e-92 < x < -8.9999999999999997e-156

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   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 27.0%

         \[\leadsto x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right) \]

   7. Applied rewrites 27.0%

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

   if -8.9999999999999997e-156 < x < 1.6e-281

   1. Initial program 30.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.2%

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

   7. Applied rewrites 42.2%

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

   8. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 39.5%

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

   10. Applied rewrites 39.5%

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

   if 1.6e-281 < x < 4.7999999999999997e70

   1. Initial program 30.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot \color{blue}{x}, k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 38.2%

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   7. Applied rewrites 38.2%

      \[\leadsto i \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)} \]

   9. Applied rewrites 38.7%

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

   10. Taylor expanded in x around 0

       \[\leadsto \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2 \cdot k - y3 \cdot j, i \cdot \left(k \cdot \color{blue}{\left(y \cdot y5\right)}\right)\right) \]
   11. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2 \cdot k - y3 \cdot j, i \cdot \left(k \cdot \left(y \cdot \color{blue}{y5}\right)\right)\right) \]

       2. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2 \cdot k - y3 \cdot j, i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right) \]

       3. lower-*.f64 36.6%

          \[\leadsto \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2 \cdot k - y3 \cdot j, i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right) \]

   12. Applied rewrites 36.6%

       \[\leadsto \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2 \cdot k - y3 \cdot j, i \cdot \left(k \cdot \color{blue}{\left(y \cdot y5\right)}\right)\right) \]

   if 4.7999999999999997e70 < x

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

      4. lower-*.f64 27.1%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

   7. Applied rewrites 27.1%

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

   8. Taylor expanded in y0 around inf

      \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - \color{blue}{b}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right) \]

      4. lower-*.f64 29.5%

         \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right) \]

   10. Applied rewrites 29.5%

       \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - \color{blue}{b}\right)\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 12: 37.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} t_1 := k \cdot y2 - j \cdot y3\\ \mathbf{if}\;y0 \leq -5.9 \cdot 10^{+221}:\\ \;\;\;\;y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-1, k \cdot y5, c \cdot x\right)\right)\\ \mathbf{elif}\;y0 \leq -5.4 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b\right)\right) + t\_1 \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{elif}\;y0 \leq 1700000:\\ \;\;\;\;j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;y0 \leq 2.35 \cdot 10^{+189}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b - c \cdot i\right)\right) + y1 \cdot \left(y4 \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \mathsf{fma}\left(-1, y5 \cdot t\_1, c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \end{array} \]

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))))
  (if (<= y0 -5.9e+221)
    (* y0 (* y2 (fma -1.0 (* k y5) (* c x))))
    (if (<= y0 -5.4e-72)
      (+ (* x (* y (* a b))) (* t_1 (- (* y4 y1) (* y5 y0))))
      (if (<= y0 1700000.0)
        (*
         j
         (fma
          -1.0
          (* y3 (- (* y1 y4) (* y0 y5)))
          (* t (- (* b y4) (* i y5)))))
        (if (<= y0 2.35e+189)
          (+ (* x (* y (- (* a b) (* c i)))) (* y1 (* y4 t_1)))
          (*
           y0
           (fma -1.0 (* y5 t_1) (* c (- (* x y2) (* y3 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 tmp;
	if (y0 <= -5.9e+221) {
		tmp = y0 * (y2 * fma(-1.0, (k * y5), (c * x)));
	} else if (y0 <= -5.4e-72) {
		tmp = (x * (y * (a * b))) + (t_1 * ((y4 * y1) - (y5 * y0)));
	} else if (y0 <= 1700000.0) {
		tmp = j * fma(-1.0, (y3 * ((y1 * y4) - (y0 * y5))), (t * ((b * y4) - (i * y5))));
	} else if (y0 <= 2.35e+189) {
		tmp = (x * (y * ((a * b) - (c * i)))) + (y1 * (y4 * t_1));
	} else {
		tmp = y0 * fma(-1.0, (y5 * t_1), (c * ((x * y2) - (y3 * 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))
	tmp = 0.0
	if (y0 <= -5.9e+221)
		tmp = Float64(y0 * Float64(y2 * fma(-1.0, Float64(k * y5), Float64(c * x))));
	elseif (y0 <= -5.4e-72)
		tmp = Float64(Float64(x * Float64(y * Float64(a * b))) + Float64(t_1 * Float64(Float64(y4 * y1) - Float64(y5 * y0))));
	elseif (y0 <= 1700000.0)
		tmp = Float64(j * fma(-1.0, Float64(y3 * Float64(Float64(y1 * y4) - Float64(y0 * y5))), Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))));
	elseif (y0 <= 2.35e+189)
		tmp = Float64(Float64(x * Float64(y * Float64(Float64(a * b) - Float64(c * i)))) + Float64(y1 * Float64(y4 * t_1)));
	else
		tmp = Float64(y0 * fma(-1.0, Float64(y5 * t_1), Float64(c * Float64(Float64(x * y2) - Float64(y3 * 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]}, If[LessEqual[y0, -5.9e+221], N[(y0 * N[(y2 * N[(-1.0 * N[(k * y5), $MachinePrecision] + N[(c * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, -5.4e-72], N[(N[(x * N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 1700000.0], N[(j * N[(-1.0 * N[(y3 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y0, 2.35e+189], N[(N[(x * N[(y * N[(N[(a * b), $MachinePrecision] - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y1 * N[(y4 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(-1.0 * N[(y5 * t$95$1), $MachinePrecision] + N[(c * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y0 < -5.9e221

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in y0 around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-1, k \cdot \color{blue}{y5}, c \cdot x\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-1, k \cdot y5, c \cdot x\right)\right) \]

      5. lower-*.f64 26.5%

         \[\leadsto y0 \cdot \left(y2 \cdot \mathsf{fma}\left(-1, k \cdot y5, c \cdot x\right)\right) \]

   7. Applied rewrites 26.5%

      \[\leadsto y0 \cdot \color{blue}{\left(y2 \cdot \mathsf{fma}\left(-1, k \cdot y5, c \cdot x\right)\right)} \]

   if -5.9e221 < y0 < -5.4000000000000003e-72

   1. Initial program 30.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.2%

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

   7. Applied rewrites 42.2%

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

   8. Taylor expanded in b around inf

      \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + \color{blue}{-1 \cdot \frac{c \cdot i}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \color{blue}{\frac{c \cdot i}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{\color{blue}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{b}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{b}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 42.5%

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{b}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   10. Applied rewrites 42.5%

       \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + \color{blue}{-1 \cdot \frac{c \cdot i}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   11. Taylor expanded in a around inf

       \[\leadsto x \cdot \left(y \cdot \left(a \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   12. Step-by-step derivation

       1. lower-*.f64 39.7%

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

   13. Applied rewrites 39.7%

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

   if -5.4000000000000003e-72 < y0 < 1.7e6

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}, t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - \color{blue}{y0 \cdot y5}\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot \color{blue}{y5}\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      9. lower-*.f64 33.9%

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

   7. Applied rewrites 33.9%

      \[\leadsto j \cdot \mathsf{fma}\left(-1, \color{blue}{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}, t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

   if 1.7e6 < y0 < 2.35e189

   1. Initial program 30.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.2%

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

   7. Applied rewrites 42.2%

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

   8. Taylor expanded in y0 around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 37.4%

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

   10. Applied rewrites 37.4%

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

   if 2.35e189 < y0

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in b around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      9. lower-*.f64 33.8%

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   7. Applied rewrites 33.8%

      \[\leadsto y0 \cdot \mathsf{fma}\left(-1, \color{blue}{y5 \cdot \left(k \cdot y2 - j \cdot y3\right)}, c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 13: 37.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-92}:\\ \;\;\;\;y2 \cdot \left(-1 \cdot \left(k \cdot \left(y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-156}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(y \cdot \left(a \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (if (<= x -1.55e+74)
  (* x (* y2 (- (* c y0) (* a y1))))
  (if (<= x -5.3e-92)
    (* y2 (- (* -1.0 (* k (* y0 y5))) (* t (- (* c y4) (* a y5)))))
    (if (<= x -9e-156)
      (* x (* y0 (- (* c y2) (* b j))))
      (if (<= x 5e+95)
        (+
         (* x (* y (* a b)))
         (* (- (* k y2) (* j y3)) (- (* y4 y1) (* y5 y0))))
        (* j (* x (* y0 (- (/ (* i y1) y0) b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.55e+74) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (x <= -5.3e-92) {
		tmp = y2 * ((-1.0 * (k * (y0 * y5))) - (t * ((c * y4) - (a * y5))));
	} else if (x <= -9e-156) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (x <= 5e+95) {
		tmp = (x * (y * (a * b))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
	} else {
		tmp = j * (x * (y0 * (((i * y1) / y0) - b)));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j, k, 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 (x <= (-1.55d+74)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (x <= (-5.3d-92)) then
        tmp = y2 * (((-1.0d0) * (k * (y0 * y5))) - (t * ((c * y4) - (a * y5))))
    else if (x <= (-9d-156)) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (x <= 5d+95) then
        tmp = (x * (y * (a * b))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)))
    else
        tmp = j * (x * (y0 * (((i * y1) / y0) - b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -1.55e+74) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (x <= -5.3e-92) {
		tmp = y2 * ((-1.0 * (k * (y0 * y5))) - (t * ((c * y4) - (a * y5))));
	} else if (x <= -9e-156) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (x <= 5e+95) {
		tmp = (x * (y * (a * b))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
	} else {
		tmp = j * (x * (y0 * (((i * y1) / y0) - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -1.55e+74:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif x <= -5.3e-92:
		tmp = y2 * ((-1.0 * (k * (y0 * y5))) - (t * ((c * y4) - (a * y5))))
	elif x <= -9e-156:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif x <= 5e+95:
		tmp = (x * (y * (a * b))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)))
	else:
		tmp = j * (x * (y0 * (((i * y1) / y0) - b)))
	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 (x <= -1.55e+74)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (x <= -5.3e-92)
		tmp = Float64(y2 * Float64(Float64(-1.0 * Float64(k * Float64(y0 * y5))) - Float64(t * Float64(Float64(c * y4) - Float64(a * y5)))));
	elseif (x <= -9e-156)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (x <= 5e+95)
		tmp = Float64(Float64(x * Float64(y * Float64(a * b))) + Float64(Float64(Float64(k * y2) - Float64(j * y3)) * Float64(Float64(y4 * y1) - Float64(y5 * y0))));
	else
		tmp = Float64(j * Float64(x * Float64(y0 * Float64(Float64(Float64(i * y1) / y0) - b))));
	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 (x <= -1.55e+74)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (x <= -5.3e-92)
		tmp = y2 * ((-1.0 * (k * (y0 * y5))) - (t * ((c * y4) - (a * y5))));
	elseif (x <= -9e-156)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (x <= 5e+95)
		tmp = (x * (y * (a * b))) + (((k * y2) - (j * y3)) * ((y4 * y1) - (y5 * y0)));
	else
		tmp = j * (x * (y0 * (((i * y1) / y0) - b)));
	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[x, -1.55e+74], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.3e-92], N[(y2 * N[(N[(-1.0 * N[(k * N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(c * y4), $MachinePrecision] - N[(a * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9e-156], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+95], N[(N[(x * N[(y * N[(a * b), $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], N[(j * N[(x * N[(y0 * N[(N[(N[(i * y1), $MachinePrecision] / y0), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.5500000000000001e74

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

      5. lower-*.f64 26.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

   7. Applied rewrites 26.9%

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

   if -1.5500000000000001e74 < x < -5.3000000000000003e-92

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in y5 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(-1 \cdot \left(k \cdot \left(y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(-1 \cdot \left(k \cdot \left(y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

      3. lower-*.f64 31.6%

         \[\leadsto y2 \cdot \left(-1 \cdot \left(k \cdot \left(y0 \cdot y5\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right) \]

   7. Applied rewrites 31.6%

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

   if -5.3000000000000003e-92 < x < -8.9999999999999997e-156

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   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 27.0%

         \[\leadsto x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right) \]

   7. Applied rewrites 27.0%

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

   if -8.9999999999999997e-156 < x < 5.0000000000000002e95

   1. Initial program 30.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 42.2%

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

   7. Applied rewrites 42.2%

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

   8. Taylor expanded in b around inf

      \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + \color{blue}{-1 \cdot \frac{c \cdot i}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \color{blue}{\frac{c \cdot i}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{\color{blue}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{b}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{b}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 42.5%

         \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + -1 \cdot \frac{c \cdot i}{b}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   10. Applied rewrites 42.5%

       \[\leadsto x \cdot \left(y \cdot \left(b \cdot \left(a + \color{blue}{-1 \cdot \frac{c \cdot i}{b}}\right)\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   11. Taylor expanded in a around inf

       \[\leadsto x \cdot \left(y \cdot \left(a \cdot b\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   12. Step-by-step derivation

       1. lower-*.f64 39.7%

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

   13. Applied rewrites 39.7%

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

   if 5.0000000000000002e95 < x

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

      4. lower-*.f64 27.1%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

   7. Applied rewrites 27.1%

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

   8. Taylor expanded in y0 around inf

      \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - \color{blue}{b}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right) \]

      4. lower-*.f64 29.5%

         \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right) \]

   10. Applied rewrites 29.5%

       \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - \color{blue}{b}\right)\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 14: 36.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-80}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-295}:\\ \;\;\;\;y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+70}:\\ \;\;\;\;\mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2 \cdot k - y3 \cdot j, i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (if (<= x -3.9e+115)
  (* x (* y2 (- (* c y0) (* a y1))))
  (if (<= x -8.2e-80)
    (*
     j
     (fma
      -1.0
      (* y3 (- (* y1 y4) (* y0 y5)))
      (* t (- (* b y4) (* i y5)))))
    (if (<= x 1.4e-295)
      (*
       y0
       (fma
        -1.0
        (* y5 (- (* k y2) (* j y3)))
        (* c (- (* x y2) (* y3 z)))))
      (if (<= x 4.8e+70)
        (fma
         (- (* y4 y1) (* y5 y0))
         (- (* y2 k) (* y3 j))
         (* i (* k (* y y5))))
        (* j (* x (* y0 (- (/ (* i y1) y0) b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -3.9e+115) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (x <= -8.2e-80) {
		tmp = j * fma(-1.0, (y3 * ((y1 * y4) - (y0 * y5))), (t * ((b * y4) - (i * y5))));
	} else if (x <= 1.4e-295) {
		tmp = y0 * fma(-1.0, (y5 * ((k * y2) - (j * y3))), (c * ((x * y2) - (y3 * z))));
	} else if (x <= 4.8e+70) {
		tmp = fma(((y4 * y1) - (y5 * y0)), ((y2 * k) - (y3 * j)), (i * (k * (y * y5))));
	} else {
		tmp = j * (x * (y0 * (((i * y1) / y0) - b)));
	}
	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 (x <= -3.9e+115)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (x <= -8.2e-80)
		tmp = Float64(j * fma(-1.0, Float64(y3 * Float64(Float64(y1 * y4) - Float64(y0 * y5))), Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))));
	elseif (x <= 1.4e-295)
		tmp = Float64(y0 * fma(-1.0, Float64(y5 * Float64(Float64(k * y2) - Float64(j * y3))), Float64(c * Float64(Float64(x * y2) - Float64(y3 * z)))));
	elseif (x <= 4.8e+70)
		tmp = fma(Float64(Float64(y4 * y1) - Float64(y5 * y0)), Float64(Float64(y2 * k) - Float64(y3 * j)), Float64(i * Float64(k * Float64(y * y5))));
	else
		tmp = Float64(j * Float64(x * Float64(y0 * Float64(Float64(Float64(i * y1) / y0) - b))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -3.9e+115], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.2e-80], N[(j * N[(-1.0 * N[(y3 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e-295], N[(y0 * N[(-1.0 * N[(y5 * N[(N[(k * y2), $MachinePrecision] - N[(j * y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+70], N[(N[(N[(y4 * y1), $MachinePrecision] - N[(y5 * y0), $MachinePrecision]), $MachinePrecision] * N[(N[(y2 * k), $MachinePrecision] - N[(y3 * j), $MachinePrecision]), $MachinePrecision] + N[(i * N[(k * N[(y * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(x * N[(y0 * N[(N[(N[(i * y1), $MachinePrecision] / y0), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.9000000000000001e115

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

      5. lower-*.f64 26.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

   7. Applied rewrites 26.9%

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

   if -3.9000000000000001e115 < x < -8.1999999999999999e-80

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}, t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - \color{blue}{y0 \cdot y5}\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot \color{blue}{y5}\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      9. lower-*.f64 33.9%

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

   7. Applied rewrites 33.9%

      \[\leadsto j \cdot \mathsf{fma}\left(-1, \color{blue}{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}, t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

   if -8.1999999999999999e-80 < x < 1.4e-295

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in b around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

      9. lower-*.f64 33.8%

         \[\leadsto y0 \cdot \mathsf{fma}\left(-1, y5 \cdot \left(k \cdot y2 - j \cdot y3\right), c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   7. Applied rewrites 33.8%

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

   if 1.4e-295 < x < 4.7999999999999997e70

   1. Initial program 30.1%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\left(-1 \cdot \left(k \cdot \left(b \cdot y4 - i \cdot y5\right)\right) + x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{fma}\left(-1, k \cdot \left(b \cdot y4 - i \cdot y5\right), x \cdot \left(a \cdot b - c \cdot i\right)\right) - -1 \cdot \left(y3 \cdot \left(c \cdot y4 - a \cdot y5\right)\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   5. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot \color{blue}{x}, k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      4. lower-*.f64 N/A

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

      5. lower-*.f64 38.2%

         \[\leadsto i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]

   7. Applied rewrites 38.2%

      \[\leadsto i \cdot \color{blue}{\left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right)} + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right) \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{i \cdot \left(y \cdot \mathsf{fma}\left(-1, c \cdot x, k \cdot y5\right)\right) + \left(k \cdot y2 - j \cdot y3\right) \cdot \left(y4 \cdot y1 - y5 \cdot y0\right)} \]

   9. Applied rewrites 38.7%

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

   10. Taylor expanded in x around 0

       \[\leadsto \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2 \cdot k - y3 \cdot j, i \cdot \left(k \cdot \color{blue}{\left(y \cdot y5\right)}\right)\right) \]
   11. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2 \cdot k - y3 \cdot j, i \cdot \left(k \cdot \left(y \cdot \color{blue}{y5}\right)\right)\right) \]

       2. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2 \cdot k - y3 \cdot j, i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right) \]

       3. lower-*.f64 36.6%

          \[\leadsto \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2 \cdot k - y3 \cdot j, i \cdot \left(k \cdot \left(y \cdot y5\right)\right)\right) \]

   12. Applied rewrites 36.6%

       \[\leadsto \mathsf{fma}\left(y4 \cdot y1 - y5 \cdot y0, y2 \cdot k - y3 \cdot j, i \cdot \left(k \cdot \color{blue}{\left(y \cdot y5\right)}\right)\right) \]

   if 4.7999999999999997e70 < x

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

      4. lower-*.f64 27.1%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

   7. Applied rewrites 27.1%

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

   8. Taylor expanded in y0 around inf

      \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - \color{blue}{b}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right) \]

      4. lower-*.f64 29.5%

         \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right) \]

   10. Applied rewrites 29.5%

       \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - \color{blue}{b}\right)\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 15: 36.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -7.9 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-87}:\\ \;\;\;\;y0 \cdot \left(-1 \cdot \left(k \cdot \left(z \cdot \left(\frac{y2 \cdot y5}{z} - b\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-156}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-195}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-5}:\\ \;\;\;\;y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(j \cdot \left(\frac{k \cdot y2}{j} - y3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (if (<= x -7.9e+93)
  (* x (* y2 (- (* c y0) (* a y1))))
  (if (<= x -1.15e-87)
    (* y0 (* -1.0 (* k (* z (- (/ (* y2 y5) z) b)))))
    (if (<= x -8e-156)
      (* x (* y0 (- (* c y2) (* b j))))
      (if (<= x -2.3e-195)
        (* y2 (* t (- (* a y5) (* c y4))))
        (if (<= x 4.4e-5)
          (* y0 (* -1.0 (* y5 (* j (- (/ (* k y2) j) y3)))))
          (* j (* x (* y0 (- (/ (* i y1) y0) b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -7.9e+93) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (x <= -1.15e-87) {
		tmp = y0 * (-1.0 * (k * (z * (((y2 * y5) / z) - b))));
	} else if (x <= -8e-156) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (x <= -2.3e-195) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (x <= 4.4e-5) {
		tmp = y0 * (-1.0 * (y5 * (j * (((k * y2) / j) - y3))));
	} else {
		tmp = j * (x * (y0 * (((i * y1) / y0) - b)));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j, k, 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 (x <= (-7.9d+93)) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else if (x <= (-1.15d-87)) then
        tmp = y0 * ((-1.0d0) * (k * (z * (((y2 * y5) / z) - b))))
    else if (x <= (-8d-156)) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (x <= (-2.3d-195)) then
        tmp = y2 * (t * ((a * y5) - (c * y4)))
    else if (x <= 4.4d-5) then
        tmp = y0 * ((-1.0d0) * (y5 * (j * (((k * y2) / j) - y3))))
    else
        tmp = j * (x * (y0 * (((i * y1) / y0) - b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (x <= -7.9e+93) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (x <= -1.15e-87) {
		tmp = y0 * (-1.0 * (k * (z * (((y2 * y5) / z) - b))));
	} else if (x <= -8e-156) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (x <= -2.3e-195) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (x <= 4.4e-5) {
		tmp = y0 * (-1.0 * (y5 * (j * (((k * y2) / j) - y3))));
	} else {
		tmp = j * (x * (y0 * (((i * y1) / y0) - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if x <= -7.9e+93:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	elif x <= -1.15e-87:
		tmp = y0 * (-1.0 * (k * (z * (((y2 * y5) / z) - b))))
	elif x <= -8e-156:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif x <= -2.3e-195:
		tmp = y2 * (t * ((a * y5) - (c * y4)))
	elif x <= 4.4e-5:
		tmp = y0 * (-1.0 * (y5 * (j * (((k * y2) / j) - y3))))
	else:
		tmp = j * (x * (y0 * (((i * y1) / y0) - b)))
	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 (x <= -7.9e+93)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (x <= -1.15e-87)
		tmp = Float64(y0 * Float64(-1.0 * Float64(k * Float64(z * Float64(Float64(Float64(y2 * y5) / z) - b)))));
	elseif (x <= -8e-156)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (x <= -2.3e-195)
		tmp = Float64(y2 * Float64(t * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (x <= 4.4e-5)
		tmp = Float64(y0 * Float64(-1.0 * Float64(y5 * Float64(j * Float64(Float64(Float64(k * y2) / j) - y3)))));
	else
		tmp = Float64(j * Float64(x * Float64(y0 * Float64(Float64(Float64(i * y1) / y0) - b))));
	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 (x <= -7.9e+93)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	elseif (x <= -1.15e-87)
		tmp = y0 * (-1.0 * (k * (z * (((y2 * y5) / z) - b))));
	elseif (x <= -8e-156)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (x <= -2.3e-195)
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	elseif (x <= 4.4e-5)
		tmp = y0 * (-1.0 * (y5 * (j * (((k * y2) / j) - y3))));
	else
		tmp = j * (x * (y0 * (((i * y1) / y0) - b)));
	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[x, -7.9e+93], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.15e-87], N[(y0 * N[(-1.0 * N[(k * N[(z * N[(N[(N[(y2 * y5), $MachinePrecision] / z), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8e-156], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.3e-195], N[(y2 * N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e-5], N[(y0 * N[(-1.0 * N[(y5 * N[(j * N[(N[(N[(k * y2), $MachinePrecision] / j), $MachinePrecision] - y3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(x * N[(y0 * N[(N[(N[(i * y1), $MachinePrecision] / y0), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -7.8999999999999999e93

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

      5. lower-*.f64 26.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

   7. Applied rewrites 26.9%

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

   if -7.8999999999999999e93 < x < -1.1500000000000001e-87

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in k around -inf

      \[\leadsto y0 \cdot \left(-1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(k \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)\right) \]

      5. lower-*.f64 26.9%

         \[\leadsto y0 \cdot \left(-1 \cdot \left(k \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)\right) \]

   7. Applied rewrites 26.9%

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

   8. Taylor expanded in z around inf

      \[\leadsto y0 \cdot \left(-1 \cdot \left(k \cdot \left(z \cdot \left(\frac{y2 \cdot y5}{z} - \color{blue}{b}\right)\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(k \cdot \left(z \cdot \left(\frac{y2 \cdot y5}{z} - b\right)\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(k \cdot \left(z \cdot \left(\frac{y2 \cdot y5}{z} - b\right)\right)\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(k \cdot \left(z \cdot \left(\frac{y2 \cdot y5}{z} - b\right)\right)\right)\right) \]

      4. lower-*.f64 29.4%

         \[\leadsto y0 \cdot \left(-1 \cdot \left(k \cdot \left(z \cdot \left(\frac{y2 \cdot y5}{z} - b\right)\right)\right)\right) \]

   10. Applied rewrites 29.4%

       \[\leadsto y0 \cdot \left(-1 \cdot \left(k \cdot \left(z \cdot \left(\frac{y2 \cdot y5}{z} - \color{blue}{b}\right)\right)\right)\right) \]

   if -1.1500000000000001e-87 < x < -8.0000000000000003e-156

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   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 27.0%

         \[\leadsto x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right) \]

   7. Applied rewrites 27.0%

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

   if -8.0000000000000003e-156 < x < -2.3000000000000002e-195

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\left(a \cdot y5 - c \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \left(a \cdot y5 - \color{blue}{c \cdot y4}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot \color{blue}{y4}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right) \]

      4. lower-*.f64 27.5%

         \[\leadsto y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right) \]

   7. Applied rewrites 27.5%

      \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\left(a \cdot y5 - c \cdot y4\right)}\right) \]

   if -2.3000000000000002e-195 < x < 4.3999999999999999e-5

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - \color{blue}{b \cdot x}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot \color{blue}{x}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

      4. lower-*.f64 26.2%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   8. Taylor expanded in y5 around inf

      \[\leadsto y0 \cdot \left(-1 \cdot \color{blue}{\left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

      5. lower-*.f64 26.7%

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

   10. Applied rewrites 26.7%

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

   11. Taylor expanded in j around inf

       \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(j \cdot \left(\frac{k \cdot y2}{j} - \color{blue}{y3}\right)\right)\right)\right) \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(j \cdot \left(\frac{k \cdot y2}{j} - y3\right)\right)\right)\right) \]

       2. lower--.f64 N/A

          \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(j \cdot \left(\frac{k \cdot y2}{j} - y3\right)\right)\right)\right) \]

       3. lower-/.f64 N/A

          \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(j \cdot \left(\frac{k \cdot y2}{j} - y3\right)\right)\right)\right) \]

       4. lower-*.f64 29.0%

          \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(j \cdot \left(\frac{k \cdot y2}{j} - y3\right)\right)\right)\right) \]

   13. Applied rewrites 29.0%

       \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(j \cdot \left(\frac{k \cdot y2}{j} - \color{blue}{y3}\right)\right)\right)\right) \]

   if 4.3999999999999999e-5 < x

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

      4. lower-*.f64 27.1%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

   7. Applied rewrites 27.1%

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

   8. Taylor expanded in y0 around inf

      \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - \color{blue}{b}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right) \]

      4. lower-*.f64 29.5%

         \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - b\right)\right)\right) \]

   10. Applied rewrites 29.5%

       \[\leadsto j \cdot \left(x \cdot \left(y0 \cdot \left(\frac{i \cdot y1}{y0} - \color{blue}{b}\right)\right)\right) \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 16: 33.2% accurate, 3.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+179}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(k \cdot z - j \cdot x\right)\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(y4 \cdot \mathsf{fma}\left(-1, y1 \cdot y3, b \cdot t\right)\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-151}:\\ \;\;\;\;y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-194}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (if (<= b -2.05e+179)
  (* y0 (* b (- (* k z) (* j x))))
  (if (<= b -4.8e-9)
    (* j (* y4 (fma -1.0 (* y1 y3) (* b t))))
    (if (<= b -1.2e-151)
      (* y0 (* c (- (* x y2) (* y3 z))))
      (if (<= b -1.1e-194)
        (* y2 (* t (- (* a y5) (* c y4))))
        (if (<= b 5.9e+69)
          (* x (* y2 (- (* c y0) (* a y1))))
          (* b (* j (- (* t y4) (* x 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) {
	double tmp;
	if (b <= -2.05e+179) {
		tmp = y0 * (b * ((k * z) - (j * x)));
	} else if (b <= -4.8e-9) {
		tmp = j * (y4 * fma(-1.0, (y1 * y3), (b * t)));
	} else if (b <= -1.2e-151) {
		tmp = y0 * (c * ((x * y2) - (y3 * z)));
	} else if (b <= -1.1e-194) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (b <= 5.9e+69) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	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 (b <= -2.05e+179)
		tmp = Float64(y0 * Float64(b * Float64(Float64(k * z) - Float64(j * x))));
	elseif (b <= -4.8e-9)
		tmp = Float64(j * Float64(y4 * fma(-1.0, Float64(y1 * y3), Float64(b * t))));
	elseif (b <= -1.2e-151)
		tmp = Float64(y0 * Float64(c * Float64(Float64(x * y2) - Float64(y3 * z))));
	elseif (b <= -1.1e-194)
		tmp = Float64(y2 * Float64(t * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (b <= 5.9e+69)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[b, -2.05e+179], N[(y0 * N[(b * N[(N[(k * z), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.8e-9], N[(j * N[(y4 * N[(-1.0 * N[(y1 * y3), $MachinePrecision] + N[(b * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.2e-151], N[(y0 * N[(c * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.1e-194], N[(y2 * N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.9e+69], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.0500000000000001e179

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(b \cdot \left(k \cdot z - j \cdot x\right)\right) \]

      4. lower-*.f64 26.9%

         \[\leadsto y0 \cdot \left(b \cdot \left(k \cdot z - j \cdot x\right)\right) \]

   7. Applied rewrites 26.9%

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

   if -2.0500000000000001e179 < b < -4.8e-9

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + \color{blue}{b \cdot t}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(-1, y1 \cdot \color{blue}{y3}, b \cdot t\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(-1, y1 \cdot y3, b \cdot t\right)\right) \]

      5. lower-*.f64 26.8%

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(-1, y1 \cdot y3, b \cdot t\right)\right) \]

   7. Applied rewrites 26.8%

      \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \mathsf{fma}\left(-1, y1 \cdot y3, b \cdot t\right)\right)} \]

   if -4.8e-9 < b < -1.2e-151

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - \color{blue}{b \cdot x}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot \color{blue}{x}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

      4. lower-*.f64 26.2%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   8. Taylor expanded in y5 around inf

      \[\leadsto y0 \cdot \left(-1 \cdot \color{blue}{\left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

      5. lower-*.f64 26.7%

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

   10. Applied rewrites 26.7%

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

   11. Taylor expanded in c around inf

       \[\leadsto y0 \cdot \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right) \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right)\right) \]

       2. lower--.f64 N/A

          \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

       3. lower-*.f64 N/A

          \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

       4. lower-*.f64 26.2%

          \[\leadsto y0 \cdot \left(c \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   13. Applied rewrites 26.2%

       \[\leadsto y0 \cdot \left(c \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right) \]

   if -1.2e-151 < b < -1.1000000000000001e-194

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\left(a \cdot y5 - c \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \left(a \cdot y5 - \color{blue}{c \cdot y4}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot \color{blue}{y4}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right) \]

      4. lower-*.f64 27.5%

         \[\leadsto y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right) \]

   7. Applied rewrites 27.5%

      \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\left(a \cdot y5 - c \cdot y4\right)}\right) \]

   if -1.1000000000000001e-194 < b < 5.9e69

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

      5. lower-*.f64 26.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

   7. Applied rewrites 26.9%

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

   if 5.9e69 < b

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 17: 33.0% accurate, 3.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;j \leq -1.05 \cdot 10^{+173}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right)\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{+65}:\\ \;\;\;\;j \cdot \left(y4 \cdot \mathsf{fma}\left(-1, y1 \cdot y3, b \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{-214}:\\ \;\;\;\;y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 1.66 \cdot 10^{+78}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y5 \cdot \left(y3 + -1 \cdot \frac{b \cdot x}{y5}\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (if (<= j -1.05e+173)
  (* y0 (* j (- (* y3 y5) (* b x))))
  (if (<= j -2.6e+65)
    (* j (* y4 (fma -1.0 (* y1 y3) (* b t))))
    (if (<= j 1.05e-214)
      (* y2 (* y4 (- (* k y1) (* c t))))
      (if (<= j 1.66e+78)
        (* c (* y0 (- (* x y2) (* y3 z))))
        (* y0 (* j (* y5 (+ y3 (* -1.0 (/ (* b x) 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 (j <= -1.05e+173) {
		tmp = y0 * (j * ((y3 * y5) - (b * x)));
	} else if (j <= -2.6e+65) {
		tmp = j * (y4 * fma(-1.0, (y1 * y3), (b * t)));
	} else if (j <= 1.05e-214) {
		tmp = y2 * (y4 * ((k * y1) - (c * t)));
	} else if (j <= 1.66e+78) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else {
		tmp = y0 * (j * (y5 * (y3 + (-1.0 * ((b * x) / 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 (j <= -1.05e+173)
		tmp = Float64(y0 * Float64(j * Float64(Float64(y3 * y5) - Float64(b * x))));
	elseif (j <= -2.6e+65)
		tmp = Float64(j * Float64(y4 * fma(-1.0, Float64(y1 * y3), Float64(b * t))));
	elseif (j <= 1.05e-214)
		tmp = Float64(y2 * Float64(y4 * Float64(Float64(k * y1) - Float64(c * t))));
	elseif (j <= 1.66e+78)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(y3 * z))));
	else
		tmp = Float64(y0 * Float64(j * Float64(y5 * Float64(y3 + Float64(-1.0 * Float64(Float64(b * x) / 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[j, -1.05e+173], N[(y0 * N[(j * N[(N[(y3 * y5), $MachinePrecision] - N[(b * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.6e+65], N[(j * N[(y4 * N[(-1.0 * N[(y1 * y3), $MachinePrecision] + N[(b * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.05e-214], N[(y2 * N[(y4 * N[(N[(k * y1), $MachinePrecision] - N[(c * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.66e+78], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y0 * N[(j * N[(y5 * N[(y3 + N[(-1.0 * N[(N[(b * x), $MachinePrecision] / y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.05e173

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - \color{blue}{b \cdot x}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot \color{blue}{x}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

      4. lower-*.f64 26.2%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   if -1.05e173 < j < -2.6e65

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \color{blue}{\left(-1 \cdot \left(y1 \cdot y3\right) + b \cdot t\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \left(-1 \cdot \left(y1 \cdot y3\right) + \color{blue}{b \cdot t}\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(-1, y1 \cdot \color{blue}{y3}, b \cdot t\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(-1, y1 \cdot y3, b \cdot t\right)\right) \]

      5. lower-*.f64 26.8%

         \[\leadsto j \cdot \left(y4 \cdot \mathsf{fma}\left(-1, y1 \cdot y3, b \cdot t\right)\right) \]

   7. Applied rewrites 26.8%

      \[\leadsto j \cdot \color{blue}{\left(y4 \cdot \mathsf{fma}\left(-1, y1 \cdot y3, b \cdot t\right)\right)} \]

   if -2.6e65 < j < 1.05e-214

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in y4 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right) \]

      4. lower-*.f64 27.2%

         \[\leadsto y2 \cdot \left(y4 \cdot \left(k \cdot y1 - c \cdot t\right)\right) \]

   7. Applied rewrites 27.2%

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

   if 1.05e-214 < j < 1.66e78

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - \color{blue}{b \cdot x}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot \color{blue}{x}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

      4. lower-*.f64 26.2%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   8. Taylor expanded in y5 around inf

      \[\leadsto y0 \cdot \left(-1 \cdot \color{blue}{\left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

      5. lower-*.f64 26.7%

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

   10. Applied rewrites 26.7%

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

   11. Taylor expanded in c around inf

       \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right) \]

       2. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right)\right) \]

       3. lower--.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

       4. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

       5. lower-*.f64 26.2%

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   13. Applied rewrites 26.2%

       \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if 1.66e78 < j

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - \color{blue}{b \cdot x}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot \color{blue}{x}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

      4. lower-*.f64 26.2%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   8. Taylor expanded in y5 around inf

      \[\leadsto y0 \cdot \left(j \cdot \left(y5 \cdot \left(y3 + \color{blue}{-1 \cdot \frac{b \cdot x}{y5}}\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y5 \cdot \left(y3 + -1 \cdot \frac{b \cdot x}{y5}\right)\right)\right) \]

      4. lower-/.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y5 \cdot \left(y3 + -1 \cdot \frac{b \cdot x}{y5}\right)\right)\right) \]

      5. lower-*.f64 28.3%

         \[\leadsto y0 \cdot \left(j \cdot \left(y5 \cdot \left(y3 + -1 \cdot \frac{b \cdot x}{y5}\right)\right)\right) \]

   10. Applied rewrites 28.3%

       \[\leadsto y0 \cdot \left(j \cdot \left(y5 \cdot \left(y3 + \color{blue}{-1 \cdot \frac{b \cdot x}{y5}}\right)\right)\right) \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 18: 32.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+122}:\\ \;\;\;\;j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (if (<= x -3.9e+115)
  (* x (* y2 (- (* c y0) (* a y1))))
  (if (<= x 1.1e+122)
    (*
     j
     (fma
      -1.0
      (* y3 (- (* y1 y4) (* y0 y5)))
      (* t (- (* b y4) (* i y5)))))
    (* j (* x (- (* i y1) (* b 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) {
	double tmp;
	if (x <= -3.9e+115) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else if (x <= 1.1e+122) {
		tmp = j * fma(-1.0, (y3 * ((y1 * y4) - (y0 * y5))), (t * ((b * y4) - (i * y5))));
	} else {
		tmp = j * (x * ((i * y1) - (b * y0)));
	}
	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 (x <= -3.9e+115)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	elseif (x <= 1.1e+122)
		tmp = Float64(j * fma(-1.0, Float64(y3 * Float64(Float64(y1 * y4) - Float64(y0 * y5))), Float64(t * Float64(Float64(b * y4) - Float64(i * y5)))));
	else
		tmp = Float64(j * Float64(x * Float64(Float64(i * y1) - Float64(b * y0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := If[LessEqual[x, -3.9e+115], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+122], N[(j * N[(-1.0 * N[(y3 * N[(N[(y1 * y4), $MachinePrecision] - N[(y0 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(x * N[(N[(i * y1), $MachinePrecision] - N[(b * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.9000000000000001e115

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

      5. lower-*.f64 26.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

   7. Applied rewrites 26.9%

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

   if -3.9000000000000001e115 < x < 1.1e122

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \color{blue}{\left(y1 \cdot y4 - y0 \cdot y5\right)}, t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - \color{blue}{y0 \cdot y5}\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot \color{blue}{y5}\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      6. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      7. lower--.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      8. lower-*.f64 N/A

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      9. lower-*.f64 33.9%

         \[\leadsto j \cdot \mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

   7. Applied rewrites 33.9%

      \[\leadsto j \cdot \mathsf{fma}\left(-1, \color{blue}{y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)}, t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

   if 1.1e122 < x

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

      4. lower-*.f64 27.1%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

   7. Applied rewrites 27.1%

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 32.0% accurate, 4.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+178}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(k \cdot z - j \cdot x\right)\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-151}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-194}:\\ \;\;\;\;y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (if (<= b -7.8e+178)
  (* y0 (* b (- (* k z) (* j x))))
  (if (<= b -1.2e-151)
    (* c (* y0 (- (* x y2) (* y3 z))))
    (if (<= b -1.1e-194)
      (* y2 (* t (- (* a y5) (* c y4))))
      (if (<= b 5.9e+69)
        (* x (* y2 (- (* c y0) (* a y1))))
        (* b (* j (- (* t y4) (* x 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) {
	double tmp;
	if (b <= -7.8e+178) {
		tmp = y0 * (b * ((k * z) - (j * x)));
	} else if (b <= -1.2e-151) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else if (b <= -1.1e-194) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (b <= 5.9e+69) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	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 (b <= (-7.8d+178)) then
        tmp = y0 * (b * ((k * z) - (j * x)))
    else if (b <= (-1.2d-151)) then
        tmp = c * (y0 * ((x * y2) - (y3 * z)))
    else if (b <= (-1.1d-194)) then
        tmp = y2 * (t * ((a * y5) - (c * y4)))
    else if (b <= 5.9d+69) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else
        tmp = b * (j * ((t * y4) - (x * y0)))
    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 (b <= -7.8e+178) {
		tmp = y0 * (b * ((k * z) - (j * x)));
	} else if (b <= -1.2e-151) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else if (b <= -1.1e-194) {
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	} else if (b <= 5.9e+69) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -7.8e+178:
		tmp = y0 * (b * ((k * z) - (j * x)))
	elif b <= -1.2e-151:
		tmp = c * (y0 * ((x * y2) - (y3 * z)))
	elif b <= -1.1e-194:
		tmp = y2 * (t * ((a * y5) - (c * y4)))
	elif b <= 5.9e+69:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	else:
		tmp = b * (j * ((t * y4) - (x * y0)))
	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 (b <= -7.8e+178)
		tmp = Float64(y0 * Float64(b * Float64(Float64(k * z) - Float64(j * x))));
	elseif (b <= -1.2e-151)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(y3 * z))));
	elseif (b <= -1.1e-194)
		tmp = Float64(y2 * Float64(t * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (b <= 5.9e+69)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	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 (b <= -7.8e+178)
		tmp = y0 * (b * ((k * z) - (j * x)));
	elseif (b <= -1.2e-151)
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	elseif (b <= -1.1e-194)
		tmp = y2 * (t * ((a * y5) - (c * y4)));
	elseif (b <= 5.9e+69)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	else
		tmp = b * (j * ((t * y4) - (x * y0)));
	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[b, -7.8e+178], N[(y0 * N[(b * N[(N[(k * z), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.2e-151], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.1e-194], N[(y2 * N[(t * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.9e+69], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -7.7999999999999995e178

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(b \cdot \left(k \cdot z - j \cdot x\right)\right) \]

      4. lower-*.f64 26.9%

         \[\leadsto y0 \cdot \left(b \cdot \left(k \cdot z - j \cdot x\right)\right) \]

   7. Applied rewrites 26.9%

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

   if -7.7999999999999995e178 < b < -1.2e-151

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - \color{blue}{b \cdot x}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot \color{blue}{x}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

      4. lower-*.f64 26.2%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   8. Taylor expanded in y5 around inf

      \[\leadsto y0 \cdot \left(-1 \cdot \color{blue}{\left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

      5. lower-*.f64 26.7%

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

   10. Applied rewrites 26.7%

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

   11. Taylor expanded in c around inf

       \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right) \]

       2. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right)\right) \]

       3. lower--.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

       4. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

       5. lower-*.f64 26.2%

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   13. Applied rewrites 26.2%

       \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -1.2e-151 < b < -1.1000000000000001e-194

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\left(a \cdot y5 - c \cdot y4\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \left(a \cdot y5 - \color{blue}{c \cdot y4}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot \color{blue}{y4}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right) \]

      4. lower-*.f64 27.5%

         \[\leadsto y2 \cdot \left(t \cdot \left(a \cdot y5 - c \cdot y4\right)\right) \]

   7. Applied rewrites 27.5%

      \[\leadsto y2 \cdot \left(t \cdot \color{blue}{\left(a \cdot y5 - c \cdot y4\right)}\right) \]

   if -1.1000000000000001e-194 < b < 5.9e69

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

      5. lower-*.f64 26.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

   7. Applied rewrites 26.9%

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

   if 5.9e69 < b

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 20: 31.9% accurate, 4.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+178}:\\ \;\;\;\;y0 \cdot \left(b \cdot \left(k \cdot z - j \cdot x\right)\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-151}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-194}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (if (<= b -7.8e+178)
  (* y0 (* b (- (* k z) (* j x))))
  (if (<= b -1.2e-151)
    (* c (* y0 (- (* x y2) (* y3 z))))
    (if (<= b -1.1e-194)
      (* t (* y2 (- (* a y5) (* c y4))))
      (if (<= b 5.9e+69)
        (* x (* y2 (- (* c y0) (* a y1))))
        (* b (* j (- (* t y4) (* x 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) {
	double tmp;
	if (b <= -7.8e+178) {
		tmp = y0 * (b * ((k * z) - (j * x)));
	} else if (b <= -1.2e-151) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else if (b <= -1.1e-194) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (b <= 5.9e+69) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	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 (b <= (-7.8d+178)) then
        tmp = y0 * (b * ((k * z) - (j * x)))
    else if (b <= (-1.2d-151)) then
        tmp = c * (y0 * ((x * y2) - (y3 * z)))
    else if (b <= (-1.1d-194)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (b <= 5.9d+69) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else
        tmp = b * (j * ((t * y4) - (x * y0)))
    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 (b <= -7.8e+178) {
		tmp = y0 * (b * ((k * z) - (j * x)));
	} else if (b <= -1.2e-151) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else if (b <= -1.1e-194) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (b <= 5.9e+69) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -7.8e+178:
		tmp = y0 * (b * ((k * z) - (j * x)))
	elif b <= -1.2e-151:
		tmp = c * (y0 * ((x * y2) - (y3 * z)))
	elif b <= -1.1e-194:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif b <= 5.9e+69:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	else:
		tmp = b * (j * ((t * y4) - (x * y0)))
	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 (b <= -7.8e+178)
		tmp = Float64(y0 * Float64(b * Float64(Float64(k * z) - Float64(j * x))));
	elseif (b <= -1.2e-151)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(y3 * z))));
	elseif (b <= -1.1e-194)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (b <= 5.9e+69)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	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 (b <= -7.8e+178)
		tmp = y0 * (b * ((k * z) - (j * x)));
	elseif (b <= -1.2e-151)
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	elseif (b <= -1.1e-194)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (b <= 5.9e+69)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	else
		tmp = b * (j * ((t * y4) - (x * y0)));
	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[b, -7.8e+178], N[(y0 * N[(b * N[(N[(k * z), $MachinePrecision] - N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.2e-151], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.1e-194], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.9e+69], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -7.7999999999999995e178

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(b \cdot \left(k \cdot z - j \cdot x\right)\right) \]

      4. lower-*.f64 26.9%

         \[\leadsto y0 \cdot \left(b \cdot \left(k \cdot z - j \cdot x\right)\right) \]

   7. Applied rewrites 26.9%

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

   if -7.7999999999999995e178 < b < -1.2e-151

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - \color{blue}{b \cdot x}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot \color{blue}{x}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

      4. lower-*.f64 26.2%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   8. Taylor expanded in y5 around inf

      \[\leadsto y0 \cdot \left(-1 \cdot \color{blue}{\left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

      5. lower-*.f64 26.7%

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

   10. Applied rewrites 26.7%

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

   11. Taylor expanded in c around inf

       \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right) \]

       2. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right)\right) \]

       3. lower--.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

       4. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

       5. lower-*.f64 26.2%

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   13. Applied rewrites 26.2%

       \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -1.2e-151 < b < -1.1000000000000001e-194

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto t \cdot \color{blue}{\left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(a \cdot y5 - c \cdot y4\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y2 \cdot \left(a \cdot y5 - \color{blue}{c \cdot y4}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot \color{blue}{y4}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right) \]

      5. lower-*.f64 27.7%

         \[\leadsto t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right) \]

   7. Applied rewrites 27.7%

      \[\leadsto t \cdot \color{blue}{\left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   if -1.1000000000000001e-194 < b < 5.9e69

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

      5. lower-*.f64 26.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

   7. Applied rewrites 26.9%

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

   if 5.9e69 < b

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 21: 31.6% accurate, 4.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;b \leq -1.22 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-151}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-194}:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;b \leq 5.9 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (if (<= b -1.22e-32)
  (* x (* y0 (- (* c y2) (* b j))))
  (if (<= b -1.2e-151)
    (* c (* y0 (- (* x y2) (* y3 z))))
    (if (<= b -1.1e-194)
      (* t (* y2 (- (* a y5) (* c y4))))
      (if (<= b 5.9e+69)
        (* x (* y2 (- (* c y0) (* a y1))))
        (* b (* j (- (* t y4) (* x 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) {
	double tmp;
	if (b <= -1.22e-32) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (b <= -1.2e-151) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else if (b <= -1.1e-194) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (b <= 5.9e+69) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	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 (b <= (-1.22d-32)) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (b <= (-1.2d-151)) then
        tmp = c * (y0 * ((x * y2) - (y3 * z)))
    else if (b <= (-1.1d-194)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (b <= 5.9d+69) then
        tmp = x * (y2 * ((c * y0) - (a * y1)))
    else
        tmp = b * (j * ((t * y4) - (x * y0)))
    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 (b <= -1.22e-32) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (b <= -1.2e-151) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else if (b <= -1.1e-194) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (b <= 5.9e+69) {
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if b <= -1.22e-32:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif b <= -1.2e-151:
		tmp = c * (y0 * ((x * y2) - (y3 * z)))
	elif b <= -1.1e-194:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif b <= 5.9e+69:
		tmp = x * (y2 * ((c * y0) - (a * y1)))
	else:
		tmp = b * (j * ((t * y4) - (x * y0)))
	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 (b <= -1.22e-32)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (b <= -1.2e-151)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(y3 * z))));
	elseif (b <= -1.1e-194)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (b <= 5.9e+69)
		tmp = Float64(x * Float64(y2 * Float64(Float64(c * y0) - Float64(a * y1))));
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	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 (b <= -1.22e-32)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (b <= -1.2e-151)
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	elseif (b <= -1.1e-194)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (b <= 5.9e+69)
		tmp = x * (y2 * ((c * y0) - (a * y1)));
	else
		tmp = b * (j * ((t * y4) - (x * y0)));
	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[b, -1.22e-32], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.2e-151], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.1e-194], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.9e+69], N[(x * N[(y2 * N[(N[(c * y0), $MachinePrecision] - N[(a * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.22e-32

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   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 27.0%

         \[\leadsto x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right) \]

   7. Applied rewrites 27.0%

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

   if -1.22e-32 < b < -1.2e-151

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - \color{blue}{b \cdot x}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot \color{blue}{x}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

      4. lower-*.f64 26.2%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   8. Taylor expanded in y5 around inf

      \[\leadsto y0 \cdot \left(-1 \cdot \color{blue}{\left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

      5. lower-*.f64 26.7%

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

   10. Applied rewrites 26.7%

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

   11. Taylor expanded in c around inf

       \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right) \]

       2. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right)\right) \]

       3. lower--.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

       4. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

       5. lower-*.f64 26.2%

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   13. Applied rewrites 26.2%

       \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if -1.2e-151 < b < -1.1000000000000001e-194

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto t \cdot \color{blue}{\left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(a \cdot y5 - c \cdot y4\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y2 \cdot \left(a \cdot y5 - \color{blue}{c \cdot y4}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot \color{blue}{y4}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right) \]

      5. lower-*.f64 27.7%

         \[\leadsto t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right) \]

   7. Applied rewrites 27.7%

      \[\leadsto t \cdot \color{blue}{\left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   if -1.1000000000000001e-194 < b < 5.9e69

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

      5. lower-*.f64 26.9%

         \[\leadsto x \cdot \left(y2 \cdot \left(c \cdot y0 - a \cdot y1\right)\right) \]

   7. Applied rewrites 26.9%

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

   if 5.9e69 < b

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 22: 31.6% accurate, 5.0× speedup

Math

\[\begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;j \leq -3.8 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{-214}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+97}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (let* ((t_1 (* b (* j (- (* t y4) (* x y0))))))
  (if (<= j -3.8e+146)
    t_1
    (if (<= j 2.9e-214)
      (* c (* y2 (- (* x y0) (* t y4))))
      (if (<= j 5e+97) (* c (* y0 (- (* x y2) (* y3 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 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (j <= -3.8e+146) {
		tmp = t_1;
	} else if (j <= 2.9e-214) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= 5e+97) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} 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 = b * (j * ((t * y4) - (x * y0)))
    if (j <= (-3.8d+146)) then
        tmp = t_1
    else if (j <= 2.9d-214) then
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    else if (j <= 5d+97) then
        tmp = c * (y0 * ((x * y2) - (y3 * z)))
    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 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (j <= -3.8e+146) {
		tmp = t_1;
	} else if (j <= 2.9e-214) {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	} else if (j <= 5e+97) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} 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 = b * (j * ((t * y4) - (x * y0)))
	tmp = 0
	if j <= -3.8e+146:
		tmp = t_1
	elif j <= 2.9e-214:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	elif j <= 5e+97:
		tmp = c * (y0 * ((x * y2) - (y3 * 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(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (j <= -3.8e+146)
		tmp = t_1;
	elseif (j <= 2.9e-214)
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	elseif (j <= 5e+97)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(y3 * z))));
	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 = b * (j * ((t * y4) - (x * y0)));
	tmp = 0.0;
	if (j <= -3.8e+146)
		tmp = t_1;
	elseif (j <= 2.9e-214)
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	elseif (j <= 5e+97)
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	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[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.8e+146], t$95$1, If[LessEqual[j, 2.9e-214], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5e+97], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.7999999999999998e146 or 5e97 < j

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

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

   if -3.7999999999999998e146 < j < 2.8999999999999999e-214

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in c around inf

      \[\leadsto c \cdot \color{blue}{\left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \color{blue}{\left(x \cdot y0 - t \cdot y4\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \left(x \cdot y0 - \color{blue}{t \cdot y4}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot \color{blue}{y4}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right) \]

   7. Applied rewrites 26.6%

      \[\leadsto c \cdot \color{blue}{\left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]

   if 2.8999999999999999e-214 < j < 5e97

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - \color{blue}{b \cdot x}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot \color{blue}{x}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

      4. lower-*.f64 26.2%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   8. Taylor expanded in y5 around inf

      \[\leadsto y0 \cdot \left(-1 \cdot \color{blue}{\left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

      5. lower-*.f64 26.7%

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

   10. Applied rewrites 26.7%

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

   11. Taylor expanded in c around inf

       \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right) \]

       2. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right)\right) \]

       3. lower--.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

       4. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

       5. lower-*.f64 26.2%

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   13. Applied rewrites 26.2%

       \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 23: 31.5% accurate, 5.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+64}:\\ \;\;\;\;j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-267}:\\ \;\;\;\;x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right)\\ \mathbf{elif}\;t \leq 10^{+135}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (if (<= t -2.6e+64)
  (* j (* t (- (* b y4) (* i y5))))
  (if (<= t 6.4e-267)
    (* x (* y0 (- (* c y2) (* b j))))
    (if (<= t 1e+135)
      (* c (* y0 (- (* x y2) (* y3 z))))
      (* b (* j (- (* t y4) (* x 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) {
	double tmp;
	if (t <= -2.6e+64) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (t <= 6.4e-267) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (t <= 1e+135) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	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 (t <= (-2.6d+64)) then
        tmp = j * (t * ((b * y4) - (i * y5)))
    else if (t <= 6.4d-267) then
        tmp = x * (y0 * ((c * y2) - (b * j)))
    else if (t <= 1d+135) then
        tmp = c * (y0 * ((x * y2) - (y3 * z)))
    else
        tmp = b * (j * ((t * y4) - (x * y0)))
    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 (t <= -2.6e+64) {
		tmp = j * (t * ((b * y4) - (i * y5)));
	} else if (t <= 6.4e-267) {
		tmp = x * (y0 * ((c * y2) - (b * j)));
	} else if (t <= 1e+135) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if t <= -2.6e+64:
		tmp = j * (t * ((b * y4) - (i * y5)))
	elif t <= 6.4e-267:
		tmp = x * (y0 * ((c * y2) - (b * j)))
	elif t <= 1e+135:
		tmp = c * (y0 * ((x * y2) - (y3 * z)))
	else:
		tmp = b * (j * ((t * y4) - (x * y0)))
	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 (t <= -2.6e+64)
		tmp = Float64(j * Float64(t * Float64(Float64(b * y4) - Float64(i * y5))));
	elseif (t <= 6.4e-267)
		tmp = Float64(x * Float64(y0 * Float64(Float64(c * y2) - Float64(b * j))));
	elseif (t <= 1e+135)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(y3 * z))));
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	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 (t <= -2.6e+64)
		tmp = j * (t * ((b * y4) - (i * y5)));
	elseif (t <= 6.4e-267)
		tmp = x * (y0 * ((c * y2) - (b * j)));
	elseif (t <= 1e+135)
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	else
		tmp = b * (j * ((t * y4) - (x * y0)));
	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[t, -2.6e+64], N[(j * N[(t * N[(N[(b * y4), $MachinePrecision] - N[(i * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.4e-267], N[(x * N[(y0 * N[(N[(c * y2), $MachinePrecision] - N[(b * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+135], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.6e64

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \left(t \cdot \color{blue}{\left(b \cdot y4 - i \cdot y5\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto j \cdot \left(t \cdot \left(b \cdot y4 - \color{blue}{i \cdot y5}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot \color{blue}{y5}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

      5. lower-*.f64 26.3%

         \[\leadsto j \cdot \left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) \]

   7. Applied rewrites 26.3%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot \left(b \cdot y4 - i \cdot y5\right)\right)} \]

   if -2.6e64 < t < 6.3999999999999997e-267

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   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 27.0%

         \[\leadsto x \cdot \left(y0 \cdot \left(c \cdot y2 - b \cdot j\right)\right) \]

   7. Applied rewrites 27.0%

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

   if 6.3999999999999997e-267 < t < 9.9999999999999996e134

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - \color{blue}{b \cdot x}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot \color{blue}{x}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

      4. lower-*.f64 26.2%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   8. Taylor expanded in y5 around inf

      \[\leadsto y0 \cdot \left(-1 \cdot \color{blue}{\left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

      5. lower-*.f64 26.7%

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

   10. Applied rewrites 26.7%

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

   11. Taylor expanded in c around inf

       \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right) \]

       2. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right)\right) \]

       3. lower--.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

       4. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

       5. lower-*.f64 26.2%

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   13. Applied rewrites 26.2%

       \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]

   if 9.9999999999999996e134 < t

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 24: 30.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y2 \leq -26000000:\\ \;\;\;\;t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)\\ \mathbf{elif}\;y2 \leq 1.6 \cdot 10^{+45}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (if (<= y2 -26000000.0)
  (* t (* y2 (- (* a y5) (* c y4))))
  (if (<= y2 1.6e+45)
    (* b (* j (- (* t y4) (* x y0))))
    (* c (* y2 (- (* x y0) (* t y4)))))))

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 (y2 <= -26000000.0) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (y2 <= 1.6e+45) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	}
	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 (y2 <= (-26000000.0d0)) then
        tmp = t * (y2 * ((a * y5) - (c * y4)))
    else if (y2 <= 1.6d+45) then
        tmp = b * (j * ((t * y4) - (x * y0)))
    else
        tmp = c * (y2 * ((x * y0) - (t * y4)))
    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 (y2 <= -26000000.0) {
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	} else if (y2 <= 1.6e+45) {
		tmp = b * (j * ((t * y4) - (x * y0)));
	} else {
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y2 <= -26000000.0:
		tmp = t * (y2 * ((a * y5) - (c * y4)))
	elif y2 <= 1.6e+45:
		tmp = b * (j * ((t * y4) - (x * y0)))
	else:
		tmp = c * (y2 * ((x * y0) - (t * y4)))
	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 (y2 <= -26000000.0)
		tmp = Float64(t * Float64(y2 * Float64(Float64(a * y5) - Float64(c * y4))));
	elseif (y2 <= 1.6e+45)
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	else
		tmp = Float64(c * Float64(y2 * Float64(Float64(x * y0) - Float64(t * y4))));
	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 (y2 <= -26000000.0)
		tmp = t * (y2 * ((a * y5) - (c * y4)));
	elseif (y2 <= 1.6e+45)
		tmp = b * (j * ((t * y4) - (x * y0)));
	else
		tmp = c * (y2 * ((x * y0) - (t * y4)));
	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[y2, -26000000.0], N[(t * N[(y2 * N[(N[(a * y5), $MachinePrecision] - N[(c * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y2, 1.6e+45], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(y2 * N[(N[(x * y0), $MachinePrecision] - N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y2 < -2.6e7

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in t around inf

      \[\leadsto t \cdot \color{blue}{\left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y2 \cdot \color{blue}{\left(a \cdot y5 - c \cdot y4\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y2 \cdot \left(a \cdot y5 - \color{blue}{c \cdot y4}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot \color{blue}{y4}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right) \]

      5. lower-*.f64 27.7%

         \[\leadsto t \cdot \left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right) \]

   7. Applied rewrites 27.7%

      \[\leadsto t \cdot \color{blue}{\left(y2 \cdot \left(a \cdot y5 - c \cdot y4\right)\right)} \]

   if -2.6e7 < y2 < 1.6000000000000001e45

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

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

   if 1.6000000000000001e45 < y2

   1. Initial program 30.1%

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

   2. Taylor expanded in y2 around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

   4. Applied rewrites 37.2%

      \[\leadsto \color{blue}{y2 \cdot \left(\mathsf{fma}\left(k, y1 \cdot y4 - y0 \cdot y5, x \cdot \left(c \cdot y0 - a \cdot y1\right)\right) - t \cdot \left(c \cdot y4 - a \cdot y5\right)\right)} \]

   5. Taylor expanded in c around inf

      \[\leadsto c \cdot \color{blue}{\left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \color{blue}{\left(x \cdot y0 - t \cdot y4\right)}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \left(x \cdot y0 - \color{blue}{t \cdot y4}\right)\right) \]

      3. lower--.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot \color{blue}{y4}\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto c \cdot \left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right) \]

   7. Applied rewrites 26.6%

      \[\leadsto c \cdot \color{blue}{\left(y2 \cdot \left(x \cdot y0 - t \cdot y4\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 25: 28.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} t_1 := b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{-246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10^{+135}:\\ \;\;\;\;c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (let* ((t_1 (* b (* j (- (* t y4) (* x y0))))))
  (if (<= t -2.9e-246)
    t_1
    (if (<= t 1e+135) (* c (* y0 (- (* x y2) (* y3 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 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (t <= -2.9e-246) {
		tmp = t_1;
	} else if (t <= 1e+135) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} 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 = b * (j * ((t * y4) - (x * y0)))
    if (t <= (-2.9d-246)) then
        tmp = t_1
    else if (t <= 1d+135) then
        tmp = c * (y0 * ((x * y2) - (y3 * z)))
    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 = b * (j * ((t * y4) - (x * y0)));
	double tmp;
	if (t <= -2.9e-246) {
		tmp = t_1;
	} else if (t <= 1e+135) {
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	} 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 = b * (j * ((t * y4) - (x * y0)))
	tmp = 0
	if t <= -2.9e-246:
		tmp = t_1
	elif t <= 1e+135:
		tmp = c * (y0 * ((x * y2) - (y3 * 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(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))))
	tmp = 0.0
	if (t <= -2.9e-246)
		tmp = t_1;
	elseif (t <= 1e+135)
		tmp = Float64(c * Float64(y0 * Float64(Float64(x * y2) - Float64(y3 * z))));
	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 = b * (j * ((t * y4) - (x * y0)));
	tmp = 0.0;
	if (t <= -2.9e-246)
		tmp = t_1;
	elseif (t <= 1e+135)
		tmp = c * (y0 * ((x * y2) - (y3 * z)));
	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[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e-246], t$95$1, If[LessEqual[t, 1e+135], N[(c * N[(y0 * N[(N[(x * y2), $MachinePrecision] - N[(y3 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9e-246 or 9.9999999999999996e134 < t

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

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

   if -2.9e-246 < t < 9.9999999999999996e134

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - \color{blue}{b \cdot x}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot \color{blue}{x}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

      4. lower-*.f64 26.2%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   8. Taylor expanded in y5 around inf

      \[\leadsto y0 \cdot \left(-1 \cdot \color{blue}{\left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)}\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

      5. lower-*.f64 26.7%

         \[\leadsto y0 \cdot \left(-1 \cdot \left(y5 \cdot \left(k \cdot y2 - j \cdot y3\right)\right)\right) \]

   10. Applied rewrites 26.7%

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

   11. Taylor expanded in c around inf

       \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \color{blue}{\left(x \cdot y2 - y3 \cdot z\right)}\right) \]

       2. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - \color{blue}{y3 \cdot z}\right)\right) \]

       3. lower--.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot \color{blue}{z}\right)\right) \]

       4. lower-*.f64 N/A

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

       5. lower-*.f64 26.2%

          \[\leadsto c \cdot \left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right) \]

   13. Applied rewrites 26.2%

       \[\leadsto c \cdot \color{blue}{\left(y0 \cdot \left(x \cdot y2 - y3 \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 26: 28.2% accurate, 7.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;i \leq -3.15 \cdot 10^{+91}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (if (<= i -3.15e+91)
  (* j (* x (* i y1)))
  (* b (* j (- (* t y4) (* x 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) {
	double tmp;
	if (i <= -3.15e+91) {
		tmp = j * (x * (i * y1));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	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 (i <= (-3.15d+91)) then
        tmp = j * (x * (i * y1))
    else
        tmp = b * (j * ((t * y4) - (x * y0)))
    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 (i <= -3.15e+91) {
		tmp = j * (x * (i * y1));
	} else {
		tmp = b * (j * ((t * y4) - (x * y0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if i <= -3.15e+91:
		tmp = j * (x * (i * y1))
	else:
		tmp = b * (j * ((t * y4) - (x * y0)))
	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 <= -3.15e+91)
		tmp = Float64(j * Float64(x * Float64(i * y1)));
	else
		tmp = Float64(b * Float64(j * Float64(Float64(t * y4) - Float64(x * y0))));
	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 (i <= -3.15e+91)
		tmp = j * (x * (i * y1));
	else
		tmp = b * (j * ((t * y4) - (x * y0)));
	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[i, -3.15e+91], N[(j * N[(x * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(j * N[(N[(t * y4), $MachinePrecision] - N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -3.1499999999999999e91

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

      4. lower-*.f64 27.1%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

   7. Applied rewrites 27.1%

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

   8. Taylor expanded in b around 0

      \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 17.8%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1\right)\right) \]

   10. Applied rewrites 17.8%

       \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1\right)\right) \]

   if -3.1499999999999999e91 < i

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 27: 22.8% accurate, 5.5× speedup

Math

\[\begin{array}{l} t_1 := \left(b \cdot \left(y4 \cdot t\right)\right) \cdot j\\ \mathbf{if}\;y4 \leq -1.7 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 2.9 \cdot 10^{-239}:\\ \;\;\;\;y0 \cdot \left(-1 \cdot \left(b \cdot \left(j \cdot x\right)\right)\right)\\ \mathbf{elif}\;y4 \leq 6.5 \cdot 10^{+110}:\\ \;\;\;\;y0 \cdot \left(-1 \cdot \left(k \cdot \left(y2 \cdot y5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (let* ((t_1 (* (* b (* y4 t)) j)))
  (if (<= y4 -1.7e+39)
    t_1
    (if (<= y4 2.9e-239)
      (* y0 (* -1.0 (* b (* j x))))
      (if (<= y4 6.5e+110) (* y0 (* -1.0 (* k (* 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 = (b * (y4 * t)) * j;
	double tmp;
	if (y4 <= -1.7e+39) {
		tmp = t_1;
	} else if (y4 <= 2.9e-239) {
		tmp = y0 * (-1.0 * (b * (j * x)));
	} else if (y4 <= 6.5e+110) {
		tmp = y0 * (-1.0 * (k * (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 = (b * (y4 * t)) * j
    if (y4 <= (-1.7d+39)) then
        tmp = t_1
    else if (y4 <= 2.9d-239) then
        tmp = y0 * ((-1.0d0) * (b * (j * x)))
    else if (y4 <= 6.5d+110) then
        tmp = y0 * ((-1.0d0) * (k * (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 = (b * (y4 * t)) * j;
	double tmp;
	if (y4 <= -1.7e+39) {
		tmp = t_1;
	} else if (y4 <= 2.9e-239) {
		tmp = y0 * (-1.0 * (b * (j * x)));
	} else if (y4 <= 6.5e+110) {
		tmp = y0 * (-1.0 * (k * (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 = (b * (y4 * t)) * j
	tmp = 0
	if y4 <= -1.7e+39:
		tmp = t_1
	elif y4 <= 2.9e-239:
		tmp = y0 * (-1.0 * (b * (j * x)))
	elif y4 <= 6.5e+110:
		tmp = y0 * (-1.0 * (k * (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(Float64(b * Float64(y4 * t)) * j)
	tmp = 0.0
	if (y4 <= -1.7e+39)
		tmp = t_1;
	elseif (y4 <= 2.9e-239)
		tmp = Float64(y0 * Float64(-1.0 * Float64(b * Float64(j * x))));
	elseif (y4 <= 6.5e+110)
		tmp = Float64(y0 * Float64(-1.0 * Float64(k * 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 = (b * (y4 * t)) * j;
	tmp = 0.0;
	if (y4 <= -1.7e+39)
		tmp = t_1;
	elseif (y4 <= 2.9e-239)
		tmp = y0 * (-1.0 * (b * (j * x)));
	elseif (y4 <= 6.5e+110)
		tmp = y0 * (-1.0 * (k * (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[(N[(b * N[(y4 * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]}, If[LessEqual[y4, -1.7e+39], t$95$1, If[LessEqual[y4, 2.9e-239], N[(y0 * N[(-1.0 * N[(b * N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y4, 6.5e+110], N[(y0 * N[(-1.0 * N[(k * N[(y2 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y4 < -1.6999999999999999e39 or 6.4999999999999997e110 < y4

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 17.5%

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

   10. Applied rewrites 17.5%

       \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. *-commutative N/A

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

       4. associate-*r* N/A

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

       5. lower-*.f64 N/A

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

       6. lower-*.f64 17.1%

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

       7. lift-*.f64 N/A

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

       8. *-commutative N/A

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

       9. lower-*.f64 17.1%

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

   12. Applied rewrites 17.1%

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

   if -1.6999999999999999e39 < y4 < 2.9000000000000002e-239

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - \color{blue}{b \cdot x}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot \color{blue}{x}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

      4. lower-*.f64 26.2%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto y0 \cdot \left(-1 \cdot \left(b \cdot \color{blue}{\left(j \cdot x\right)}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(b \cdot \left(j \cdot \color{blue}{x}\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(b \cdot \left(j \cdot x\right)\right)\right) \]

      3. lower-*.f64 17.2%

         \[\leadsto y0 \cdot \left(-1 \cdot \left(b \cdot \left(j \cdot x\right)\right)\right) \]

   10. Applied rewrites 17.2%

       \[\leadsto y0 \cdot \left(-1 \cdot \left(b \cdot \color{blue}{\left(j \cdot x\right)}\right)\right) \]

   if 2.9000000000000002e-239 < y4 < 6.4999999999999997e110

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in k around -inf

      \[\leadsto y0 \cdot \left(-1 \cdot \color{blue}{\left(k \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(k \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)\right) \]

      5. lower-*.f64 26.9%

         \[\leadsto y0 \cdot \left(-1 \cdot \left(k \cdot \left(y2 \cdot y5 - b \cdot z\right)\right)\right) \]

   7. Applied rewrites 26.9%

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

   8. Taylor expanded in z around 0

      \[\leadsto y0 \cdot \left(-1 \cdot \left(k \cdot \left(y2 \cdot y5\right)\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 17.4%

         \[\leadsto y0 \cdot \left(-1 \cdot \left(k \cdot \left(y2 \cdot y5\right)\right)\right) \]

   10. Applied rewrites 17.4%

       \[\leadsto y0 \cdot \left(-1 \cdot \left(k \cdot \left(y2 \cdot y5\right)\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 28: 22.5% accurate, 6.6× speedup

Math

\[\begin{array}{l} t_1 := \left(b \cdot \left(y4 \cdot t\right)\right) \cdot j\\ \mathbf{if}\;y4 \leq -1.7 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y4 \leq 3.4 \cdot 10^{+132}:\\ \;\;\;\;y0 \cdot \left(-1 \cdot \left(b \cdot \left(j \cdot x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (let* ((t_1 (* (* b (* y4 t)) j)))
  (if (<= y4 -1.7e+39)
    t_1
    (if (<= y4 3.4e+132) (* y0 (* -1.0 (* b (* j x)))) 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 = (b * (y4 * t)) * j;
	double tmp;
	if (y4 <= -1.7e+39) {
		tmp = t_1;
	} else if (y4 <= 3.4e+132) {
		tmp = y0 * (-1.0 * (b * (j * x)));
	} 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 = (b * (y4 * t)) * j
    if (y4 <= (-1.7d+39)) then
        tmp = t_1
    else if (y4 <= 3.4d+132) then
        tmp = y0 * ((-1.0d0) * (b * (j * x)))
    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 = (b * (y4 * t)) * j;
	double tmp;
	if (y4 <= -1.7e+39) {
		tmp = t_1;
	} else if (y4 <= 3.4e+132) {
		tmp = y0 * (-1.0 * (b * (j * x)));
	} 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 = (b * (y4 * t)) * j
	tmp = 0
	if y4 <= -1.7e+39:
		tmp = t_1
	elif y4 <= 3.4e+132:
		tmp = y0 * (-1.0 * (b * (j * x)))
	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(Float64(b * Float64(y4 * t)) * j)
	tmp = 0.0
	if (y4 <= -1.7e+39)
		tmp = t_1;
	elseif (y4 <= 3.4e+132)
		tmp = Float64(y0 * Float64(-1.0 * Float64(b * Float64(j * x))));
	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 = (b * (y4 * t)) * j;
	tmp = 0.0;
	if (y4 <= -1.7e+39)
		tmp = t_1;
	elseif (y4 <= 3.4e+132)
		tmp = y0 * (-1.0 * (b * (j * x)));
	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[(N[(b * N[(y4 * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]}, If[LessEqual[y4, -1.7e+39], t$95$1, If[LessEqual[y4, 3.4e+132], N[(y0 * N[(-1.0 * N[(b * N[(j * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y4 < -1.6999999999999999e39 or 3.4000000000000003e132 < y4

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 17.5%

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

   10. Applied rewrites 17.5%

       \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. *-commutative N/A

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

       4. associate-*r* N/A

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

       5. lower-*.f64 N/A

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

       6. lower-*.f64 17.1%

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

       7. lift-*.f64 N/A

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

       8. *-commutative N/A

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

       9. lower-*.f64 17.1%

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

   12. Applied rewrites 17.1%

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

   if -1.6999999999999999e39 < y4 < 3.4000000000000003e132

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - \color{blue}{b \cdot x}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot \color{blue}{x}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

      4. lower-*.f64 26.2%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto y0 \cdot \left(-1 \cdot \left(b \cdot \color{blue}{\left(j \cdot x\right)}\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(b \cdot \left(j \cdot \color{blue}{x}\right)\right)\right) \]

      2. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(-1 \cdot \left(b \cdot \left(j \cdot x\right)\right)\right) \]

      3. lower-*.f64 17.2%

         \[\leadsto y0 \cdot \left(-1 \cdot \left(b \cdot \left(j \cdot x\right)\right)\right) \]

   10. Applied rewrites 17.2%

       \[\leadsto y0 \cdot \left(-1 \cdot \left(b \cdot \color{blue}{\left(j \cdot x\right)}\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 29: 22.5% accurate, 6.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+64}:\\ \;\;\;\;\left(j \cdot b\right) \cdot \left(y4 \cdot t\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+172}:\\ \;\;\;\;b \cdot \left(j \cdot \left(-1 \cdot \left(x \cdot y0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot \left(y4 \cdot t\right)\right) \cdot j\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (if (<= t -4.7e+64)
  (* (* j b) (* y4 t))
  (if (<= t 4.8e+172)
    (* b (* j (* -1.0 (* x y0))))
    (* (* b (* y4 t)) j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -4.7e+64) {
		tmp = (j * b) * (y4 * t);
	} else if (t <= 4.8e+172) {
		tmp = b * (j * (-1.0 * (x * y0)));
	} else {
		tmp = (b * (y4 * t)) * j;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j, k, 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 (t <= (-4.7d+64)) then
        tmp = (j * b) * (y4 * t)
    else if (t <= 4.8d+172) then
        tmp = b * (j * ((-1.0d0) * (x * y0)))
    else
        tmp = (b * (y4 * t)) * j
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k, double y0, double y1, double y2, double y3, double y4, double y5) {
	double tmp;
	if (t <= -4.7e+64) {
		tmp = (j * b) * (y4 * t);
	} else if (t <= 4.8e+172) {
		tmp = b * (j * (-1.0 * (x * y0)));
	} else {
		tmp = (b * (y4 * t)) * j;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if t <= -4.7e+64:
		tmp = (j * b) * (y4 * t)
	elif t <= 4.8e+172:
		tmp = b * (j * (-1.0 * (x * y0)))
	else:
		tmp = (b * (y4 * t)) * j
	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 (t <= -4.7e+64)
		tmp = Float64(Float64(j * b) * Float64(y4 * t));
	elseif (t <= 4.8e+172)
		tmp = Float64(b * Float64(j * Float64(-1.0 * Float64(x * y0))));
	else
		tmp = Float64(Float64(b * Float64(y4 * t)) * j);
	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 (t <= -4.7e+64)
		tmp = (j * b) * (y4 * t);
	elseif (t <= 4.8e+172)
		tmp = b * (j * (-1.0 * (x * y0)));
	else
		tmp = (b * (y4 * t)) * j;
	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[t, -4.7e+64], N[(N[(j * b), $MachinePrecision] * N[(y4 * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+172], N[(b * N[(j * N[(-1.0 * N[(x * y0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(y4 * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.7000000000000003e64

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 17.5%

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

   10. Applied rewrites 17.5%

       \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-*r* N/A

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

       4. lower-*.f64 N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 17.0%

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

       7. lift-*.f64 N/A

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

       8. *-commutative N/A

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

       9. lower-*.f64 17.0%

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

   12. Applied rewrites 17.0%

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

   if -4.7000000000000003e64 < t < 4.8000000000000001e172

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 17.5%

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

   10. Applied rewrites 17.5%

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

   11. Taylor expanded in x around inf

       \[\leadsto b \cdot \left(j \cdot \left(-1 \cdot \left(x \cdot \color{blue}{y0}\right)\right)\right) \]
   12. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto b \cdot \left(j \cdot \left(-1 \cdot \left(x \cdot y0\right)\right)\right) \]

       2. lower-*.f64 16.9%

          \[\leadsto b \cdot \left(j \cdot \left(-1 \cdot \left(x \cdot y0\right)\right)\right) \]

   13. Applied rewrites 16.9%

       \[\leadsto b \cdot \left(j \cdot \left(-1 \cdot \left(x \cdot \color{blue}{y0}\right)\right)\right) \]

   if 4.8000000000000001e172 < t

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 17.5%

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

   10. Applied rewrites 17.5%

       \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. *-commutative N/A

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

       4. associate-*r* N/A

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

       5. lower-*.f64 N/A

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

       6. lower-*.f64 17.1%

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

       7. lift-*.f64 N/A

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

       8. *-commutative N/A

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

       9. lower-*.f64 17.1%

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

   12. Applied rewrites 17.1%

       \[\leadsto \left(b \cdot \left(y4 \cdot t\right)\right) \cdot j \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 30: 22.4% accurate, 6.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y1 \leq -31000000000000:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq -2.4 \cdot 10^{-289}:\\ \;\;\;\;y0 \cdot \left(j \cdot \left(y3 \cdot y5\right)\right)\\ \mathbf{elif}\;y1 \leq 3.7 \cdot 10^{+105}:\\ \;\;\;\;\left(j \cdot b\right) \cdot \left(y4 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (if (<= y1 -31000000000000.0)
  (* j (* i (* x y1)))
  (if (<= y1 -2.4e-289)
    (* y0 (* j (* y3 y5)))
    (if (<= y1 3.7e+105) (* (* j b) (* y4 t)) (* j (* x (* i 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 tmp;
	if (y1 <= -31000000000000.0) {
		tmp = j * (i * (x * y1));
	} else if (y1 <= -2.4e-289) {
		tmp = y0 * (j * (y3 * y5));
	} else if (y1 <= 3.7e+105) {
		tmp = (j * b) * (y4 * t);
	} else {
		tmp = j * (x * (i * y1));
	}
	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 (y1 <= (-31000000000000.0d0)) then
        tmp = j * (i * (x * y1))
    else if (y1 <= (-2.4d-289)) then
        tmp = y0 * (j * (y3 * y5))
    else if (y1 <= 3.7d+105) then
        tmp = (j * b) * (y4 * t)
    else
        tmp = j * (x * (i * y1))
    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 (y1 <= -31000000000000.0) {
		tmp = j * (i * (x * y1));
	} else if (y1 <= -2.4e-289) {
		tmp = y0 * (j * (y3 * y5));
	} else if (y1 <= 3.7e+105) {
		tmp = (j * b) * (y4 * t);
	} else {
		tmp = j * (x * (i * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -31000000000000.0:
		tmp = j * (i * (x * y1))
	elif y1 <= -2.4e-289:
		tmp = y0 * (j * (y3 * y5))
	elif y1 <= 3.7e+105:
		tmp = (j * b) * (y4 * t)
	else:
		tmp = j * (x * (i * y1))
	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 <= -31000000000000.0)
		tmp = Float64(j * Float64(i * Float64(x * y1)));
	elseif (y1 <= -2.4e-289)
		tmp = Float64(y0 * Float64(j * Float64(y3 * y5)));
	elseif (y1 <= 3.7e+105)
		tmp = Float64(Float64(j * b) * Float64(y4 * t));
	else
		tmp = Float64(j * Float64(x * Float64(i * y1)));
	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 (y1 <= -31000000000000.0)
		tmp = j * (i * (x * y1));
	elseif (y1 <= -2.4e-289)
		tmp = y0 * (j * (y3 * y5));
	elseif (y1 <= 3.7e+105)
		tmp = (j * b) * (y4 * t);
	else
		tmp = j * (x * (i * y1));
	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[y1, -31000000000000.0], N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, -2.4e-289], N[(y0 * N[(j * N[(y3 * y5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 3.7e+105], N[(N[(j * b), $MachinePrecision] * N[(y4 * t), $MachinePrecision]), $MachinePrecision], N[(j * N[(x * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y1 < -3.1e13

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

      4. lower-*.f64 27.1%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

   7. Applied rewrites 27.1%

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

   8. Taylor expanded in b around 0

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

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \left(i \cdot \left(x \cdot y1\right)\right) \]

      2. lower-*.f64 17.5%

         \[\leadsto j \cdot \left(i \cdot \left(x \cdot y1\right)\right) \]

   10. Applied rewrites 17.5%

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

   if -3.1e13 < y1 < -2.3999999999999999e-289

   1. Initial program 30.1%

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

   2. Taylor expanded in 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 36.0%

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

   5. Taylor expanded in j around inf

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - \color{blue}{b \cdot x}\right)\right) \]

      2. lower--.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot \color{blue}{x}\right)\right) \]

      3. lower-*.f64 N/A

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

      4. lower-*.f64 26.2%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5 - b \cdot x\right)\right) \]

   7. Applied rewrites 26.2%

      \[\leadsto y0 \cdot \left(j \cdot \color{blue}{\left(y3 \cdot y5 - b \cdot x\right)}\right) \]

   8. Taylor expanded in x around 0

      \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 16.7%

         \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5\right)\right) \]

   10. Applied rewrites 16.7%

       \[\leadsto y0 \cdot \left(j \cdot \left(y3 \cdot y5\right)\right) \]

   if -2.3999999999999999e-289 < y1 < 3.6999999999999998e105

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 17.5%

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

   10. Applied rewrites 17.5%

       \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-*r* N/A

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

       4. lower-*.f64 N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 17.0%

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

       7. lift-*.f64 N/A

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

       8. *-commutative N/A

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

       9. lower-*.f64 17.0%

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

   12. Applied rewrites 17.0%

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

   if 3.6999999999999998e105 < y1

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

      4. lower-*.f64 27.1%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

   7. Applied rewrites 27.1%

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

   8. Taylor expanded in b around 0

      \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 17.8%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1\right)\right) \]

   10. Applied rewrites 17.8%

       \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1\right)\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 31: 22.2% accurate, 7.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y1 \leq -1.6 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{elif}\;y1 \leq 10^{-27}:\\ \;\;\;\;\left(b \cdot \left(y4 \cdot t\right)\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(x \cdot \left(i \cdot y1\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (if (<= y1 -1.6e+17)
  (* j (* i (* x y1)))
  (if (<= y1 1e-27) (* (* b (* y4 t)) j) (* j (* x (* i 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 tmp;
	if (y1 <= -1.6e+17) {
		tmp = j * (i * (x * y1));
	} else if (y1 <= 1e-27) {
		tmp = (b * (y4 * t)) * j;
	} else {
		tmp = j * (x * (i * y1));
	}
	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 (y1 <= (-1.6d+17)) then
        tmp = j * (i * (x * y1))
    else if (y1 <= 1d-27) then
        tmp = (b * (y4 * t)) * j
    else
        tmp = j * (x * (i * y1))
    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 (y1 <= -1.6e+17) {
		tmp = j * (i * (x * y1));
	} else if (y1 <= 1e-27) {
		tmp = (b * (y4 * t)) * j;
	} else {
		tmp = j * (x * (i * y1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j, k, y0, y1, y2, y3, y4, y5):
	tmp = 0
	if y1 <= -1.6e+17:
		tmp = j * (i * (x * y1))
	elif y1 <= 1e-27:
		tmp = (b * (y4 * t)) * j
	else:
		tmp = j * (x * (i * y1))
	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 <= -1.6e+17)
		tmp = Float64(j * Float64(i * Float64(x * y1)));
	elseif (y1 <= 1e-27)
		tmp = Float64(Float64(b * Float64(y4 * t)) * j);
	else
		tmp = Float64(j * Float64(x * Float64(i * y1)));
	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 (y1 <= -1.6e+17)
		tmp = j * (i * (x * y1));
	elseif (y1 <= 1e-27)
		tmp = (b * (y4 * t)) * j;
	else
		tmp = j * (x * (i * y1));
	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[y1, -1.6e+17], N[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y1, 1e-27], N[(N[(b * N[(y4 * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], N[(j * N[(x * N[(i * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y1 < -1.6e17

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

      4. lower-*.f64 27.1%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

   7. Applied rewrites 27.1%

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

   8. Taylor expanded in b around 0

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

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \left(i \cdot \left(x \cdot y1\right)\right) \]

      2. lower-*.f64 17.5%

         \[\leadsto j \cdot \left(i \cdot \left(x \cdot y1\right)\right) \]

   10. Applied rewrites 17.5%

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

   if -1.6e17 < y1 < 1e-27

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 17.5%

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

   10. Applied rewrites 17.5%

       \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. *-commutative N/A

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

       4. associate-*r* N/A

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

       5. lower-*.f64 N/A

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

       6. lower-*.f64 17.1%

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

       7. lift-*.f64 N/A

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

       8. *-commutative N/A

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

       9. lower-*.f64 17.1%

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

   12. Applied rewrites 17.1%

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

   if 1e-27 < y1

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

      4. lower-*.f64 27.1%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

   7. Applied rewrites 27.1%

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

   8. Taylor expanded in b around 0

      \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 17.8%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1\right)\right) \]

   10. Applied rewrites 17.8%

       \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 32: 21.1% accurate, 7.7× speedup

Math

\[\begin{array}{l} t_1 := j \cdot \left(i \cdot \left(x \cdot y1\right)\right)\\ \mathbf{if}\;y1 \leq -1.6 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y1 \leq 10^{-27}:\\ \;\;\;\;\left(b \cdot \left(y4 \cdot t\right)\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k y0 y1 y2 y3 y4 y5)
  :precision binary64
  (let* ((t_1 (* j (* i (* x y1)))))
  (if (<= y1 -1.6e+17)
    t_1
    (if (<= y1 1e-27) (* (* b (* y4 t)) j) 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 * (i * (x * y1));
	double tmp;
	if (y1 <= -1.6e+17) {
		tmp = t_1;
	} else if (y1 <= 1e-27) {
		tmp = (b * (y4 * t)) * j;
	} 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 = j * (i * (x * y1))
    if (y1 <= (-1.6d+17)) then
        tmp = t_1
    else if (y1 <= 1d-27) then
        tmp = (b * (y4 * t)) * j
    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 = j * (i * (x * y1));
	double tmp;
	if (y1 <= -1.6e+17) {
		tmp = t_1;
	} else if (y1 <= 1e-27) {
		tmp = (b * (y4 * t)) * j;
	} 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 = j * (i * (x * y1))
	tmp = 0
	if y1 <= -1.6e+17:
		tmp = t_1
	elif y1 <= 1e-27:
		tmp = (b * (y4 * t)) * j
	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(j * Float64(i * Float64(x * y1)))
	tmp = 0.0
	if (y1 <= -1.6e+17)
		tmp = t_1;
	elseif (y1 <= 1e-27)
		tmp = Float64(Float64(b * Float64(y4 * t)) * j);
	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 = j * (i * (x * y1));
	tmp = 0.0;
	if (y1 <= -1.6e+17)
		tmp = t_1;
	elseif (y1 <= 1e-27)
		tmp = (b * (y4 * t)) * j;
	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[(j * N[(i * N[(x * y1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y1, -1.6e+17], t$95$1, If[LessEqual[y1, 1e-27], N[(N[(b * N[(y4 * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y1 < -1.6e17 or 1e-27 < y1

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto j \cdot \left(x \cdot \color{blue}{\left(i \cdot y1 - b \cdot y0\right)}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

      4. lower-*.f64 27.1%

         \[\leadsto j \cdot \left(x \cdot \left(i \cdot y1 - b \cdot y0\right)\right) \]

   7. Applied rewrites 27.1%

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

   8. Taylor expanded in b around 0

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

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \left(i \cdot \left(x \cdot y1\right)\right) \]

      2. lower-*.f64 17.5%

         \[\leadsto j \cdot \left(i \cdot \left(x \cdot y1\right)\right) \]

   10. Applied rewrites 17.5%

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

   if -1.6e17 < y1 < 1e-27

   1. Initial program 30.1%

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

   2. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

      2. lower--.f64 N/A

         \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

   4. Applied rewrites 36.2%

      \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

      5. lower-*.f64 26.6%

         \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   7. Applied rewrites 26.6%

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

   8. Taylor expanded in x around 0

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   9. Step-by-step derivation

      1. lower-*.f64 17.5%

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

   10. Applied rewrites 17.5%

       \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
   11. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. *-commutative N/A

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

       4. associate-*r* N/A

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

       5. lower-*.f64 N/A

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

       6. lower-*.f64 17.1%

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

       7. lift-*.f64 N/A

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

       8. *-commutative N/A

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

       9. lower-*.f64 17.1%

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

   12. Applied rewrites 17.1%

       \[\leadsto \left(b \cdot \left(y4 \cdot t\right)\right) \cdot j \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 33: 17.5% accurate, 13.5× speedup

Math

\[\left(b \cdot \left(y4 \cdot t\right)\right) \cdot j \]

FPCore

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

C

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

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 = (b * (y4 * t)) * j
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 (b * (y4 * t)) * j;
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(N[(b * N[(y4 * t), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]

Derivation

1. Initial program 30.1%

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

2. Taylor expanded in j around inf

   \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   2. lower--.f64 N/A

      \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

4. Applied rewrites 36.2%

   \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

5. Taylor expanded in b around inf

   \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
6. Step-by-step derivation

   1. lower-*.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

   4. lower-*.f64 N/A

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   5. lower-*.f64 26.6%

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

7. Applied rewrites 26.6%

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

8. Taylor expanded in x around 0

   \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
9. Step-by-step derivation

   1. lower-*.f64 17.5%

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

10. Applied rewrites 17.5%

    \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
11. Step-by-step derivation

    1. lift-*.f64 N/A

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

    2. lift-*.f64 N/A

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

    3. *-commutative N/A

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

    4. associate-*r* N/A

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

    5. lower-*.f64 N/A

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

    6. lower-*.f64 17.1%

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

    7. lift-*.f64 N/A

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

    8. *-commutative N/A

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

    9. lower-*.f64 17.1%

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

12. Applied rewrites 17.1%

    \[\leadsto \left(b \cdot \left(y4 \cdot t\right)\right) \cdot j \]
13. Add Preprocessing

Alternative 34: 17.1% accurate, 13.5× speedup

Math

\[b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]

FPCore

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

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 b * (j * (t * y4));
}

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 = b * (j * (t * y4))
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 b * (j * (t * y4));
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_, y0_, y1_, y2_, y3_, y4_, y5_] := N[(b * N[(j * N[(t * y4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 30.1%

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

2. Taylor expanded in j around inf

   \[\leadsto \color{blue}{j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto j \cdot \color{blue}{\left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

   2. lower--.f64 N/A

      \[\leadsto j \cdot \left(\left(-1 \cdot \left(y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right)\right) + t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - \color{blue}{x \cdot \left(b \cdot y0 - i \cdot y1\right)}\right) \]

4. Applied rewrites 36.2%

   \[\leadsto \color{blue}{j \cdot \left(\mathsf{fma}\left(-1, y3 \cdot \left(y1 \cdot y4 - y0 \cdot y5\right), t \cdot \left(b \cdot y4 - i \cdot y5\right)\right) - x \cdot \left(b \cdot y0 - i \cdot y1\right)\right)} \]

5. Taylor expanded in b around inf

   \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]
6. Step-by-step derivation

   1. lower-*.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot \color{blue}{y0}\right)\right) \]

   4. lower-*.f64 N/A

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

   5. lower-*.f64 26.6%

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right) \]

7. Applied rewrites 26.6%

   \[\leadsto b \cdot \color{blue}{\left(j \cdot \left(t \cdot y4 - x \cdot y0\right)\right)} \]

8. Taylor expanded in x around 0

   \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
9. Step-by-step derivation

   1. lower-*.f64 17.5%

      \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]

10. Applied rewrites 17.5%

    \[\leadsto b \cdot \left(j \cdot \left(t \cdot y4\right)\right) \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025212 
(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)))))